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"2A3(9)": 5, "M22": 1 } }, { "name": "G^{24,24,48}_1", "name_utf8": "G²⁴'²⁴'⁴⁸₁", "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^-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, "hyperbolic": true, "witnesses_non_hyperbolictity": null, "virtually_torsion_free": true, "Kazdhdan_property_T": false, "abelianization_dimension": 3, "L2_quotients": [], "quotients": { "HS": 1, "M_{12}": 1, "Alt(8) or A_{2}(4)": 2, "J_{2}": 1, "C_{3}(2)": 3, "Alt(7)": 3, "B_{2}(5)": 3, "A_{4}(2)": 1, "{}^2A_{3}(9)": 1, "{}^2A_{2}(25)": 1, "A_{2}(7)": 1, "{}^2A_{4}(4)": 2 }, "alternating_quotients": [ 3, 4, 7, 8, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ], "maximal_degree_alternating_quotients": 30, "L2_quotients_utf8": 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* 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, "witnesses_non_hyperbolictity": null, "virtually_torsion_free": null, "Kazdhdan_property_T": null, "abelianization_dimension": 2, "L2_quotients": [], "quotients": {}, "alternating_quotients": [ 3, 13, 27 ], "maximal_degree_alternating_quotients": 30, "L2_quotients_utf8": [], "quotients_utf8": {}, "quotients_plain": {} }, { "name": "G^{26,26,40}_0", "name_utf8": "G²⁶'²⁶'⁴⁰₀", "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 * 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