SmallHyperbolic/data/table_3_3_3.csv

order1 & order2 & order3 & index & presentation length & hyperbolic & witnesses for non-hyperbolicity & virtually torsion-free & Kazhdan & abelianization dimension & L2-quotients & quotients & alternating quotients & maximal order for alternating quotients
14 & 14 & 14 & 0 & 27  & ? &  & Yes & Yes & 0& [L_2(7)]& [(${}^2A_{2}(9)$, 1), (${}^2A_{2}(25)$, 1)] & [  ] & 36
14 & 14 & 14 & 1 & 27 & No & c^-1 * a * b^-1 * a * c * a * b^-1 * a, a^-1 * b * c * a * b^-1 * a * c^-1 * b & ? & Yes & 1& []& [] & [ 3  ] & 36
14 & 14 & 14 & 2 & 27 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & Yes & Yes & 0& []& [($\textrm{Alt}_{7}$, 1)] & [ 7  ] & 36
14 & 14 & 14 & 6 & 27 & No & c * a * b * a, b^-1 * a^-1 * c * a & Yes & Yes & 1& []& [($A_{2}(8)$, 2)] & [ 3  ] & 36
14 & 14 & 16 & 0 & 27 & No & c * a * b * a, a^-1 * b^-1 * c^-1 * b & Yes & No & 1& [L_2(7)]& [($\textrm{Alt}_{8}$ or $A_{2}(4)$, 1)] & [ 3, 8  ] & 36
14 & 14 & 16 & 1 & 27 & No & c * a * b * a * c^-1 * a^-1 * b^-1 * a^-1, b^-1 * a * c * a^-1 * b^-1 * a * c * a^-1 & ? & ? & 0& [L_2(7)]& [] & [  ] & 36
14 & 14 & 16 & 4 & 27 & No & c * a * b * a * c^-1 * a^-1 * b^-1 * a, a^-1 * b * c^-1 * a * b * a * c * b^-1 & ? & ? & 0& []& [] & [  ] & 36
14 & 14 & 16 & 5 & 27 & No & c * a * b * a * c^-1 * b * a * c^-1 * b * a^-1, b * a^-1 * c^-1 * a * b^-1 * c^-1 * a * b * c * a^-1 & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 14 & 18 & 0 & 33 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & Yes & ? & 1& []& [(${}^2A_{2}(9)$, 1)] & [ 3  ] & 36
14 & 14 & 18 & 4 & 33 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 14 & 24 & 0 & 35 & Yes &  & ? & ? & 1& [L_2(7)]& [] & [ 3  ] & 36
14 & 14 & 24 & 1 & 35 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & Yes & No & 1& [L_2(7)]& [($\textrm{Alt}_{7}$, 1), (${}^2A_{2}(25)$, 1)] & [ 3, 7  ] & 36
14 & 14 & 24 & 4 & 35 & No & a^-1 * b * c * b, c * a * b^-1 * a & Yes & No & 1& []& [($\textrm{Alt}_{8}$ or $A_{2}(4)$, 1), ($\textrm{M}_{22}$, 1)] & [ 3, 8  ] & 36
14 & 14 & 24 & 5 & 35 & No & b * a^-1 * c * a^-1 * b^-1 * a * c^-1 * a, c^-1 * a * b * a^-1 * c * a^-1 * b^-1 * a & Yes & ? & 1& []& [($\textrm{Alt}_{7}$, 1)] & [ 3, 7  ] & 36
14 & 14 & 26 & 0 & 35 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 14 & 26 & 1 & 35 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & Yes & ? & 0& []& [($A_{2}(9)$, 1)] & [ 14  ] & 36
14 & 14 & 26 & 3 & 35 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & ? & ? & 0& []& [] & [  ] & 36
14 & 14 & 26 & 4 & 35 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 0& []& [] & [  ] & 36
14 & 14 & 26 & 5 & 35 & No & b * a^-1 * c * a^-1 * b^-1 * a * c^-1 * a, c^-1 * a * b * a^-1 * c * a^-1 * b^-1 * a & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 14 & 26 & 7 & 35 & No & b * a^-1 * c * a^-1 * b^-1 * a * c^-1 * a, c^-1 * a * b * a^-1 * c * a^-1 * b^-1 * a & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 16 & 16 & 0 & 27 & No & b^-1 * a * c * b * a^-1 * c^-1, b^-1 * c * a * b^-1 * c^-1 * a & ? & No & 0& [L_2(7)]& [] & [  ] & 36
14 & 16 & 16 & 1 & 27 & No & a^-1 * b * c * a^-1 * b * a * c^-1 * a^-1 * b^-1 * a * c^-1 * b^-1, c * a^-1 * b * a * c * a^-1 * b^-1 * a * c^-1 * a^-1 * b^-1 * a & ? & ? & 1& []& [] & [ 3, 4  ] & 36
14 & 16 & 18 & 0 & 33 & No & a * c * b^-1 * a^-1 * c * b, c^-1 * a^-1 * b^-1 * c^-1 * a * b & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 16 & 24 & 0 & 35 & Yes &  & ? & No & 1& [L_2(7)]& [] & [ 3  ] & 36
14 & 16 & 24 & 1 & 35 & Yes &  & ? & ? & 1& []& [] & [ 3, 4  ] & 36
14 & 16 & 26 & 0 & 35 & Yes &  & ? & ? & 0& []& [] & [  ] & 36
14 & 16 & 26 & 1 & 35 & Yes &  & ? & No & 1& []& [] & [ 3  ] & 36
14 & 16 & 26 & 3 & 35 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 16 & 26 & 7 & 35 & Yes &  & ? & ? & 0& []& [] & [  ] & 36
14 & 18 & 18 & 0 & 39 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & No & 2& []& [] & [ 3  ] & 36
14 & 18 & 24 & 0 & 41 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 2& []& [] & [ 3  ] & 36
14 & 18 & 26 & 0 & 41 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 18 & 26 & 3 & 41 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 24 & 24 & 0 & 43 & No & a^-1 * b * c * b, c * a * b^-1 * a & Yes & No & 2& [L_2(7)]& [($\textrm{Alt}_{7}$, 1), ($\textrm{Alt}_{8}$ or $A_{2}(4)$, 1), ($\textrm{J}_{2}$, 1), (${}^2A_{3}(9)$, 1)] & [ 3, 7, 8, 22, 28, 29, 31, 35, 36  ] & 36
14 & 24 & 24 & 1 & 43 & Yes &  & ? & No & 2& []& [] & [ 3, 4  ] & 36
14 & 24 & 26 & 0 & 43 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 24 & 26 & 1 & 43 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 24 & 26 & 3 & 43 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 24 & 26 & 7 & 43 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 26 & 26 & 0 & 43 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 0& []& [] & [  ] & 36
14 & 26 & 26 & 1 & 43 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 26 & 26 & 3 & 43 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 26 & 26 & 4 & 43 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
14 & 26 & 26 & 5 & 43 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & ? & ? & 0& []& [] & [ 14  ] & 36
14 & 26 & 26 & 15 & 43 & No & c^-1 * a * b^-1 * a, a^-1 * b * c^-1 * b & ? & ? & 0& []& [] & [ 13  ] & 36
16 & 16 & 16 & 0 & 27 & No & c * a * b * a, a^-1 * b^-1 * c^-1 * b & Yes & No & 1& []& [(${}^2A_{2}(9)$, 1), ($\textrm{J}_{2}$, 1), (${}^2A_{2}(64)$, 2), ($A_{2}(9)$, 1), (${}^2A_{2}(81)$, 2)] & [ 3, 4  ] & 36
16 & 16 & 16 & 1 & 27 & No & c * a * b * a * c^-1 * a^-1 * b^-1 * a^-1, b * a * c^-1 * a^-1 * b^-1 * a * c * a^-1 & Yes & No & 0& []& [($A_{2}(3)$, 1), (${}^2A_{2}(9)$, 2), (${}^2A_{2}(81)$, 2)] & [ 5, 29  ] & 36
16 & 16 & 18 & 0 & 33 & No & b^-1 * a * c^-1 * b * a * c^-1, a * c^-1 * b^-1 * a * c^-1 * b & Yes & No & 1& []& [($A_{2}(3)$, 2), ($A_{2}(9)$, 3)] & [ 3, 4  ] & 36
16 & 16 & 24 & 0 & 35 & Yes &  & Yes & No & 1& []& [($\textrm{Alt}_{10}$, 1), ($A_{4}(2)$, 1)] & [ 3, 4, 10, 34, 36  ] & 36
16 & 16 & 24 & 1 & 35 & No & b^-1 * a * c^-1 * b * a * c^-1, a * c^-1 * b^-1 * a * c^-1 * b & Yes & No & 1& []& [($\textrm{Alt}_{9}$, 1), ($\textrm{HS}_{}$, 1)] & [ 3, 4, 5, 9, 21, 29, 33, 34  ] & 36
16 & 16 & 26 & 0 & 35 & Yes &  & ? & ? & 1& []& [] & [ 3, 4  ] & 36
16 & 16 & 26 & 1 & 35 & No & b^-1 * a * c^-1 * b * a * c^-1, a * c^-1 * b^-1 * a * c^-1 * b & ? & No & 0& [L_2(13)]& [] & [ 16, 30  ] & 36
16 & 18 & 18 & 0 & 39 & No & b^-1 * a^-1 * c^-1 * a^-1 * b * a * c^-1 * a, c^-1 * a * b * a * c^-1 * a * b * a & Yes & No & 2& []& [($A_{2}(3)$, 2), (${}^2A_{2}(64)$, 2), ($A_{2}(9)$, 3)] & [ 3, 4  ] & 36
16 & 18 & 24 & 0 & 41 & Yes &  & Yes & No & 2& []& [($\textrm{Alt}_{10}$, 1)] & [ 3, 4, 10, 19, 34  ] & 36
16 & 18 & 26 & 0 & 41 & Yes &  & ? & ? & 1& []& [] & [ 3  ] & 36
16 & 24 & 24 & 0 & 43 & Yes &  & Yes & No & 2& []& [($\textrm{Alt}_{7}$, 1), ($\textrm{Alt}_{8}$ or $A_{2}(4)$, 2), (${}^2A_{2}(25)$, 1), ($\textrm{J}_{2}$, 1), ($C_{3}(2)$, 1), (${}^2A_{3}(9)$, 1), ($B_{2}(5)$, 1), ($\textrm{HS}_{}$, 1)] & [ 3, 4, 7, 8, 15, 18, 19, 20, 22, 23, 24, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36  ] & 36
16 & 24 & 24 & 1 & 43 & Yes &  & Yes & No & 2& []& [($C_{3}(2)$, 2)] & [ 3, 4, 5, 17, 18, 19, 21, 22, 27, 29, 30, 31, 32, 33, 34, 35, 36  ] & 36
16 & 24 & 26 & 0 & 43 & Yes &  & ? & ? & 1& []& [] & [ 3, 4  ] & 36
16 & 24 & 26 & 1 & 43 & Yes &  & ? & ? & 1& [L_2(13)]& [] & [ 3  ] & 36
16 & 26 & 26 & 0 & 43 & Yes &  & ? & No & 1& []& [] & [ 3, 26  ] & 36
16 & 26 & 26 & 1 & 43 & Yes &  & ? & ? & 0& [L_2(13)]& [($A_{2}(3)$, 1)] & [  ] & 36
16 & 26 & 26 & 3 & 43 & Yes &  & Yes & No & 0& []& [($A_{2}(3)$, 2), ($G_{2}(3)$, 1)] & [ 26  ] & 36
16 & 26 & 26 & 5 & 43 & Yes &  & Yes & ? & 1& [L_2(13)]& [($A_{2}(3)$, 1), ($G_{2}(3)$, 1), ($A_{3}(3)$, 1)] & [ 3, 14, 26, 28, 29  ] & 36
18 & 18 & 18 & 0 & 45 & No & c * a * b * a, b * a * c * a & Yes & No & 3& []& [($A_{2}(3)$, 2), ($A_{2}(9)$, 3)] & [ 3, 27, 36  ] & 36
18 & 18 & 24 & 0 & 47 & No & c * a * b * a, b * a * c * a & Yes & No & 3& []& [($\textrm{Alt}_{10}$, 1), ($\textrm{Alt}_{11}$, 1)] & [ 3, 4, 10, 11, 12, 15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36  ] & 36
18 & 18 & 26 & 0 & 47 & No & c * a * b * a, b * a * c * a & Yes & No & 2& []& [($A_{2}(3)$, 2), ($A_{2}(9)$, 3)] & [ 3, 13  ] & 36
18 & 24 & 24 & 0 & 49 & No & a^-1 * b * c * b, c * a * b^-1 * a & Yes & No & 3& []& [($\textrm{Alt}_{10}$, 1), (${}^2A_{3}(9)$, 1), ($\textrm{Alt}_{11}$, 1)] & [ 3, 4, 10, 11, 15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36  ] & 36
18 & 24 & 26 & 0 & 49 & No & a^-1 * b * c * b, c * a * b^-1 * a & ? & ? & 2& []& [] & [ 3, 27  ] & 36
18 & 26 & 26 & 0 & 49 & No & a^-1 * b * c * b, c * a * b^-1 * a & Yes & No & 1& []& [($G_{2}(3)$, 2)] & [ 3, 13  ] & 36
18 & 26 & 26 & 1 & 49 & No & a^-1 * b^-1 * c^-1 * b^-1, b * a * c^-1 * a & Yes & No & 1& []& [($A_{2}(3)$, 2), ($G_{2}(3)$, 1)] & [ 3, 13, 27  ] & 36
24 & 24 & 24 & 0 & 51 & Yes &  & Yes & No & 3& []& [($\textrm{Alt}_{7}$, 3), ($\textrm{M}_{12}$, 1), ($A_{2}(7)$, 1), ($B_{2}(5)$, 3), ($A_{4}(2)$, 1)] & [ 3, 4, 7, 13, 15, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36  ] & 36
24 & 24 & 24 & 1 & 51 & No & a^-1 * b^-1 * c^-1 * b^-1, b * a * c^-1 * a & Yes & No & 3& []& [($\textrm{M}_{22}$, 1), (${}^2A_{3}(9)$, 3)] & [ 3, 4, 5, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36  ] & 36
24 & 24 & 26 & 0 & 51 & Yes &  & ? & No & 2& []& [] & [ 3, 4  ] & 36
24 & 24 & 26 & 1 & 51 & No & a^-1 * b^-1 * c^-1 * b^-1, b * a * c^-1 * a & Yes & No & 2& [L_2(13)]& [($A_{3}(3)$, 1)] & [ 3, 13, 14, 15, 16, 26, 27, 28  ] & 36
24 & 26 & 26 & 0 & 51 & Yes &  & ? & No & 1& []& [] & [ 3, 26, 28  ] & 36
24 & 26 & 26 & 1 & 51 & No & a^-1 * b^-1 * c^-1 * b^-1, b * a * c^-1 * a & Yes & No & 1& [L_2(13)]& [($A_{2}(3)$, 2), ($A_{3}(3)$, 1)] & [ 3, 13, 14, 27  ] & 36
24 & 26 & 26 & 3 & 51 & No & a^-1 * b^-1 * c^-1 * b^-1, b * a * c^-1 * a & ? & No & 1& []& [($A_{2}(3)$, 2)] & [ 3, 13, 14, 16, 26  ] & 36
24 & 26 & 26 & 5 & 51 & Yes &  & ? & No & 1& [L_2(13)]& [($A_{2}(3)$, 2), ($A_{3}(3)$, 1)] & [ 3, 13, 14, 26, 27, 28  ] & 36
26 & 26 & 26 & 0 & 51 & Yes &  & Yes & No & 1& []& [($A_{2}(3)$, 1), ($A_{2}(9)$, 3)] & [ 3, 26  ] & 36
26 & 26 & 26 & 1 & 51 & No & a^-1 * b^-1 * c^-1 * b^-1, b * a * c^-1 * a & Yes & No & 0& []& [($A_{2}(3)$, 2), (${}^2A_{2}(16)$, 2), ($G_{2}(3)$, 6)] & [ 13, 26  ] & 36
26 & 26 & 26 & 5 & 51 & Yes &  & Yes & No & 1& []& [($A_{2}(3)$, 2), (${}^2A_{2}(16)$, 1)] & [ 3  ] & 36
26 & 26 & 26 & 21 & 51 & No & b^-1 * a * c^-1 * a, a^-1 * b * c^-1 * b & Yes & No & 0& [L_2(13)]& [($A_{2}(3)$, 5), (${}^2A_{2}(16)$, 3), ($G_{2}(3)$, 1), (${}^2F_4(2)'$, 1)] & [ 13, 30  ] & 36