SmallHyperbolic/data/table_4_4_4.csv

1	order1 & order2 & order3 & index & presentation length & virtually torsion-free & Kazhdan & abelianization dimension & L2-quotients & quotients & alternating quotients & maximal order for alternating quotients
2	40 & 40 & 40 & 0 & 57 & Yes & No & 0& [L_2(\infty^4), L_2(\infty^4), L_2(\infty^4), L_2(\infty^4)]& [($\textrm{Alt}_{7}$, 1), ($B_{2}(3)$, 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), (${}^2A_{3}(9)$, 12), ($B_{2}(5)$, 90), ($A_{3}(3)$, 7), ($\textrm{HS}_{}$, 12)] & [ 6, 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 ] & 40
3	40 & 40 & 48 & 0 & 49 & Yes & No & 0& [L_2(\infty^4)]& [($\textrm{Alt}_{7}$, 2), ($\textrm{M}_{11}$, 4), ($B_{2}(3)$, 8), (${}^2A_{2}(25)$, 1), ($\textrm{M}_{22}$, 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), (${}^2A_{4}(4)$, 10), ($\textrm{Alt}_{11}$, 7)] & [ 5, 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 ] & 40
4	40 & 40 & 54 & 0 & 61 & Yes & No & 0& []& [($\textrm{Alt}_{7}$, 2), ($B_{2}(3)$, 5), ($\textrm{M}_{12}$, 2), ($\textrm{Alt}_{10}$, 8), (${}^2A_{3}(9)$, 15), ($A_{3}(3)$, 4), (${}^2A_{4}(4)$, 7)] & [ 5, 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 ] & 40
5	40 & 48 & 48 & 0 & 41 & Yes & No & 1& [L_2(3^2), L_2(3^2)]& [($\textrm{Alt}_{7}$, 2), ($\textrm{M}_{11}$, 1), ($B_{2}(3)$, 18), ($\textrm{M}_{22}$, 2), ($\textrm{J}_{2}$, 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)] & [ 3, 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 ] & 40
6	40 & 48 & 54 & 0 & 53 & Yes & No & 1& [L_2(3^2)]& [($B_{2}(3)$, 11), ($\textrm{M}_{12}$, 7), ($\textrm{Alt}_{9}$, 2), ($C_{3}(2)$, 4), ($\textrm{Alt}_{10}$, 7), (${}^2A_{3}(9)$, 14), ($A_{3}(3)$, 16), (${}^2A_{4}(4)$, 3), ($\textrm{Alt}_{11}$, 7)] & [ 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 ] & 40
7	40 & 48 & 54 & 2 & 53 & Yes & No & 1& [L_2(3^2)]& [($B_{2}(3)$, 17), ($\textrm{M}_{12}$, 7), ($C_{3}(2)$, 2), ($\textrm{Alt}_{10}$, 12), (${}^2A_{3}(9)$, 20), ($A_{3}(3)$, 22), (${}^2A_{4}(4)$, 24), ($\textrm{Alt}_{11}$, 15)] & [ 3, 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 ] & 40
8	40 & 54 & 54 & 0 & 65 & Yes & No & 1& []& [($B_{2}(3)$, 8), ($\textrm{M}_{12}$, 2), ($\textrm{Alt}_{9}$, 2), ($\textrm{Alt}_{10}$, 4), (${}^2A_{3}(9)$, 9), ($A_{3}(3)$, 17), (${}^2A_{4}(4)$, 7)] & [ 3, 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 ] & 40
9	40 & 54 & 54 & 2 & 65 & Yes & No & 1& []& [($B_{2}(3)$, 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), ($\textrm{Alt}_{11}$, 10)] & [ 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 ] & 40
10	40 & 54 & 54 & 8 & 65 & Yes & No & 1& []& [($B_{2}(3)$, 8), ($\textrm{M}_{12}$, 2), ($\textrm{Alt}_{9}$, 12), (${}^2A_{3}(9)$, 12), ($A_{3}(3)$, 8), (${}^2A_{4}(4)$, 16)] & [ 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 ] & 40
11	48 & 48 & 48 & 0 & 33 & ? & No & 3& []& [($A_{2}(3)$, 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)] & [ 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 ] & 40
12	48 & 48 & 48 & 1 & 33 & Yes & No & 3& []& [($\textrm{Alt}_{7}$, 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)] & [ 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 ] & 40
13	48 & 48 & 54 & 0 & 45 & Yes & No & 3& []& [($A_{2}(3)$, 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)] & [ 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 ] & 40
14	48 & 54 & 54 & 0 & 57 & ? & No & 3& []& [($A_{2}(3)$, 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)] & [ 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 ] & 40
15	48 & 54 & 54 & 2 & 57 & Yes & No & 3& []& [($A_{2}(3)$, 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)] & [ 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 ] & 40
16	48 & 54 & 54 & 8 & 57 & ? & No & 3& []& [($A_{2}(3)$, 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)] & [ 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 ] & 40
17	54 & 54 & 54 & 0 & 69 & ? & No & 3& []& [($A_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 6), (${}^2A_{4}(4)$, 10), ($A_{2}(9)$, 3)] & [ 3, 9, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 ] & 40
18	54 & 54 & 54 & 2 & 69 & ? & No & 3& []& [($A_{2}(3)$, 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)] & [ 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 ] & 40