| Label |
Name |
Family name |
Order |
Exponent |
Nilp. class |
Der. length |
Comp. length |
Rank |
$\card{\mathrm{conj}(G)}$ |
Subgroups |
Subgroup classes |
Normal subgroups |
Center |
Central quotient |
Commutator |
Abelianization |
$\card{\mathrm{Aut}(G)}$ |
$\card{\mathrm{Out}(G)}$ |
Tr. deg |
Perm. deg |
$\C$-irrep deg |
$\R$-irrep deg |
$\Q$-irrep deg |
$\C$-rep deg |
$\R$-rep deg |
$\Q$-rep deg |
Type - length |
| 6.1 |
$S_3$ |
$A(1,2), B(1,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
3 |
$6$ |
$4$ |
$3$ |
$C_1$ |
$S_3$ |
$C_3$ |
$C_{2}$ |
$2 \cdot 3$ |
$1$ |
$3$ |
$3$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
Solvable - 2 |
| 12.3 |
$A_4$ |
$B(1,3)$ |
$2^{2} \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$3$ |
$2$ |
4 |
$10$ |
$5$ |
$3$ |
$C_1$ |
$A_4$ |
$C_2^2$ |
$C_{3}$ |
$2^{3} \cdot 3$ |
$2$ |
$4$ |
$4$ |
$3$ |
$3$ |
$3$ |
$3$ |
$3$ |
$3$ |
Solvable - 2 |
| 24.3 |
$\SL(2,3)$ |
$A(1,3)$ |
$2^{3} \cdot 3$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$4$ |
$2$ |
7 |
$15$ |
$7$ |
$4$ |
$C_2$ |
$A_4$ |
$Q_8$ |
$C_{3}$ |
$2^{3} \cdot 3$ |
$2$ |
$8$ |
$8$ |
$2$ |
$4$ |
$4$ |
$2$ |
$4$ |
$4$ |
Solvable - 3 |
| 36.10 |
$S_3^2$ |
$D(2,2)$ |
$2^{2} \cdot 3^{2}$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$4$ |
$2$ |
9 |
$60$ |
$22$ |
$10$ |
$C_1$ |
$S_3^2$ |
$C_3^2$ |
$C_{2}^{2}$ |
$2^{3} \cdot 3^{2}$ |
$2$ |
$6$ |
$6$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Solvable - 2 |
| 60.5 |
$A_5$ |
$A(1,4), B(1,4), B(1,5)$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
5 |
$59$ |
$9$ |
$2$ |
$C_1$ |
$A_5$ |
$A_5$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$5$ |
$5$ |
$3$ |
$3$ |
$4$ |
$3$ |
$3$ |
$4$ |
Simple |
| 120.5 |
$\SL(2,5)$ |
$A(1,5)$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
9 |
$76$ |
$12$ |
$3$ |
$C_2$ |
$A_5$ |
$\SL(2,5)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$24$ |
$24$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Non-Solvable - 2 |
| 168.42 |
$\PSL(2,7)$ |
$B(1,7), A(2,2)$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
6 |
$179$ |
$15$ |
$2$ |
$C_1$ |
$\PSL(2,7)$ |
$\PSL(2,7)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 7$ |
$2$ |
$7$ |
$7$ |
$3$ |
$6$ |
$6$ |
$3$ |
$6$ |
$6$ |
Simple |
| 288.860 |
$\OmegaPlus(4,3)$ |
$D(2,3)$ |
$2^{5} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$7$ |
$2$ |
25 |
$339$ |
$52$ |
$12$ |
$C_2$ |
$A_4^2$ |
$D_4:C_2^2$ |
$C_{3}^{2}$ |
$2^{7} \cdot 3^{2}$ |
$2^{3}$ |
$24$ |
$24$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Solvable - 3 |
| 336.114 |
$\SL(2,7)$ |
$A(1,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
11 |
$224$ |
$19$ |
$3$ |
$C_2$ |
$\PSL(2,7)$ |
$\SL(2,7)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 7$ |
$2$ |
$16$ |
$16$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 360.118 |
$A_6$ |
$B(1,9)$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
7 |
$501$ |
$22$ |
$2$ |
$C_1$ |
$A_6$ |
$A_6$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$6$ |
$6$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Simple |
| 504.156 |
$\SL(2,8)$ |
$A(1,8), B(1,8)$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
9 |
$386$ |
$12$ |
$2$ |
$C_1$ |
$\SL(2,8)$ |
$\SL(2,8)$ |
$C_1$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$3$ |
$9$ |
$9$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Simple |
| 660.13 |
$\PSL(2,11)$ |
$B(1,11)$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$2 \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$1$ |
$2$ |
8 |
$620$ |
$16$ |
$2$ |
$C_1$ |
$\PSL(2,11)$ |
$\PSL(2,11)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2$ |
$11$ |
$11$ |
$5$ |
$10$ |
$10$ |
$5$ |
$10$ |
$10$ |
Simple |
| 720.409 |
$\SL(2,9)$ |
$A(1,9)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
13 |
$588$ |
$27$ |
$3$ |
$C_2$ |
$A_6$ |
$\SL(2,9)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$80$ |
$80$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 720.763 |
$S_6$ |
$B(2,2), C(2,2)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
11 |
$1455$ |
$56$ |
$3$ |
$C_1$ |
$S_6$ |
$A_6$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2$ |
$6$ |
$6$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Non-Solvable - 2 |
| 1092.25 |
$\PSL(2,13)$ |
$B(1,13)$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$2 \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
9 |
$942$ |
$16$ |
$2$ |
$C_1$ |
$\PSL(2,13)$ |
$\PSL(2,13)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2$ |
$14$ |
$14$ |
$7$ |
$7$ |
$13$ |
$7$ |
$7$ |
$13$ |
Simple |
| 1320.13 |
$\SL(2,11)$ |
$A(1,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$2$ |
$2$ |
15 |
$766$ |
$21$ |
$3$ |
$C_2$ |
$\PSL(2,11)$ |
$\SL(2,11)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2$ |
$24$ |
$24$ |
$6$ |
$12$ |
$12$ |
$6$ |
$12$ |
$12$ |
Non-Solvable - 2 |
| 2184.a |
$\SL(2,13)$ |
$A(1,13)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
$2$ |
17 |
|
|
|
$C_2$ |
$\PSL(2,13)$ |
$\SL(2,13)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2$ |
|
$56$ |
$6$ |
$12$ |
$24$ |
? |
? |
? |
Non-Solvable - 2 |
| 2448.a |
$\PSL(2,17)$ |
$B(1,17)$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$2^{3} \cdot 3^{2} \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
11 |
$2420$ |
$22$ |
$2$ |
$C_1$ |
$\PSL(2,17)$ |
$\PSL(2,17)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2$ |
$18$ |
$18$ |
$9$ |
$9$ |
$16$ |
$9$ |
$9$ |
$16$ |
Simple |
| 3420.a |
$\PSL(2,19)$ |
$B(1,19)$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2 \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$0$ |
$1$ |
$2$ |
12 |
$2912$ |
$19$ |
$2$ |
$C_1$ |
$\PSL(2,19)$ |
$\PSL(2,19)$ |
$C_1$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2$ |
$20$ |
$20$ |
$9$ |
$18$ |
$18$ |
$9$ |
$18$ |
$18$ |
Simple |
| 3600.a |
$A_5^2$ |
$D(2,4)$ |
$2^{4} \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
25 |
$8381$ |
$113$ |
$4$ |
$C_1$ |
$A_5^2$ |
$A_5^2$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5^{2}$ |
$2^{3}$ |
$25$ |
$10$ |
$9$ |
$9$ |
$16$ |
$6$ |
$6$ |
$8$ |
Non-Solvable - 2 |
| 4080.a |
$\SL(2,16)$ |
$A(1,16), B(1,16)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
17 |
$3455$ |
$21$ |
$2$ |
$C_1$ |
$\SL(2,16)$ |
$\SL(2,16)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5 \cdot 17$ |
$2^{2}$ |
$17$ |
$17$ |
$15$ |
$15$ |
$16$ |
$15$ |
$15$ |
$16$ |
Simple |
| 4896.a |
$\SL(2,17)$ |
$A(1,17)$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$-1$ |
$0$ |
$2$ |
$2$ |
21 |
|
|
|
$C_2$ |
$\PSL(2,17)$ |
$\SL(2,17)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2$ |
|
$288$ |
$8$ |
$16$ |
$32$ |
? |
? |
? |
Non-Solvable - 2 |
| 5616.a |
$\SL(3,3)$ |
$A(2,3)$ |
$2^{4} \cdot 3^{3} \cdot 13$ |
$2^{3} \cdot 3 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
12 |
$6374$ |
$51$ |
$2$ |
$C_1$ |
$\SL(3,3)$ |
$\SL(3,3)$ |
$C_1$ |
$2^{5} \cdot 3^{3} \cdot 13$ |
$2$ |
$13$ |
$13$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Simple |
| 6072.a |
$\PSL(2,23)$ |
$B(1,23)$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$2^{2} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$0$ |
$1$ |
$2$ |
14 |
$5915$ |
$23$ |
$2$ |
$C_1$ |
$\PSL(2,23)$ |
$\PSL(2,23)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2$ |
$24$ |
$24$ |
$11$ |
$22$ |
$22$ |
$11$ |
$22$ |
$22$ |
Simple |
| 6840.a |
$\SL(2,19)$ |
$A(1,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$0$ |
$2$ |
$2$ |
23 |
|
|
|
$C_2$ |
$\PSL(2,19)$ |
$\SL(2,19)$ |
$C_1$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2$ |
|
$40$ |
$10$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 7200.c |
$\OmegaPlus(4,5)$ |
$D(2,5)$ |
$2^{5} \cdot 3^{2} \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$3$ |
$2$ |
41 |
$14896$ |
$150$ |
$5$ |
$C_2$ |
$A_5^2$ |
$\OmegaPlus(4,5)$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5^{2}$ |
$2^{3}$ |
$120$ |
$120$ |
$4$ |
$4$ |
$8$ |
$4$ |
$4$ |
$8$ |
Non-Solvable - 3 |
| 7800.a |
$\PSL(2,25)$ |
$B(1,25)$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
15 |
$9559$ |
$37$ |
$2$ |
$C_1$ |
$\PSL(2,25)$ |
$\PSL(2,25)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2}$ |
$26$ |
$26$ |
$13$ |
$13$ |
$13$ |
$13$ |
$13$ |
$13$ |
Simple |
| 9828.a |
$\PSL(2,27)$ |
$B(1,27)$ |
$2^{2} \cdot 3^{3} \cdot 7 \cdot 13$ |
$2 \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
16 |
$5286$ |
$16$ |
$2$ |
$C_1$ |
$\PSL(2,27)$ |
$\PSL(2,27)$ |
$C_1$ |
$2^{3} \cdot 3^{4} \cdot 7 \cdot 13$ |
$2 \cdot 3$ |
$28$ |
$28$ |
$13$ |
$26$ |
$26$ |
$13$ |
$26$ |
$26$ |
Simple |
| 12096.a |
$G(2,2)$ |
$G(2,2)$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
16 |
|
|
|
$C_1$ |
$G(2,2)$ |
$\SU(3,3)$ |
$C_{2}$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$1$ |
|
$28$ |
$6$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 12144.a |
$\SL(2,23)$ |
$A(1,23)$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$0$ |
$2$ |
$2$ |
27 |
|
|
|
$C_2$ |
$\PSL(2,23)$ |
$\SL(2,23)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2$ |
|
$48$ |
$12$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 12180.a |
$\PSL(2,29)$ |
$B(1,29)$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2 \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$0$ |
$1$ |
$2$ |
17 |
$10040$ |
$22$ |
$2$ |
$C_1$ |
$\PSL(2,29)$ |
$\PSL(2,29)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2$ |
$30$ |
$30$ |
$15$ |
$15$ |
$28$ |
$15$ |
$15$ |
$28$ |
Simple |
| 14880.a |
$\PSL(2,31)$ |
$B(1,31)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 31$ |
$2^{4} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
18 |
$15413$ |
$29$ |
$2$ |
$C_1$ |
$\PSL(2,31)$ |
$\PSL(2,31)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2$ |
$32$ |
$32$ |
$15$ |
$30$ |
$30$ |
$15$ |
$30$ |
$30$ |
Simple |
| 15600.a |
$\SL(2,25)$ |
$A(1,25)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
$2$ |
29 |
|
|
|
$C_2$ |
$\PSL(2,25)$ |
$\SL(2,25)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2}$ |
|
$208$ |
$12$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 19656.a |
$\SL(2,27)$ |
$A(1,27)$ |
$2^{3} \cdot 3^{3} \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
$2$ |
31 |
|
|
|
$C_2$ |
$\PSL(2,27)$ |
$\SL(2,27)$ |
$C_1$ |
$2^{3} \cdot 3^{4} \cdot 7 \cdot 13$ |
$2 \cdot 3$ |
|
$56$ |
$14$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 20160.a |
$A_8$ |
$D(3,2)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
14 |
$48337$ |
$137$ |
$2$ |
$C_1$ |
$A_8$ |
$A_8$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2$ |
$8$ |
$8$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Simple |
| 24360.a |
$\SL(2,29)$ |
$A(1,29)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$0$ |
$2$ |
$2$ |
33 |
|
|
|
$C_2$ |
$\PSL(2,29)$ |
$\SL(2,29)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2$ |
|
$120$ |
$14$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 25920.a |
$\SU(4,2)$ |
$B(2,3)$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
20 |
$45649$ |
$116$ |
$2$ |
$C_1$ |
$\SU(4,2)$ |
$\SU(4,2)$ |
$C_1$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$2$ |
$27$ |
$27$ |
$5$ |
$6$ |
$6$ |
$5$ |
$6$ |
$6$ |
Simple |
| 29760.a |
$\SL(2,31)$ |
$A(1,31)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2^{5} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$0$ |
$2$ |
$2$ |
35 |
|
|
|
$C_2$ |
$\PSL(2,31)$ |
$\SL(2,31)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2$ |
|
$64$ |
$16$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 32736.a |
$\SL(2,32)$ |
$A(1,32), B(1,32)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 11 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
33 |
$22328$ |
$24$ |
$2$ |
$C_1$ |
$\SL(2,32)$ |
$\SL(2,32)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5 \cdot 11 \cdot 31$ |
$5$ |
$33$ |
$33$ |
$31$ |
$31$ |
$31$ |
$31$ |
$31$ |
$31$ |
Simple |
| 50616.a |
$\SL(2,37)$ |
$A(1,37)$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$2^{2} \cdot 3^{2} \cdot 19 \cdot 37$ |
$-1$ |
$0$ |
$2$ |
$2$ |
41 |
|
|
|
$C_2$ |
$\PSL(2,37)$ |
$\SL(2,37)$ |
$C_1$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$2$ |
|
$152$ |
$18$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 51840.a |
$\Sp(4,3)$ |
$C(2,3)$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
34 |
$63906$ |
$162$ |
$3$ |
$C_2$ |
$\SU(4,2)$ |
$\Sp(4,3)$ |
$C_1$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$2$ |
$80$ |
$80$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 56448.a |
$\OmegaPlus(4,7)$ |
$D(2,7)$ |
$2^{7} \cdot 3^{2} \cdot 7^{2}$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$3$ |
$2$ |
61 |
$164849$ |
$438$ |
$5$ |
$C_2$ |
$\GL(3,2)^2$ |
$\OmegaPlus(4,7)$ |
$C_1$ |
$2^{9} \cdot 3^{2} \cdot 7^{2}$ |
$2^{3}$ |
$128$ |
$128$ |
$16$ |
$32$ |
$32$ |
? |
? |
? |
Non-Solvable - 3 |
| 60480.a |
$\SL(3,4)$ |
$A(2,4)$ |
$2^{6} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
28 |
$109075$ |
$200$ |
$3$ |
$C_3$ |
$\PSL(3,4)$ |
$\SL(3,4)$ |
$C_1$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3$ |
$63$ |
$63$ |
$15$ |
$30$ |
$30$ |
? |
? |
? |
Non-Solvable - 2 |
| 68880.a |
$\SL(2,41)$ |
$A(1,41)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$-1$ |
$0$ |
$2$ |
$2$ |
45 |
|
|
|
$C_2$ |
|
$\SL(2,41)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$2$ |
|
$336$ |
$20$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 79464.a |
$\SL(2,43)$ |
$A(1,43)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$-1$ |
$0$ |
$2$ |
$2$ |
47 |
|
|
|
$C_2$ |
$\PSL(2,43)$ |
$\SL(2,43)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$2$ |
|
$88$ |
$22$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 103776.a |
$\SL(2,47)$ |
$A(1,47)$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$2^{4} \cdot 3 \cdot 23 \cdot 47$ |
$-1$ |
$0$ |
$2$ |
$2$ |
51 |
|
|
|
$C_2$ |
$\PSL(2,47)$ |
$\SL(2,47)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$2$ |
|
$96$ |
$24$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 117600.a |
$\SL(2,49)$ |
$A(1,49)$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
53 |
|
|
|
$C_2$ |
$\PSL(2,49)$ |
$\SL(2,49)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{2}$ |
|
$800$ |
$24$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 148824.a |
$\SL(2,53)$ |
$A(1,53)$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$2^{2} \cdot 3^{3} \cdot 13 \cdot 53$ |
$-1$ |
$0$ |
$2$ |
$2$ |
57 |
|
|
|
$C_2$ |
$\PSL(2,53)$ |
$\SL(2,53)$ |
$C_1$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$2$ |
|
$216$ |
$26$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 205320.a |
$\SL(2,59)$ |
$A(1,59)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$2^{2} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$-1$ |
$0$ |
$2$ |
$2$ |
63 |
|
|
|
$C_2$ |
$\PSL(2,59)$ |
$\SL(2,59)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$2$ |
|
$120$ |
$30$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 226920.a |
$\SL(2,61)$ |
$A(1,61)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$-1$ |
$0$ |
$2$ |
$2$ |
65 |
|
|
|
$C_2$ |
$\PSL(2,61)$ |
$\SL(2,61)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$2$ |
|
$248$ |
$30$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
