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SmallHyperbolic/data/triangle_groups.json
Marek Kaluba afdb05b958
add generated json
2022-01-18 11:34:50 +01:00

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[
{
"name": "$G^{6,40,40}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"(a*c^-1*a*c)^2",
"(a^-1*c^-1*a*c^-1)^2"
],
"order1": 6,
"order2": 40,
"order3": 40,
"index": 0,
"presentation_length": 45,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a^-1 * c * b * c * a^-1 * c * b * c^-1",
"b * c * a^-1 * c * b * c * a^-1 * c^-1"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 2
},
{
"$B_{2}(3)$": 1
}
],
"alternating_quotients": [
5,
7
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,40,48}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"(a*c)^2*(a^-1*c^-1)^2"
],
"order1": 6,
"order2": 40,
"order3": 48,
"index": 0,
"presentation_length": 37,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"b * c * a * c^-1 * b * c^-1 * a^-1 * c^-1",
"a^-1 * c * b * c * a * c * b * c^-1"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 3
},
{
"$A_{3}(3)$": 1
}
],
"alternating_quotients": [
3,
5,
6
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,40,54}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"a*c*a^-1*c^-1*a^-1*c*a*c^-1",
"(a*c*a^-1*c)^3"
],
"order1": 6,
"order2": 40,
"order3": 54,
"index": 0,
"presentation_length": 49,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a * c^-1 * b^-1 * c^-1 * a * c * b * c",
"b^-1 * c * a^-1 * c^-1 * b * c^-1 * a * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"${}^2A_{4}(4)$": 1
}
],
"alternating_quotients": [
3,
5,
10,
15,
20,
25
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,40,54}_2",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"c*a*c^-1*a^-1*c^-1*a*c*a^-1",
"(c*a*c^-1*a)^3"
],
"order1": 6,
"order2": 40,
"order3": 54,
"index": 2,
"presentation_length": 49,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"b * c * a * c^-1 * b * c * a^-1 * c",
"a * c^-1 * b^-1 * c * a^-1 * c * b^-1 * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{9}$": 2
},
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 1
}
],
"alternating_quotients": [
3,
5,
9
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,48,48}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b)^2*(c^-1*b^-1)^2",
"(a*c)^2*(a^-1*c^-1)^2"
],
"order1": 6,
"order2": 48,
"order3": 48,
"index": 0,
"presentation_length": 29,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a^-1 * c^-1 * b * c",
"b * c * a * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 1
},
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 1
}
],
"alternating_quotients": [
3,
4
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,48,54}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b)^2*(c^-1*b^-1)^2",
"a*c*a^-1*c^-1*a^-1*c*a*c^-1",
"(a*c*a^-1*c)^3"
],
"order1": 6,
"order2": 48,
"order3": 54,
"index": 0,
"presentation_length": 41,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"b * c * a * c^-1 * b * c * a * c^-1",
"a^-1 * c * b * c * a^-1 * c^-1 * b^-1 * c^-1"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"$\\textrm{Alt}_{11}$": 2
}
],
"alternating_quotients": [
3,
4,
10,
11,
14,
15,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,48,54}_2",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"(c*b)^2*(c^-1*b^-1)^2",
"c*a*c^-1*a^-1*c^-1*a*c*a^-1",
"(c*a*c^-1*a)^3"
],
"order1": 6,
"order2": 48,
"order3": 54,
"index": 2,
"presentation_length": 41,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"b * c * a * c^-1 * b * c * a^-1 * c",
"a * c^-1 * b^-1 * c^-1 * a^-1 * c^-1 * b^-1 * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 1
},
{
"${}^2A_{4}(4)$": 1
}
],
"alternating_quotients": [
3,
4
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,54,54}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"c*b*c^-1*b^-1*c^-1*b*c*b^-1",
"(c*b*c^-1*b)^3",
"a*c*a^-1*c^-1*a^-1*c*a*c^-1",
"(a*c*a^-1*c)^3"
],
"order1": 6,
"order2": 54,
"order3": 54,
"index": 0,
"presentation_length": 53,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a * c^-1 * b^-1 * c^-1 * a * c * b * c",
"b^-1 * c^-1 * a^-1 * c * b * c^-1 * a * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{9}$": 2
},
{
"${}^2A_{4}(4)$": 2
}
],
"alternating_quotients": [
3,
9,
27
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,54,54}_2",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"c*b*c^-1*b^-1*c^-1*b*c*b^-1",
"(c*b*c^-1*b)^3",
"c*a*c^-1*a^-1*c^-1*a*c*a^-1",
"(c*a*c^-1*a)^3"
],
"order1": 6,
"order2": 54,
"order3": 54,
"index": 2,
"presentation_length": 53,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a^-1 * c * b^-1 * c * a * c^-1 * b * c",
"b^-1 * c * a^-1 * c * b * c^-1 * a * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{9}$": 2
},
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 1
},
{
"${}^2A_{4}(4)$": 1
}
],
"alternating_quotients": [
3,
9,
12,
15,
18,
21,
24,
27
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{6,54,54}_8",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b^-1*a^-1",
"b*c*b^-1*c^-1*b^-1*c*b*c^-1",
"(b*c*b^-1*c)^3",
"a*c*a^-1*c^-1*a^-1*c*a*c^-1",
"(a*c*a^-1*c)^3"
],
"order1": 6,
"order2": 54,
"order3": 54,
"index": 8,
"presentation_length": 53,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a^-1 * c^-1 * b * c",
"b^-1 * c^-1 * a * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{9}$": 4
}
],
"alternating_quotients": [
3,
9,
12,
18,
21,
24,
27
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,40,40}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"(a*c^-1*a*c)^2",
"(a^-1*c^-1*a*c^-1)^2"
],
"order1": 8,
"order2": 40,
"order3": 40,
"index": 0,
"presentation_length": 45,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"a^-1 * c^-1 * b * c",
"b * c^-1 * a^-1 * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(\\infty^4)"
],
"quotients": [
{
"$B_{2}(3)$": 1
},
{
"$C_{2}(4)$": 2
},
{
"$\\textrm{Alt}_{10}$": 2
},
{
"$B_{2}(5)$": 5
},
{
"$\\textrm{Alt}_{11}$": 2
}
],
"alternating_quotients": [
5,
6,
10,
11,
15,
20,
21,
25,
26
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,40,48}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"(a*c)^2*(a^-1*c^-1)^2"
],
"order1": 8,
"order2": 40,
"order3": 48,
"index": 0,
"presentation_length": 37,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(5)$": 4
}
],
"alternating_quotients": [
5,
6
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,40,54}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"a*c*a^-1*c^-1*a^-1*c*a*c^-1",
"(a*c*a^-1*c)^3"
],
"order1": 8,
"order2": 40,
"order3": 54,
"index": 0,
"presentation_length": 49,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{M}_{12}$": 4
}
],
"alternating_quotients": [
6
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,40,54}_2",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b^-1*c*b)^2",
"(c^-1*b^-1*c*b^-1)^2",
"c*a*c^-1*a^-1*c^-1*a*c*a^-1",
"(c*a*c^-1*a)^3"
],
"order1": 8,
"order2": 40,
"order3": 54,
"index": 2,
"presentation_length": 49,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"b * c * a * c^-1 * b * c^-1 * a * c",
"a^-1 * c * b^-1 * c * a^-1 * c * b^-1 * c"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{M}_{12}$": 4
},
{
"$\\textrm{Alt}_{10}$": 3
},
{
"$A_{3}(3)$": 2
},
{
"${}^2A_{4}(4)$": 1
}
],
"alternating_quotients": [
6,
10,
12,
15,
16,
21,
22,
27,
28
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,48,48}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b)^2*(c^-1*b^-1)^2",
"(a*c)^2*(a^-1*c^-1)^2"
],
"order1": 8,
"order2": 48,
"order3": 48,
"index": 0,
"presentation_length": 29,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 3
},
{
"$C_{3}(2)$": 4
},
{
"$\\textrm{Alt}_{11}$": 1
}
],
"alternating_quotients": [
3,
4,
5,
11,
19,
25,
28
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,48,48}_1",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b)^2*(c^-1*b^-1)^2",
"(a*c^-1)^2*(a^-1*c)^2"
],
"order1": 8,
"order2": 48,
"order3": 48,
"index": 1,
"presentation_length": 29,
"hyperbolic": false,
"witnesses_non_hyperbolictity": [
"b^-1 * c^-1 * a^-1 * c * b * c * a * c^-1",
"a * c^-1 * b * c * a^-1 * c * b^-1 * c^-1"
],
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 1
},
{
"$B_{2}(3)$": 2
},
{
"$C_{3}(2)$": 1
},
{
"$B_{2}(5)$": 3
},
{
"$\\textrm{Alt}_{11}$": 1
}
],
"alternating_quotients": [
3,
4,
7,
11,
15,
19,
22,
23,
24,
25,
26,
27,
28
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,48,54}_0",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b)^2*(c^-1*b^-1)^2",
"a*c*a^-1*c^-1*a^-1*c*a*c^-1",
"(a*c*a^-1*c)^3"
],
"order1": 8,
"order2": 48,
"order3": 54,
"index": 0,
"presentation_length": 41,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{9}$": 1
}
],
"alternating_quotients": [
3,
4,
9
],
"maximal_degree_alternating_quotients": 28
},
{
"name": "$G^{8,48,54}_2",
"half_girth_type": [
2,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b*a*b*a",
"(c*b)^2*(c^-1*b^-1)^2",
"c*a*c^-1*a^-1*c^-1*a*c*a^-1",
"(c*a*c^-1*a)^3"
],
"order1": 8,
"order2": 48,
"order3": 54,
"index": 2,
"presentation_length": 41,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$C_{3}(2)$": 1
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{
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26
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3,
3
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"b",
"c"
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"c^3",
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"(c * b)^3",
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"(a * c^-1)^3",
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"index": 1,
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""
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{
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{
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}
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26
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3,
3,
3
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"b",
"c"
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"b^3",
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"(b * a)^3",
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"(c * b^-1)^3",
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"order3": 26,
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""
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{
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3,
3
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"b",
"c"
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"b^3",
"c^3",
"(b * a^-1)^3",
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"(c * b^-1)^3",
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"(a * c^-1)^3",
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{
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{
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{
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30
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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"a * c^-1 * a * c * a * c^-1 * a * c",
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{
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{
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}
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7
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{
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3,
3,
4
],
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"b",
"c"
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"b^3",
"c^3",
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""
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{
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28
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{
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3,
3,
4
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"b",
"c"
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"c^3",
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{
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7
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3,
3,
4
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"b",
"c"
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8
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3,
3,
4
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"b",
"c"
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"c^3",
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""
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7
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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""
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{
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}
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8,
21
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
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],
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"order3": 54,
"index": 0,
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""
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}
],
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3
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{
"name": "$G^{14,14,54}_4",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c^-1 * b * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
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],
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"order2": 14,
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"index": 4,
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"L2_quotients": [
""
],
"quotients": [],
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3
],
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
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"order2": 16,
"order3": 40,
"index": 0,
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],
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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"index": 0,
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""
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3,
4
],
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{
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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],
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"order3": 48,
"index": 1,
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3
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{
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b^-1 * c^-1 * b^-1",
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],
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"order3": 54,
"index": 0,
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"L2_quotients": [
""
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3
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b^-1 * c^-1 * b^-1",
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],
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""
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3
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
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"order2": 18,
"order3": 40,
"index": 0,
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""
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{
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}
],
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21,
25
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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"c * b^-1 * c * b^-1 * c * b^-1",
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"order3": 48,
"index": 0,
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""
],
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{
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}
],
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3
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{
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3,
3,
4
],
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"b",
"c"
],
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"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
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""
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
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"L2_quotients": [
""
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3,
21,
28,
29
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{
"name": "$G^{14,24,40}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
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"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
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{
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{
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}
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10
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3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 14,
"order2": 24,
"order3": 48,
"index": 0,
"presentation_length": 37,
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""
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3,
4
],
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{
"name": "$G^{14,24,48}_1",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
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"order2": 24,
"order3": 48,
"index": 1,
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],
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{
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},
{
"$\\textrm{J}_{2}$": 1
},
{
"$C_{3}(2)$": 1
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{
"${}^2A_{3}(9)$": 1
}
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3,
7,
8,
15,
22,
28,
29
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
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"order3": 54,
"index": 0,
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""
],
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3,
18
],
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{
"name": "$G^{14,24,54}_2",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
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""
],
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},
{
"${}^2A_{3}(9)$": 1
}
],
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3,
14,
21,
28
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"name": "$G^{14,26,40}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
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"order2": 26,
"order3": 40,
"index": 0,
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""
],
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},
{
"name": "$G^{14,26,40}_4",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c^-1 * a * c * a * c^-1 * a * c",
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],
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"order2": 26,
"order3": 40,
"index": 4,
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""
],
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 14,
"order2": 26,
"order3": 48,
"index": 0,
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""
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3
],
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{
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
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"order3": 48,
"index": 1,
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"L2_quotients": [
""
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3
],
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{
"name": "$G^{14,26,48}_4",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 14,
"order2": 26,
"order3": 48,
"index": 4,
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"Kazdhdan_property_T": null,
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"L2_quotients": [
""
],
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3
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{
"name": "$G^{14,26,48}_5",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 14,
"order2": 26,
"order3": 48,
"index": 5,
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"L2_quotients": [
""
],
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3
],
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{
"name": "$G^{14,26,54}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 14,
"order2": 26,
"order3": 54,
"index": 0,
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"L2_quotients": [
""
],
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3
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,26,54}_2",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 14,
"order2": 26,
"order3": 54,
"index": 2,
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"hyperbolic": true,
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"Kazdhdan_property_T": null,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [],
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3
],
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{
"name": "$G^{14,26,54}_4",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 14,
"order2": 26,
"order3": 54,
"index": 4,
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"Kazdhdan_property_T": null,
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"L2_quotients": [
""
],
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3
],
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},
{
"name": "$G^{14,26,54}_6",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 14,
"order2": 26,
"order3": 54,
"index": 6,
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"Kazdhdan_property_T": null,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [],
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3
],
"maximal_degree_alternating_quotients": 30
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{
"name": "$G^{16,16,40}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b^-1 * c^-1 * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 16,
"order2": 16,
"order3": 40,
"index": 0,
"presentation_length": 37,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{M}_{11}$": 1
},
{
"$B_{2}(3)$": 1
},
{
"$\\textrm{J}_{2}$": 2
},
{
"${}^2A_{3}(9)$": 1
},
{
"$B_{2}(5)$": 1
},
{
"$A_{3}(3)$": 2
}
],
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5,
21,
26,
28
],
"maximal_degree_alternating_quotients": 30
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{
"name": "$G^{16,16,48}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b^-1 * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 16,
"order2": 16,
"order3": 48,
"index": 0,
"presentation_length": 29,
"hyperbolic": true,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 1
},
{
"${}^2A_{2}(9)$": 2
},
{
"$\\textrm{Alt}_{9}$": 1
},
{
"${}^2A_{2}(81)$": 2
},
{
"$\\textrm{HS}_{}$": 1
}
],
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3,
4,
5,
9,
21,
26,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,16,48}_1",
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3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b^-1 * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 16,
"order2": 16,
"order3": 48,
"index": 1,
"presentation_length": 29,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"${}^2A_{2}(9)$": 1
},
{
"$\\textrm{J}_{2}$": 1
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"$B_{2}(5)$": 1
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{4}(2)$": 1
},
{
"$A_{2}(9)$": 1
},
{
"${}^2A_{2}(81)$": 2
}
],
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3,
4,
10
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,16,54}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 16,
"order3": 54,
"index": 0,
"presentation_length": 41,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 1
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
18,
22,
25,
26,
27
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,18,40}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 16,
"order2": 18,
"order3": 40,
"index": 0,
"presentation_length": 43,
"hyperbolic": true,
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"virtually_torsion_free": true,
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"L2_quotients": [
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],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{M}_{12}$": 5
}
],
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6,
18,
24,
27,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,18,48}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 16,
"order2": 18,
"order3": 48,
"index": 0,
"presentation_length": 35,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
10,
17,
19,
30
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3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 18,
"order3": 54,
"index": 0,
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""
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},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{2}(9)$": 3
}
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3,
4,
25,
26,
27
],
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
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"order2": 18,
"order3": 54,
"index": 2,
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""
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},
{
"${}^2A_{2}(64)$": 2
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{
"$A_{2}(9)$": 3
}
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3,
4,
20,
21,
22,
24,
25,
26,
27,
29,
30
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},
{
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 16,
"order2": 24,
"order3": 40,
"index": 0,
"presentation_length": 45,
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],
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"$B_{2}(5)$": 2
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{
"$A_{4}(2)$": 3
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{
"$\\textrm{Alt}_{11}$": 2
}
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5,
6,
11,
21,
22
],
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 16,
"order2": 24,
"order3": 48,
"index": 0,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
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{
"$\\textrm{Alt}_{9}$": 1
},
{
"$C_{3}(2)$": 5
},
{
"$\\textrm{HS}_{}$": 1
}
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4,
5,
9,
14,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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{
"name": "$G^{16,24,48}_1",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 16,
"order2": 24,
"order3": 48,
"index": 1,
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"L2_quotients": [
""
],
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"$\\textrm{Alt}_{7}$": 1
},
{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 2
},
{
"${}^2A_{2}(25)$": 1
},
{
"$\\textrm{J}_{2}$": 1
},
{
"$C_{3}(2)$": 2
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"${}^2A_{3}(9)$": 1
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{
"$B_{2}(5)$": 1
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{
"$A_{4}(2)$": 1
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{
"$\\textrm{HS}_{}$": 1
}
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4,
7,
8,
10,
12,
15,
16,
18,
19,
20,
22,
23,
24,
25,
26,
27,
28,
29,
30
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"name": "$G^{16,24,54}_0",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 24,
"order3": 54,
"index": 0,
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"L2_quotients": [
""
],
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{
"$\\textrm{Alt}_{9}$": 1
},
{
"$C_{3}(2)$": 1
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{
"$\\textrm{Alt}_{10}$": 1
}
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4,
9,
10,
12,
18,
19,
21,
25,
27,
28,
29,
30
],
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{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 16,
"order2": 24,
"order3": 54,
"index": 2,
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""
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"$B_{2}(3)$": 1
},
{
"$\\textrm{Alt}_{10}$": 3
}
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3,
4,
10,
12,
14,
16,
19,
20,
22,
23,
24,
26,
27,
28,
30
],
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{
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 16,
"order2": 26,
"order3": 40,
"index": 0,
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],
"quotients": [
{
"${}^2F_4(2)'$": 1
}
],
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},
{
"name": "$G^{16,26,48}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 16,
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"order3": 48,
"index": 0,
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],
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3,
16,
30
],
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},
{
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
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"order2": 26,
"order3": 48,
"index": 1,
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"L2_quotients": [
""
],
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3,
4
],
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{
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
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"order2": 26,
"order3": 54,
"index": 0,
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""
],
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3
],
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},
{
"name": "$G^{16,26,54}_2",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
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"order3": 54,
"index": 2,
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"L2_quotients": [
""
],
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3,
28
],
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},
{
"name": "$G^{18,18,40}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 18,
"order2": 18,
"order3": 40,
"index": 0,
"presentation_length": 49,
"hyperbolic": true,
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"abelianization_dimension": 1,
"L2_quotients": [
""
],
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{
"$\\textrm{M}_{12}$": 2
},
{
"$A_{3}(3)$": 4
}
],
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3,
5,
12,
17,
18,
19,
20,
21,
22,
24,
26,
27,
29,
30
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},
{
"name": "$G^{18,18,48}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 18,
"order2": 18,
"order3": 48,
"index": 0,
"presentation_length": 41,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"${}^2A_{2}(64)$": 2
},
{
"$\\textrm{Alt}_{11}$": 1
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
10,
11,
12,
15,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,18,54}_0",
"half_girth_type": [
3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b^-1 * c * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 18,
"order2": 18,
"order3": 54,
"index": 0,
"presentation_length": 53,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$A_{2}(9)$": 3
}
],
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3,
19,
22,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,24,40}_0",
"half_girth_type": [
3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 18,
"order2": 24,
"order3": 40,
"index": 0,
"presentation_length": 51,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$\\textrm{M}_{12}$": 6
},
{
"$\\textrm{Alt}_{10}$": 2
},
{
"${}^2A_{3}(9)$": 2
},
{
"$A_{3}(3)$": 3
},
{
"$\\textrm{Alt}_{11}$": 4
}
],
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3,
5,
6,
10,
11,
12,
15,
16,
17,
18,
21,
22,
23,
24,
25,
26,
27,
28,
30
],
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},
{
"name": "$G^{18,24,48}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 18,
"order2": 24,
"order3": 48,
"index": 0,
"presentation_length": 43,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{10}$": 2
},
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 2
},
{
"$\\textrm{Alt}_{11}$": 1
}
],
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3,
4,
10,
11,
12,
13,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
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},
{
"name": "$G^{18,24,54}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 18,
"order2": 24,
"order3": 54,
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""
],
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"$\\textrm{Alt}_{10}$": 2
},
{
"$A_{3}(3)$": 4
},
{
"$\\textrm{Alt}_{11}$": 2
}
],
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3,
4,
10,
11,
12,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
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{
"name": "$G^{18,24,54}_2",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 18,
"order2": 24,
"order3": 54,
"index": 2,
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"abelianization_dimension": 3,
"L2_quotients": [
""
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"$\\textrm{Alt}_{9}$": 2
},
{
"$\\textrm{Alt}_{10}$": 1
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{
"$\\textrm{Alt}_{11}$": 1
}
],
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3,
4,
9,
10,
11,
12,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
30
],
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},
{
"name": "$G^{18,26,40}_0",
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3,
3,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 18,
"order2": 26,
"order3": 40,
"index": 0,
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"L2_quotients": [
""
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{
"name": "$G^{18,26,48}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 18,
"order2": 26,
"order3": 48,
"index": 0,
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"L2_quotients": [
""
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{
"$G_{2}(3)$": 1
}
],
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3,
27
],
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},
{
"name": "$G^{18,26,54}_0",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 18,
"order2": 26,
"order3": 54,
"index": 0,
"presentation_length": 55,
"hyperbolic": true,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
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{
"$A_{2}(3)$": 2
},
{
"$A_{2}(9)$": 3
}
],
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3,
13,
26,
27
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,26,54}_2",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 18,
"order2": 26,
"order3": 54,
"index": 2,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
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{
"$A_{2}(3)$": 2
},
{
"$A_{2}(9)$": 3
}
],
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3,
13
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,24,40}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 24,
"order2": 24,
"order3": 40,
"index": 0,
"presentation_length": 53,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
"L_2(3^2)",
"L_2(3^2)"
],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 2
},
{
"$\\textrm{M}_{22}$": 2
},
{
"$\\textrm{J}_{2}$": 4
},
{
"$C_{2}(4)$": 4
},
{
"$C_{3}(2)$": 1
},
{
"$B_{2}(5)$": 8
},
{
"$A_{3}(3)$": 1
},
{
"$A_{4}(2)$": 2
}
],
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3,
5,
6,
7,
12,
13,
15,
16,
17,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,24,48}_0",
"half_girth_type": [
3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 24,
"order2": 24,
"order3": 48,
"index": 0,
"presentation_length": 45,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
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{
"$\\textrm{M}_{22}$": 1
},
{
"$C_{3}(2)$": 6
},
{
"${}^2A_{3}(9)$": 5
},
{
"$B_{2}(5)$": 2
},
{
"$A_{3}(3)$": 1
}
],
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3,
4,
5,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
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},
{
"name": "$G^{24,24,48}_1",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 24,
"order2": 24,
"order3": 48,
"index": 1,
"presentation_length": 45,
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"Kazdhdan_property_T": false,
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"L2_quotients": [
""
],
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{
"$\\textrm{Alt}_{7}$": 3
},
{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 2
},
{
"$\\textrm{M}_{12}$": 1
},
{
"${}^2A_{2}(25)$": 1
},
{
"$\\textrm{J}_{2}$": 1
},
{
"$C_{3}(2)$": 3
},
{
"$A_{2}(7)$": 1
},
{
"${}^2A_{3}(9)$": 1
},
{
"$B_{2}(5)$": 3
},
{
"$A_{4}(2)$": 1
},
{
"${}^2A_{4}(4)$": 2
},
{
"$\\textrm{HS}_{}$": 1
}
],
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3,
4,
7,
8,
13,
14,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
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},
{
"name": "$G^{24,24,54}_0",
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3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 24,
"order2": 24,
"order3": 54,
"index": 0,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
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{
"$\\textrm{Alt}_{9}$": 3
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"${}^2A_{3}(9)$": 1
},
{
"$\\textrm{Alt}_{11}$": 2
}
],
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3,
4,
9,
10,
11,
12,
13,
15,
16,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,26,40}_0",
"half_girth_type": [
3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 24,
"order2": 26,
"order3": 40,
"index": 0,
"presentation_length": 53,
"hyperbolic": true,
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"Kazdhdan_property_T": null,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(13^2)"
],
"quotients": [],
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"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,26,48}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 24,
"order2": 26,
"order3": 48,
"index": 0,
"presentation_length": 45,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
"L_2(13)"
],
"quotients": [
{
"$A_{3}(3)$": 1
}
],
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3,
13,
14,
15,
16,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,26,48}_1",
"half_girth_type": [
3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 24,
"order2": 26,
"order3": 48,
"index": 1,
"presentation_length": 45,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [],
"alternating_quotients": [
3,
4,
14,
28
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,26,54}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 24,
"order2": 26,
"order3": 54,
"index": 0,
"presentation_length": 57,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{3}(3)$": 1
}
],
"alternating_quotients": [
3,
13,
26,
27,
28
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{24,26,54}_2",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 24,
"order2": 26,
"order3": 54,
"index": 2,
"presentation_length": 57,
"hyperbolic": true,
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"Kazdhdan_property_T": null,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [],
"alternating_quotients": [
3,
13,
27
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{26,26,40}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 26,
"order2": 26,
"order3": 40,
"index": 0,
"presentation_length": 53,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": null,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
"quotients": [],
"alternating_quotients": [
13
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{26,26,40}_4",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 26,
"order2": 26,
"order3": 40,
"index": 4,
"presentation_length": 53,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": null,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(13^2)"
],
"quotients": [
{
"${}^2A_{2}(16)$": 1
},
{
"$A_{3}(3)$": 1
}
],
"alternating_quotients": [
13,
26
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{26,26,48}_0",
"half_girth_type": [
3,
3,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 26,
"order2": 26,
"order3": 48,
"index": 0,
"presentation_length": 45,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
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{
"$G_{2}(3)$": 1
}
],
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3,
13,
14,
16,
26
],
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{
"name": "$G^{26,26,48}_1",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 26,
"order2": 26,
"order3": 48,
"index": 1,
"presentation_length": 45,
"hyperbolic": true,
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"L2_quotients": [
""
],
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3,
26,
28
],
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},
{
"name": "$G^{26,26,48}_4",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 26,
"order2": 26,
"order3": 48,
"index": 4,
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],
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{
"$A_{2}(3)$": 2
},
{
"$G_{2}(3)$": 1
},
{
"$A_{3}(3)$": 1
}
],
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3,
13,
14,
26,
27,
28,
29
],
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{
"name": "$G^{26,26,48}_5",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 26,
"order2": 26,
"order3": 48,
"index": 5,
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"L_2(13)"
],
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{
"$A_{2}(3)$": 2
},
{
"$A_{3}(3)$": 1
}
],
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3,
13,
14,
27
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{26,26,54}_0",
"half_girth_type": [
3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c * b * c * b",
"c * b * c^-1 * b * c^-1 * b * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 26,
"order2": 26,
"order3": 54,
"index": 0,
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"hyperbolic": true,
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"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$G_{2}(3)$": 2
}
],
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3,
13
],
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{
"name": "$G^{26,26,54}_4",
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3,
3,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b^-1 * c * b^-1 * c * b^-1",
"c * b^-1 * c^-1 * b^-1 * c^-1 * b^-1 * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 26,
"order2": 26,
"order3": 54,
"index": 4,
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"hyperbolic": true,
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"Kazdhdan_property_T": false,
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"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$G_{2}(3)$": 1
}
],
"alternating_quotients": [
3,
13,
27
],
"maximal_degree_alternating_quotients": 30
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{
"name": "$G^{14,40,40}_0",
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3,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 14,
"order2": 40,
"order3": 40,
"index": 0,
"presentation_length": 47,
"hyperbolic": true,
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"Kazdhdan_property_T": false,
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"L2_quotients": [
"L_2(7^2)"
],
"quotients": [
{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 5
},
{
"$C_{3}(2)$": 2
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"${}^2A_{3}(9)$": 2
},
{
"$A_{4}(2)$": 3
},
{
"$\\textrm{Alt}_{11}$": 3
},
{
"$A_{2}(9)$": 1
}
],
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5,
10,
11,
20,
21,
30
],
"maximal_degree_alternating_quotients": 30
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{
"name": "$G^{14,40,48}_0",
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3,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 14,
"order2": 40,
"order3": 48,
"index": 0,
"presentation_length": 39,
"hyperbolic": true,
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"Kazdhdan_property_T": null,
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"L2_quotients": [
"L_2(7^2)"
],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 1
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"$A_{4}(2)$": 1
}
],
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7,
10
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,40,54}_0",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 14,
"order2": 40,
"order3": 54,
"index": 0,
"presentation_length": 51,
"hyperbolic": true,
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"Kazdhdan_property_T": null,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{J}_{2}$": 1
},
{
"$C_{3}(2)$": 2
}
],
"alternating_quotients": [
21,
25
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,40,54}_2",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 14,
"order2": 40,
"order3": 54,
"index": 2,
"presentation_length": 51,
"hyperbolic": true,
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"Kazdhdan_property_T": null,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{J}_{2}$": 1
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{
"$C_{3}(2)$": 2
}
],
"alternating_quotients": [
20,
21,
22,
25,
27,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,48,48}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 14,
"order2": 48,
"order3": 48,
"index": 0,
"presentation_length": 31,
"hyperbolic": true,
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"L2_quotients": [
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],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 1
},
{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 1
},
{
"$\\textrm{J}_{2}$": 1
},
{
"$C_{3}(2)$": 2
},
{
"${}^2A_{3}(9)$": 1
},
{
"$G_{2}(3)$": 2
}
],
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3,
7,
8,
15,
16,
22,
23,
24,
27,
28,
29,
30
],
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},
{
"name": "$G^{14,48,48}_1",
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3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 14,
"order2": 48,
"order3": 48,
"index": 1,
"presentation_length": 31,
"hyperbolic": true,
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"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [],
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3,
4
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,48,54}_0",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 14,
"order2": 48,
"order3": 54,
"index": 0,
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"Kazdhdan_property_T": null,
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"L2_quotients": [
""
],
"quotients": [
{
"$G_{2}(3)$": 1
}
],
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3,
18
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,48,54}_2",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 14,
"order2": 48,
"order3": 54,
"index": 2,
"presentation_length": 43,
"hyperbolic": true,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$C_{3}(2)$": 3
},
{
"${}^2A_{3}(9)$": 1
},
{
"$G_{2}(3)$": 1
}
],
"alternating_quotients": [
3,
14,
15,
21,
22,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,54,54}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 14,
"order2": 54,
"order3": 54,
"index": 0,
"presentation_length": 55,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [],
"alternating_quotients": [
3,
21,
28,
29
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{14,54,54}_2",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 14,
"order2": 54,
"order3": 54,
"index": 2,
"presentation_length": 55,
"hyperbolic": true,
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"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{10}$": 6
},
{
"${}^2A_{3}(9)$": 2
}
],
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3,
10,
13,
14,
17,
19,
20,
21,
23,
24,
27,
28,
29,
30
],
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{
"name": "$G^{14,54,54}_8",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b * a",
"b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1",
"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 14,
"order2": 54,
"order3": 54,
"index": 8,
"presentation_length": 55,
"hyperbolic": true,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [],
"alternating_quotients": [
3,
18,
21,
27,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,40,40}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 16,
"order2": 40,
"order3": 40,
"index": 0,
"presentation_length": 47,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(\\infty^4)"
],
"quotients": [
{
"$\\textrm{M}_{11}$": 4
},
{
"$B_{2}(3)$": 7
},
{
"${}^2A_{2}(25)$": 1
},
{
"$\\textrm{J}_{2}$": 2
},
{
"$C_{2}(4)$": 2
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"${}^2A_{3}(9)$": 4
},
{
"$B_{2}(5)$": 11
},
{
"$A_{3}(3)$": 2
},
{
"$\\textrm{Alt}_{11}$": 6
}
],
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5,
6,
10,
11,
15,
16,
17,
20,
21,
22,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,40,48}_0",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 16,
"order2": 40,
"order3": 48,
"index": 0,
"presentation_length": 39,
"hyperbolic": true,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$\\textrm{M}_{11}$": 1
},
{
"$B_{2}(3)$": 1
},
{
"$\\textrm{J}_{2}$": 2
},
{
"${}^2A_{3}(9)$": 1
},
{
"$B_{2}(5)$": 5
},
{
"$A_{3}(3)$": 2
},
{
"$A_{4}(2)$": 3
},
{
"$\\textrm{Alt}_{11}$": 2
}
],
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5,
6,
11,
16,
18,
21,
22,
23,
24,
26,
27,
28,
29,
30
],
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},
{
"name": "$G^{16,40,54}_0",
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3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 40,
"order3": 54,
"index": 0,
"presentation_length": 51,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 5
},
{
"$\\textrm{M}_{12}$": 5
},
{
"$C_{3}(2)$": 1
},
{
"${}^2A_{3}(9)$": 2
},
{
"$A_{3}(3)$": 3
},
{
"${}^2A_{4}(4)$": 1
}
],
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6,
12,
17,
18,
21,
23,
24,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,40,54}_2",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 16,
"order2": 40,
"order3": 54,
"index": 2,
"presentation_length": 51,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 4
},
{
"$\\textrm{M}_{12}$": 5
},
{
"$\\textrm{Alt}_{10}$": 3
},
{
"${}^2A_{3}(9)$": 4
},
{
"$A_{3}(3)$": 4
},
{
"${}^2A_{4}(4)$": 1
}
],
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6,
10,
12,
15,
16,
18,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,48,48}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 16,
"order2": 48,
"order3": 48,
"index": 0,
"presentation_length": 31,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 1
},
{
"${}^2A_{2}(9)$": 1
},
{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 2
},
{
"$B_{2}(3)$": 5
},
{
"${}^2A_{2}(25)$": 1
},
{
"$\\textrm{J}_{2}$": 2
},
{
"$C_{3}(2)$": 5
},
{
"$\\textrm{Alt}_{10}$": 2
},
{
"${}^2A_{3}(9)$": 4
},
{
"$B_{2}(5)$": 5
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 5
},
{
"$A_{4}(2)$": 2
},
{
"$\\textrm{Alt}_{11}$": 1
},
{
"$A_{2}(9)$": 1
},
{
"${}^2A_{2}(81)$": 2
},
{
"$\\textrm{HS}_{}$": 1
}
],
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3,
4,
7,
8,
10,
11,
12,
15,
16,
18,
19,
20,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,48,48}_1",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 16,
"order2": 48,
"order3": 48,
"index": 1,
"presentation_length": 31,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 1
},
{
"${}^2A_{2}(9)$": 2
},
{
"$B_{2}(3)$": 8
},
{
"$\\textrm{Alt}_{9}$": 2
},
{
"$C_{3}(2)$": 10
},
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 6
},
{
"$\\textrm{Alt}_{11}$": 1
},
{
"${}^2A_{2}(81)$": 2
},
{
"$\\textrm{HS}_{}$": 2
}
],
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3,
4,
5,
9,
11,
14,
15,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,48,54}_0",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 48,
"order3": 54,
"index": 0,
"presentation_length": 43,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 4
},
{
"$\\textrm{Alt}_{9}$": 1
},
{
"$C_{3}(2)$": 1
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"${}^2A_{3}(9)$": 3
},
{
"$A_{3}(3)$": 1
},
{
"${}^2A_{4}(4)$": 1
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
9,
10,
12,
17,
18,
19,
21,
22,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,48,54}_2",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 16,
"order2": 48,
"order3": 54,
"index": 2,
"presentation_length": 43,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
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{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 4
},
{
"$C_{3}(2)$": 1
},
{
"$\\textrm{Alt}_{10}$": 3
},
{
"${}^2A_{3}(9)$": 2
},
{
"$A_{3}(3)$": 3
},
{
"${}^2A_{4}(4)$": 5
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
10,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,54,54}_0",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 54,
"order3": 54,
"index": 0,
"presentation_length": 55,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"${}^2A_{2}(64)$": 2
},
{
"${}^2A_{4}(4)$": 2
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
20,
21,
22,
24,
25,
26,
27,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,54,54}_2",
"half_girth_type": [
3,
4,
4
],
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"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 16,
"order2": 54,
"order3": 54,
"index": 2,
"presentation_length": 55,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
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{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 6
},
{
"$\\textrm{Alt}_{9}$": 2
},
{
"$C_{3}(2)$": 4
},
{
"$\\textrm{Alt}_{10}$": 12
},
{
"${}^2A_{3}(9)$": 3
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 5
},
{
"${}^2A_{4}(4)$": 5
},
{
"$\\textrm{Alt}_{11}$": 6
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{16,54,54}_8",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a^-1 * b^-1 * a^-1",
"b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1",
"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 16,
"order2": 54,
"order3": 54,
"index": 8,
"presentation_length": 55,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 2,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 4
},
{
"$\\textrm{Alt}_{9}$": 2
},
{
"${}^2A_{3}(9)$": 3
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 7
},
{
"${}^2A_{4}(4)$": 3
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
9,
12,
18,
19,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,40,40}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
"order1": 18,
"order2": 40,
"order3": 40,
"index": 0,
"presentation_length": 53,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
"quotients": [
{
"$\\textrm{Alt}_{7}$": 2
},
{
"$B_{2}(3)$": 5
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$\\textrm{Alt}_{10}$": 8
},
{
"${}^2A_{3}(9)$": 1
},
{
"${}^2A_{4}(4)$": 3
}
],
"alternating_quotients": [
5,
7,
10,
15,
17,
20,
21,
22,
24,
25,
26,
27,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,40,48}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 18,
"order2": 40,
"order3": 48,
"index": 0,
"presentation_length": 45,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 5
},
{
"$\\textrm{M}_{12}$": 7
},
{
"$\\textrm{Alt}_{10}$": 2
},
{
"${}^2A_{3}(9)$": 4
},
{
"$A_{3}(3)$": 10
},
{
"$\\textrm{Alt}_{11}$": 5
}
],
"alternating_quotients": [
3,
5,
6,
10,
11,
12,
14,
15,
16,
17,
18,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,40,54}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 18,
"order2": 40,
"order3": 54,
"index": 0,
"presentation_length": 57,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"$A_{3}(3)$": 14
},
{
"${}^2A_{4}(4)$": 3
}
],
"alternating_quotients": [
3,
5,
10,
12,
15,
17,
18,
19,
20,
21,
22,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,40,54}_2",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a^-1 * b * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 18,
"order2": 40,
"order3": 54,
"index": 2,
"presentation_length": 57,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
"quotients": [
{
"$B_{2}(3)$": 2
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$\\textrm{Alt}_{9}$": 2
},
{
"${}^2A_{3}(9)$": 3
},
{
"$A_{3}(3)$": 5
},
{
"${}^2A_{4}(4)$": 4
}
],
"alternating_quotients": [
3,
5,
9,
12,
15,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
],
"maximal_degree_alternating_quotients": 30
},
{
"name": "$G^{18,48,48}_0",
"half_girth_type": [
3,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b * a",
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21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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{
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{
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{
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10,
11,
12,
14,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
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""
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{
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{
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{
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{
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9,
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11,
12,
13,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
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"c^3",
"b * a * b * a * b * a",
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"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
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"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
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"order2": 54,
"order3": 54,
"index": 0,
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""
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{
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{
"${}^2A_{4}(4)$": 2
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{
"$A_{2}(9)$": 3
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9,
19,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
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"c^3",
"b * a * b * a * b * a",
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"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
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""
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{
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{
"$\\textrm{Alt}_{9}$": 10
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{
"${}^2A_{3}(9)$": 3
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{
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{
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{
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12,
15,
18,
19,
21,
22,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
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"c^3",
"b * a * b * a * b * a",
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"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
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""
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{
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9,
12,
18,
19,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
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"b^3",
"c^3",
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"c * b^-1 * c * b * c * b^-1 * c * b",
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"order2": 40,
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{
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{
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{
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{
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{
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{
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6,
7,
10,
11,
12,
15,
17,
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
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"b^3",
"c^3",
"b * a * b * a * b * a",
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"L_2(3^2)"
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{
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{
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{
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{
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{
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{
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{
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{
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{
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5,
6,
7,
11,
12,
13,
15,
16,
17,
18,
19,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
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"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
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{
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{
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{
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{
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{
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{
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5,
6,
10,
11,
12,
15,
16,
17,
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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{
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3,
4,
4
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"b",
"c"
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"b^3",
"c^3",
"b * a * b * a * b * a",
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"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
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"order3": 54,
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{
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{
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{
"$C_{3}(2)$": 4
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{
"$\\textrm{Alt}_{10}$": 7
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{
"${}^2A_{3}(9)$": 6
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{
"$A_{3}(3)$": 7
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{
"${}^2A_{4}(4)$": 1
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{
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5,
6,
9,
10,
11,
12,
13,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"b",
"c"
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"b^3",
"c^3",
"b * a * b * a * b * a",
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"index": 0,
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"L2_quotients": [
""
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{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 4
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{
"$B_{2}(3)$": 3
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{
"$\\textrm{M}_{12}$": 1
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{
"${}^2A_{2}(25)$": 2
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{
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{
"$C_{3}(2)$": 11
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{
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{
"$A_{2}(7)$": 1
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{
"${}^2A_{3}(9)$": 3
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{
"$B_{2}(5)$": 7
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{
"$A_{3}(3)$": 1
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{
"$A_{4}(2)$": 2
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{
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{
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{
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4,
7,
8,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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{
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4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
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"order2": 48,
"order3": 48,
"index": 1,
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"L2_quotients": [
""
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{
"$\\textrm{Alt}_{9}$": 1
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{
"$\\textrm{M}_{22}$": 1
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{
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{
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{
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{
"$A_{3}(3)$": 3
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{
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{
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{
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}
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4,
5,
9,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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{
"name": "$G^{24,48,54}_0",
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3,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
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"order1": 24,
"order2": 48,
"order3": 54,
"index": 0,
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"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
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},
{
"$\\textrm{Alt}_{9}$": 3
},
{
"$\\textrm{Alt}_{10}$": 5
},
{
"${}^2A_{3}(9)$": 1
},
{
"$A_{3}(3)$": 2
},
{
"${}^2A_{4}(4)$": 3
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{
"$\\textrm{Alt}_{11}$": 4
}
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4,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"c"
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"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
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""
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{
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{
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{
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{
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{
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{
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{
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4,
9,
10,
11,
12,
13,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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4,
4
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"c"
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""
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{
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{
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{
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{
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4,
9,
10,
11,
12,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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3,
4,
4
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"b",
"c"
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"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
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""
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{
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{
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{
"$\\textrm{Alt}_{10}$": 22
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{
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{
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{
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{
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4,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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3,
4,
4
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"b",
"c"
],
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"c^3",
"b * a * b * a * b * a",
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"b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1",
"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
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""
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{
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{
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{
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{
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4,
9,
10,
11,
12,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
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3,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
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"index": 0,
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}
],
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5,
20,
21,
27,
28
],
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{
"name": "$G^{26,40,48}_0",
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3,
4,
4
],
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"b",
"c"
],
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"c^3",
"b * a * b * a * b * a",
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"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
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{
"${}^2F_4(2)'$": 1
}
],
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{
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3,
4,
4
],
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"b",
"c"
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"b^3",
"c^3",
"b * a * b * a * b * a",
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"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
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""
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}
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{
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3,
4,
4
],
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"b",
"c"
],
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"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
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""
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15
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{
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3,
4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
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"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
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""
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}
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3,
4,
14,
28
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3,
4,
4
],
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"b",
"c"
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"c^3",
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{
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13,
14,
15,
16,
26,
27,
28,
29,
30
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{
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3,
4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
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],
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""
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}
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13,
26,
27,
28
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{
"name": "$G^{26,48,54}_2",
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3,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
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""
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"$G_{2}(3)$": 1
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{
"$A_{3}(3)$": 1
}
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13,
26,
27,
28,
29
],
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{
"name": "$G^{26,54,54}_0",
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3,
4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
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"index": 0,
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""
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"$A_{2}(3)$": 2
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{
"$A_{2}(9)$": 3
}
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3,
13,
26,
27,
30
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{
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3,
4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
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"order2": 54,
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"L2_quotients": [
""
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"$A_{2}(3)$": 2
},
{
"$A_{3}(3)$": 20
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{
"$A_{2}(9)$": 3
}
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3,
13,
16,
19,
22,
25,
26,
27,
28,
29,
30
],
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{
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3,
4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a * b * a * b * a",
"b * a * b^-1 * a * b^-1 * a * b^-1 * a^-1",
"b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1",
"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
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],
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""
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"$A_{2}(3)$": 2
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{
"$A_{3}(3)$": 6
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{
"$A_{2}(9)$": 3
}
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3,
13
],
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{
"name": "$G^{40,40,40}_0",
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4,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c^-1 * a * c * a * c^-1 * a * c",
"a^-1 * c^-1 * a * c^-1 * a^-1 * c^-1 * a * c^-1"
],
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"order2": 40,
"order3": 40,
"index": 0,
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"L2_quotients": [
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"L_2(\\infty^4)",
"L_2(\\infty^4)",
"L_2(\\infty^4)"
],
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{
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},
{
"$B_{2}(3)$": 18
},
{
"$\\textrm{M}_{12}$": 7
},
{
"${}^2A_{2}(25)$": 2
},
{
"$\\textrm{J}_{1}$": 4
},
{
"$A_{2}(5)$": 2
},
{
"$\\textrm{J}_{2}$": 8
},
{
"$C_{2}(4)$": 21
},
{
"$\\textrm{Alt}_{10}$": 15
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{
"${}^2A_{3}(9)$": 12
},
{
"$B_{2}(5)$": 90
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{
"$A_{3}(3)$": 7
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{
"$\\textrm{HS}_{}$": 12
}
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7,
10,
12,
15,
16,
17,
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
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{
"name": "$G^{40,40,48}_0",
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4,
4,
4
],
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"b",
"c"
],
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"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 40,
"order2": 40,
"order3": 48,
"index": 0,
"presentation_length": 49,
"hyperbolic": true,
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"abelianization_dimension": 0,
"L2_quotients": [
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],
"quotients": [
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"$\\textrm{Alt}_{7}$": 2
},
{
"$\\textrm{M}_{11}$": 4
},
{
"$B_{2}(3)$": 8
},
{
"${}^2A_{2}(25)$": 1
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{
"$\\textrm{M}_{22}$": 2
},
{
"$\\textrm{J}_{2}$": 4
},
{
"$C_{2}(4)$": 2
},
{
"$C_{3}(2)$": 2
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"${}^2A_{3}(9)$": 4
},
{
"$B_{2}(5)$": 16
},
{
"$A_{3}(3)$": 2
},
{
"$A_{4}(2)$": 4
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{
"${}^2A_{4}(4)$": 10
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{
"$\\textrm{Alt}_{11}$": 7
}
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6,
7,
10,
11,
12,
15,
16,
17,
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
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},
{
"name": "$G^{40,40,54}_0",
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4,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b^-1 * c * b * c * b^-1 * c * b",
"c^-1 * b^-1 * c * b^-1 * c^-1 * b^-1 * c * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 40,
"order2": 40,
"order3": 54,
"index": 0,
"presentation_length": 61,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 0,
"L2_quotients": [
""
],
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"$\\textrm{Alt}_{7}$": 2
},
{
"$B_{2}(3)$": 5
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$\\textrm{Alt}_{10}$": 8
},
{
"${}^2A_{3}(9)$": 15
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{
"$A_{3}(3)$": 4
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{
"${}^2A_{4}(4)$": 7
}
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7,
10,
15,
16,
17,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
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},
{
"name": "$G^{40,48,48}_0",
"half_girth_type": [
4,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 40,
"order2": 48,
"order3": 48,
"index": 0,
"presentation_length": 41,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
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"L_2(3^2)"
],
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{
"$\\textrm{Alt}_{7}$": 2
},
{
"$\\textrm{M}_{11}$": 1
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{
"$B_{2}(3)$": 18
},
{
"$\\textrm{M}_{22}$": 2
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{
"$\\textrm{J}_{2}$": 6
},
{
"$C_{2}(4)$": 4
},
{
"$C_{3}(2)$": 6
},
{
"${}^2A_{3}(9)$": 10
},
{
"$B_{2}(5)$": 20
},
{
"$A_{3}(3)$": 15
},
{
"$A_{4}(2)$": 8
},
{
"${}^2A_{4}(4)$": 15
},
{
"$\\textrm{Alt}_{11}$": 9
}
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5,
6,
7,
11,
12,
13,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{40,48,54}_0",
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4,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 40,
"order2": 48,
"order3": 54,
"index": 0,
"presentation_length": 53,
"hyperbolic": true,
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"virtually_torsion_free": true,
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"abelianization_dimension": 1,
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"L_2(3^2)"
],
"quotients": [
{
"$B_{2}(3)$": 11
},
{
"$\\textrm{M}_{12}$": 7
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{
"$\\textrm{Alt}_{9}$": 2
},
{
"$C_{3}(2)$": 4
},
{
"$\\textrm{Alt}_{10}$": 7
},
{
"${}^2A_{3}(9)$": 14
},
{
"$A_{3}(3)$": 16
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{
"${}^2A_{4}(4)$": 3
},
{
"$\\textrm{Alt}_{11}$": 7
}
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3,
5,
6,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{40,48,54}_2",
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4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 40,
"order2": 48,
"order3": 54,
"index": 2,
"presentation_length": 53,
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],
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"$B_{2}(3)$": 17
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{
"$\\textrm{M}_{12}$": 7
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{
"$C_{3}(2)$": 2
},
{
"$\\textrm{Alt}_{10}$": 12
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{
"${}^2A_{3}(9)$": 20
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{
"$A_{3}(3)$": 22
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{
"${}^2A_{4}(4)$": 24
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{
"$\\textrm{Alt}_{11}$": 15
}
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5,
6,
10,
11,
12,
14,
15,
16,
17,
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
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},
{
"name": "$G^{40,54,54}_0",
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4,
4,
4
],
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"a",
"b",
"c"
],
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"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 40,
"order2": 54,
"order3": 54,
"index": 0,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
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{
"$B_{2}(3)$": 8
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$\\textrm{Alt}_{9}$": 2
},
{
"$\\textrm{Alt}_{10}$": 4
},
{
"${}^2A_{3}(9)$": 9
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{
"$A_{3}(3)$": 17
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{
"${}^2A_{4}(4)$": 7
}
],
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5,
9,
10,
12,
15,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
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},
{
"name": "$G^{40,54,54}_2",
"half_girth_type": [
4,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 40,
"order2": 54,
"order3": 54,
"index": 2,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
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{
"$B_{2}(3)$": 12
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$C_{3}(2)$": 4
},
{
"$\\textrm{Alt}_{10}$": 16
},
{
"${}^2A_{3}(9)$": 14
},
{
"$A_{3}(3)$": 26
},
{
"${}^2A_{4}(4)$": 40
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{
"$\\textrm{Alt}_{11}$": 10
}
],
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3,
5,
10,
11,
12,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
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},
{
"name": "$G^{40,54,54}_8",
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4,
4,
4
],
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"a",
"b",
"c"
],
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"a^3",
"b^3",
"c^3",
"b * a^-1 * b * a * b * a^-1 * b * a",
"b^-1 * a^-1 * b * a^-1 * b^-1 * a^-1 * b * a^-1",
"b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1",
"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 40,
"order2": 54,
"order3": 54,
"index": 8,
"presentation_length": 65,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 1,
"L2_quotients": [
""
],
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{
"$B_{2}(3)$": 8
},
{
"$\\textrm{M}_{12}$": 2
},
{
"$\\textrm{Alt}_{9}$": 12
},
{
"${}^2A_{3}(9)$": 12
},
{
"$A_{3}(3)$": 8
},
{
"${}^2A_{4}(4)$": 16
}
],
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3,
5,
9,
12,
15,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{48,48,48}_0",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a * c * a^-1 * c^-1 * a^-1 * c^-1"
],
"order1": 48,
"order2": 48,
"order3": 48,
"index": 0,
"presentation_length": 33,
"hyperbolic": true,
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"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
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{
"$A_{2}(3)$": 1
},
{
"${}^2A_{2}(9)$": 2
},
{
"$B_{2}(3)$": 27
},
{
"$\\textrm{Alt}_{9}$": 3
},
{
"$\\textrm{M}_{22}$": 1
},
{
"$C_{3}(2)$": 39
},
{
"${}^2A_{3}(9)$": 21
},
{
"$B_{2}(5)$": 9
},
{
"$A_{3}(3)$": 33
},
{
"${}^2A_{4}(4)$": 60
},
{
"$\\textrm{Alt}_{11}$": 3
},
{
"${}^2A_{2}(81)$": 2
},
{
"$\\textrm{HS}_{}$": 3
}
],
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3,
4,
5,
9,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{48,48,48}_1",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c^-1 * a * c^-1 * a^-1 * c * a^-1 * c"
],
"order1": 48,
"order2": 48,
"order3": 48,
"index": 1,
"presentation_length": 33,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
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{
"$\\textrm{Alt}_{7}$": 3
},
{
"${}^2A_{2}(9)$": 1
},
{
"$\\textrm{Alt}_{8}$ or $A_{2}(4)$": 6
},
{
"$B_{2}(3)$": 24
},
{
"$\\textrm{M}_{12}$": 1
},
{
"${}^2A_{2}(25)$": 3
},
{
"$\\textrm{J}_{2}$": 4
},
{
"$C_{3}(2)$": 27
},
{
"$\\textrm{Alt}_{10}$": 3
},
{
"$A_{2}(7)$": 1
},
{
"${}^2A_{3}(9)$": 15
},
{
"$B_{2}(5)$": 19
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 30
},
{
"$A_{4}(2)$": 4
},
{
"${}^2A_{4}(4)$": 63
},
{
"$\\textrm{Alt}_{11}$": 3
},
{
"$A_{2}(9)$": 1
},
{
"${}^2A_{2}(81)$": 2
},
{
"$\\textrm{HS}_{}$": 3
}
],
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3,
4,
7,
8,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{48,48,54}_0",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1",
"c * b * c * b * c^-1 * b^-1 * c^-1 * b^-1",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 48,
"order2": 48,
"order3": 54,
"index": 0,
"presentation_length": 45,
"hyperbolic": true,
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"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 19
},
{
"$\\textrm{Alt}_{9}$": 3
},
{
"$C_{3}(2)$": 3
},
{
"$\\textrm{Alt}_{10}$": 6
},
{
"${}^2A_{3}(9)$": 17
},
{
"$A_{3}(3)$": 28
},
{
"${}^2A_{4}(4)$": 40
},
{
"$\\textrm{Alt}_{11}$": 6
},
{
"$A_{2}(9)$": 3
}
],
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3,
4,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{48,54,54}_0",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 48,
"order2": 54,
"order3": 54,
"index": 0,
"presentation_length": 57,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 8
},
{
"$\\textrm{Alt}_{9}$": 6
},
{
"$\\textrm{Alt}_{10}$": 2
},
{
"${}^2A_{3}(9)$": 9
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 11
},
{
"${}^2A_{4}(4)$": 25
},
{
"$\\textrm{Alt}_{11}$": 4
},
{
"$A_{2}(9)$": 3
}
],
"alternating_quotients": [
3,
4,
9,
10,
11,
12,
13,
14,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{48,54,54}_2",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 48,
"order2": 54,
"order3": 54,
"index": 2,
"presentation_length": 57,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": true,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 10
},
{
"$\\textrm{Alt}_{9}$": 9
},
{
"$C_{3}(2)$": 6
},
{
"$\\textrm{Alt}_{10}$": 22
},
{
"${}^2A_{3}(9)$": 14
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 36
},
{
"${}^2A_{4}(4)$": 28
},
{
"$\\textrm{Alt}_{11}$": 20
},
{
"$A_{2}(9)$": 3
}
],
"alternating_quotients": [
3,
4,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{48,54,54}_8",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b * a * b^-1 * a^-1 * b^-1 * a^-1",
"b * c * b^-1 * c^-1 * b^-1 * c * b * c^-1",
"b * c * b^-1 * c * b * c * b^-1 * c * b * c * b^-1 * c",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 48,
"order2": 54,
"order3": 54,
"index": 8,
"presentation_length": 57,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 18
},
{
"$\\textrm{Alt}_{9}$": 14
},
{
"$\\textrm{Alt}_{10}$": 1
},
{
"${}^2A_{3}(9)$": 15
},
{
"${}^2A_{2}(64)$": 2
},
{
"$A_{3}(3)$": 19
},
{
"${}^2A_{4}(4)$": 52
},
{
"$\\textrm{Alt}_{11}$": 1
},
{
"$A_{2}(9)$": 3
}
],
"alternating_quotients": [
3,
4,
9,
10,
11,
12,
13,
15,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{54,54,54}_0",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b^-1 * a * b * a^-1",
"b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"a * c * a^-1 * c^-1 * a^-1 * c * a * c^-1",
"a * c * a^-1 * c * a * c * a^-1 * c * a * c * a^-1 * c"
],
"order1": 54,
"order2": 54,
"order3": 54,
"index": 0,
"presentation_length": 69,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$\\textrm{Alt}_{9}$": 6
},
{
"${}^2A_{4}(4)$": 10
},
{
"$A_{2}(9)$": 3
}
],
"alternating_quotients": [
3,
9,
19,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
},
{
"name": "$G^{54,54,54}_2",
"half_girth_type": [
4,
4,
4
],
"generators": [
"a",
"b",
"c"
],
"relations": [
"a^3",
"b^3",
"c^3",
"b * a * b^-1 * a^-1 * b^-1 * a * b * a^-1",
"b * a * b^-1 * a * b * a * b^-1 * a * b * a * b^-1 * a",
"c * b * c^-1 * b^-1 * c^-1 * b * c * b^-1",
"c * b * c^-1 * b * c * b * c^-1 * b * c * b * c^-1 * b",
"c * a * c^-1 * a^-1 * c^-1 * a * c * a^-1",
"c * a * c^-1 * a * c * a * c^-1 * a * c * a * c^-1 * a"
],
"order1": 54,
"order2": 54,
"order3": 54,
"index": 2,
"presentation_length": 69,
"hyperbolic": true,
"witnesses_non_hyperbolictity": null,
"virtually_torsion_free": null,
"Kazdhdan_property_T": false,
"abelianization_dimension": 3,
"L2_quotients": [
""
],
"quotients": [
{
"$A_{2}(3)$": 2
},
{
"$B_{2}(3)$": 8
},
{
"$\\textrm{Alt}_{9}$": 24
},
{
"${}^2A_{3}(9)$": 9
},
{
"$A_{3}(3)$": 13
},
{
"${}^2A_{4}(4)$": 41
},
{
"$A_{2}(9)$": 3
}
],
"alternating_quotients": [
3,
9,
12,
15,
18,
19,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40
],
"maximal_degree_alternating_quotients": 40
}
]
Reference in New Issue View Git Blame Copy Permalink