SmallHyperbolic/data/table_3_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	14 & 40 & 40 & 0 & 47 & Yes & No & 0& [L_2(7^2)]& [($\textrm{Alt}_{8}$ 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)] & [ 5, 10, 11, 20, 21, 30 ] & 30
3	14 & 40 & 48 & 0 & 39 & ? & ? & 0& [L_2(7^2)]& [($\textrm{Alt}_{7}$, 1), ($\textrm{Alt}_{10}$, 1), ($A_{4}(2)$, 1)] & [ 7, 10 ] & 30
4	14 & 40 & 54 & 0 & 51 & Yes & ? & 0& []& [($\textrm{J}_{2}$, 1), ($C_{3}(2)$, 2)] & [ 21, 25 ] & 30
5	14 & 40 & 54 & 2 & 51 & Yes & ? & 0& []& [($\textrm{J}_{2}$, 1), ($C_{3}(2)$, 2)] & [ 20, 21, 22, 25, 27, 30 ] & 30
6	14 & 48 & 48 & 0 & 31 & Yes & No & 2& [L_2(7)]& [($\textrm{Alt}_{7}$, 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)] & [ 3, 7, 8, 15, 16, 22, 23, 24, 27, 28, 29, 30 ] & 30
7	14 & 48 & 48 & 1 & 31 & ? & No & 2& []& [] & [ 3, 4 ] & 30
8	14 & 48 & 54 & 0 & 43 & ? & ? & 2& []& [($G_{2}(3)$, 1)] & [ 3, 18 ] & 30
9	14 & 48 & 54 & 2 & 43 & Yes & No & 2& []& [($C_{3}(2)$, 3), (${}^2A_{3}(9)$, 1), ($G_{2}(3)$, 1)] & [ 3, 14, 15, 21, 22, 28, 29, 30 ] & 30
10	14 & 54 & 54 & 0 & 55 & ? & No & 2& []& [] & [ 3, 21, 28, 29 ] & 30
11	14 & 54 & 54 & 2 & 55 & Yes & No & 2& []& [($\textrm{Alt}_{10}$, 6), (${}^2A_{3}(9)$, 2)] & [ 3, 10, 13, 14, 17, 19, 20, 21, 23, 24, 27, 28, 29, 30 ] & 30
12	14 & 54 & 54 & 8 & 55 & ? & No & 2& []& [] & [ 3, 18, 21, 27, 30 ] & 30
13	16 & 40 & 40 & 0 & 47 & Yes & No & 0& [L_2(\infty^4)]& [($\textrm{M}_{11}$, 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)] & [ 5, 6, 10, 11, 15, 16, 17, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30 ] & 30
14	16 & 40 & 48 & 0 & 39 & ? & No & 0& [L_2(3^2)]& [($\textrm{M}_{11}$, 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)] & [ 5, 6, 11, 16, 18, 21, 22, 23, 24, 26, 27, 28, 29, 30 ] & 30
15	16 & 40 & 54 & 0 & 51 & Yes & No & 0& [L_2(3^2)]& [($B_{2}(3)$, 5), ($\textrm{M}_{12}$, 5), ($C_{3}(2)$, 1), (${}^2A_{3}(9)$, 2), ($A_{3}(3)$, 3), (${}^2A_{4}(4)$, 1)] & [ 6, 12, 17, 18, 21, 23, 24, 26, 27, 28, 29, 30 ] & 30
16	16 & 40 & 54 & 2 & 51 & Yes & No & 0& [L_2(3^2)]& [($B_{2}(3)$, 4), ($\textrm{M}_{12}$, 5), ($\textrm{Alt}_{10}$, 3), (${}^2A_{3}(9)$, 4), ($A_{3}(3)$, 4), (${}^2A_{4}(4)$, 1)] & [ 6, 10, 12, 15, 16, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
17	16 & 48 & 48 & 0 & 31 & Yes & No & 2& []& [($\textrm{Alt}_{7}$, 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)] & [ 3, 4, 7, 8, 10, 11, 12, 15, 16, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
18	16 & 48 & 48 & 1 & 31 & Yes & No & 2& []& [($A_{2}(3)$, 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)] & [ 3, 4, 5, 9, 11, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
19	16 & 48 & 54 & 0 & 43 & Yes & No & 2& []& [($A_{2}(3)$, 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)] & [ 3, 4, 9, 10, 12, 17, 18, 19, 21, 22, 24, 25, 26, 27, 28, 29, 30 ] & 30
20	16 & 48 & 54 & 2 & 43 & Yes & No & 2& []& [($A_{2}(3)$, 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)] & [ 3, 4, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
21	16 & 54 & 54 & 0 & 55 & Yes & No & 2& []& [($A_{2}(3)$, 2), (${}^2A_{2}(64)$, 2), (${}^2A_{4}(4)$, 2), ($A_{2}(9)$, 3)] & [ 3, 4, 20, 21, 22, 24, 25, 26, 27, 29, 30 ] & 30
22	16 & 54 & 54 & 2 & 55 & Yes & No & 2& []& [($A_{2}(3)$, 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)] & [ 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
23	16 & 54 & 54 & 8 & 55 & Yes & No & 2& []& [($A_{2}(3)$, 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)] & [ 3, 4, 9, 12, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
24	18 & 40 & 40 & 0 & 53 & Yes & No & 0& []& [($\textrm{Alt}_{7}$, 2), ($B_{2}(3)$, 5), ($\textrm{M}_{12}$, 2), ($\textrm{Alt}_{10}$, 8), (${}^2A_{3}(9)$, 1), (${}^2A_{4}(4)$, 3)] & [ 5, 7, 10, 15, 17, 20, 21, 22, 24, 25, 26, 27, 30 ] & 30
25	18 & 40 & 48 & 0 & 45 & Yes & No & 1& [L_2(3^2)]& [($B_{2}(3)$, 5), ($\textrm{M}_{12}$, 7), ($\textrm{Alt}_{10}$, 2), (${}^2A_{3}(9)$, 4), ($A_{3}(3)$, 10), ($\textrm{Alt}_{11}$, 5)] & [ 3, 5, 6, 10, 11, 12, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
26	18 & 40 & 54 & 0 & 57 & ? & No & 1& []& [($B_{2}(3)$, 2), ($\textrm{M}_{12}$, 2), ($\textrm{Alt}_{10}$, 4), ($A_{3}(3)$, 14), (${}^2A_{4}(4)$, 3)] & [ 3, 5, 10, 12, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30 ] & 30
27	18 & 40 & 54 & 2 & 57 & Yes & No & 1& []& [($B_{2}(3)$, 2), ($\textrm{M}_{12}$, 2), ($\textrm{Alt}_{9}$, 2), (${}^2A_{3}(9)$, 3), ($A_{3}(3)$, 5), (${}^2A_{4}(4)$, 4)] & [ 3, 5, 9, 12, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
28	18 & 48 & 48 & 0 & 37 & Yes & No & 3& []& [($A_{2}(3)$, 2), ($B_{2}(3)$, 3), ($\textrm{Alt}_{10}$, 3), (${}^2A_{3}(9)$, 4), ($A_{3}(3)$, 9), ($\textrm{Alt}_{11}$, 2), ($A_{2}(9)$, 3)] & [ 3, 4, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
29	18 & 48 & 54 & 0 & 49 & Yes & No & 3& []& [($A_{2}(3)$, 2), ($B_{2}(3)$, 2), ($\textrm{Alt}_{10}$, 2), (${}^2A_{2}(64)$, 2), ($A_{3}(3)$, 8), ($\textrm{Alt}_{11}$, 4), ($A_{2}(9)$, 3)] & [ 3, 4, 10, 11, 12, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
30	18 & 48 & 54 & 2 & 49 & Yes & No & 3& []& [($A_{2}(3)$, 2), ($B_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 2), ($\textrm{Alt}_{10}$, 1), (${}^2A_{3}(9)$, 3), (${}^2A_{2}(64)$, 2), ($A_{3}(3)$, 1), (${}^2A_{4}(4)$, 3), ($\textrm{Alt}_{11}$, 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 ] & 30
31	18 & 54 & 54 & 0 & 61 & ? & No & 3& []& [($A_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 2), (${}^2A_{4}(4)$, 2), ($A_{2}(9)$, 3)] & [ 3, 9, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
32	18 & 54 & 54 & 2 & 61 & Yes & No & 3& []& [($A_{2}(3)$, 2), ($B_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 10), (${}^2A_{3}(9)$, 3), ($A_{3}(3)$, 1), (${}^2A_{4}(4)$, 9), ($A_{2}(9)$, 3)] & [ 3, 9, 12, 15, 18, 19, 21, 22, 24, 25, 26, 27, 28, 29, 30 ] & 30
33	18 & 54 & 54 & 8 & 61 & Yes & No & 3& []& [($A_{2}(3)$, 2), ($B_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 8), ($A_{3}(3)$, 10), (${}^2A_{4}(4)$, 4), ($A_{2}(9)$, 3)] & [ 3, 9, 12, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
34	24 & 40 & 40 & 0 & 55 & Yes & No & 0& [L_2(\infty^4)]& [($\textrm{Alt}_{7}$, 2), ($B_{2}(3)$, 2), ($\textrm{M}_{22}$, 2), ($\textrm{J}_{2}$, 2), ($C_{2}(4)$, 2), ($C_{3}(2)$, 2), ($\textrm{Alt}_{10}$, 2), ($B_{2}(5)$, 10), ($A_{4}(2)$, 4), (${}^2A_{4}(4)$, 4), ($\textrm{Alt}_{11}$, 3)] & [ 5, 6, 7, 10, 11, 12, 15, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
35	24 & 40 & 48 & 0 & 47 & Yes & No & 1& [L_2(3^2), L_2(3^2)]& [($\textrm{Alt}_{7}$, 2), ($B_{2}(3)$, 3), ($\textrm{M}_{22}$, 2), ($\textrm{J}_{2}$, 4), ($C_{2}(4)$, 4), ($C_{3}(2)$, 3), ($B_{2}(5)$, 12), ($A_{3}(3)$, 2), ($A_{4}(2)$, 5), (${}^2A_{4}(4)$, 1), ($\textrm{Alt}_{11}$, 4)] & [ 3, 5, 6, 7, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
36	24 & 40 & 54 & 0 & 59 & Yes & No & 1& [L_2(3^2)]& [($B_{2}(3)$, 4), ($\textrm{M}_{12}$, 6), ($\textrm{Alt}_{10}$, 12), (${}^2A_{3}(9)$, 2), ($A_{3}(3)$, 3), (${}^2A_{4}(4)$, 4), ($\textrm{Alt}_{11}$, 12)] & [ 3, 5, 6, 10, 11, 12, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
37	24 & 40 & 54 & 2 & 59 & Yes & No & 1& [L_2(3^2)]& [($B_{2}(3)$, 2), ($\textrm{M}_{12}$, 6), ($\textrm{Alt}_{9}$, 2), ($C_{3}(2)$, 4), ($\textrm{Alt}_{10}$, 7), (${}^2A_{3}(9)$, 6), ($A_{3}(3)$, 7), (${}^2A_{4}(4)$, 1), ($\textrm{Alt}_{11}$, 6)] & [ 3, 5, 6, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
38	24 & 48 & 48 & 0 & 39 & Yes & No & 3& []& [($\textrm{Alt}_{7}$, 3), ($\textrm{Alt}_{8}$ or $A_{2}(4)$, 4), ($B_{2}(3)$, 3), ($\textrm{M}_{12}$, 1), (${}^2A_{2}(25)$, 2), ($\textrm{J}_{2}$, 2), ($C_{3}(2)$, 11), ($\textrm{Alt}_{10}$, 1), ($A_{2}(7)$, 1), (${}^2A_{3}(9)$, 3), ($B_{2}(5)$, 7), ($A_{3}(3)$, 1), ($A_{4}(2)$, 2), (${}^2A_{4}(4)$, 13), ($\textrm{Alt}_{11}$, 1), ($\textrm{HS}_{}$, 2)] & [ 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 ] & 30
39	24 & 48 & 48 & 1 & 39 & Yes & No & 3& []& [($B_{2}(3)$, 4), ($\textrm{Alt}_{9}$, 1), ($\textrm{M}_{22}$, 1), ($C_{3}(2)$, 17), (${}^2A_{3}(9)$, 8), ($B_{2}(5)$, 5), ($A_{3}(3)$, 3), (${}^2A_{4}(4)$, 8), ($\textrm{Alt}_{11}$, 1), ($\textrm{HS}_{}$, 1)] & [ 3, 4, 5, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
40	24 & 48 & 54 & 0 & 51 & Yes & No & 3& []& [($B_{2}(3)$, 4), ($\textrm{Alt}_{9}$, 3), ($\textrm{Alt}_{10}$, 5), (${}^2A_{3}(9)$, 1), ($A_{3}(3)$, 2), (${}^2A_{4}(4)$, 3), ($\textrm{Alt}_{11}$, 4)] & [ 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
41	24 & 48 & 54 & 2 & 51 & ? & No & 3& []& [($B_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 3), ($C_{3}(2)$, 3), ($\textrm{Alt}_{10}$, 5), (${}^2A_{3}(9)$, 5), ($A_{3}(3)$, 10), (${}^2A_{4}(4)$, 12), ($\textrm{Alt}_{11}$, 2)] & [ 3, 4, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
42	24 & 54 & 54 & 0 & 63 & ? & No & 3& []& [($\textrm{Alt}_{9}$, 6), ($\textrm{Alt}_{10}$, 2), ($A_{3}(3)$, 4), (${}^2A_{4}(4)$, 8), ($\textrm{Alt}_{11}$, 2)] & [ 3, 4, 9, 10, 11, 12, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
43	24 & 54 & 54 & 2 & 63 & ? & No & 3& []& [($B_{2}(3)$, 2), ($\textrm{Alt}_{9}$, 9), ($C_{3}(2)$, 6), ($\textrm{Alt}_{10}$, 22), (${}^2A_{3}(9)$, 8), ($A_{3}(3)$, 26), (${}^2A_{4}(4)$, 12), ($\textrm{Alt}_{11}$, 12)] & [ 3, 4, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
44	24 & 54 & 54 & 8 & 63 & Yes & No & 3& []& [($B_{2}(3)$, 4), ($\textrm{Alt}_{9}$, 14), ($\textrm{Alt}_{10}$, 1), (${}^2A_{4}(4)$, 9), ($\textrm{Alt}_{11}$, 1)] & [ 3, 4, 9, 10, 11, 12, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] & 30
45	26 & 40 & 40 & 0 & 55 & Yes & No & 0& [L_2(13^2)]& [($A_{3}(3)$, 3)] & [ 5, 20, 21, 27, 28 ] & 30
46	26 & 40 & 48 & 0 & 47 & ? & ? & 0& [L_2(13^2)]& [(${}^2F_4(2)'$, 1)] & [ ] & 30
47	26 & 40 & 54 & 0 & 59 & Yes & ? & 0& []& [($A_{3}(3)$, 3)] & [ 30 ] & 30
48	26 & 40 & 54 & 2 & 59 & ? & ? & 0& []& [] & [ 15 ] & 30
49	26 & 48 & 48 & 0 & 39 & Yes & No & 2& []& [($G_{2}(3)$, 1)] & [ 3, 4, 14, 28 ] & 30
50	26 & 48 & 48 & 1 & 39 & Yes & No & 2& [L_2(13)]& [($G_{2}(3)$, 4), ($A_{3}(3)$, 1)] & [ 3, 13, 14, 15, 16, 26, 27, 28, 29, 30 ] & 30
51	26 & 48 & 54 & 0 & 51 & ? & ? & 2& []& [($G_{2}(3)$, 1)] & [ 3, 13, 26, 27, 28 ] & 30
52	26 & 48 & 54 & 2 & 51 & ? & No & 2& []& [($G_{2}(3)$, 1), ($A_{3}(3)$, 1)] & [ 3, 13, 26, 27, 28, 29 ] & 30
53	26 & 54 & 54 & 0 & 63 & ? & No & 2& []& [($A_{2}(3)$, 2), ($A_{2}(9)$, 3)] & [ 3, 13, 26, 27, 30 ] & 30
54	26 & 54 & 54 & 2 & 63 & Yes & No & 2& []& [($A_{2}(3)$, 2), ($A_{3}(3)$, 20), ($A_{2}(9)$, 3)] & [ 3, 13, 16, 19, 22, 25, 26, 27, 28, 29, 30 ] & 30
55	26 & 54 & 54 & 8 & 63 & Yes & ? & 2& []& [($A_{2}(3)$, 2), ($A_{3}(3)$, 6), ($A_{2}(9)$, 3)] & [ 3, 13 ] & 30