| 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 |
$S_3$ |
${}^2A(1,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
| 24.3 |
$\SL(2,3)$ |
${}^2A(1,3)$ |
$2^{3} \cdot 3$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$4$ |
$2$ |
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 |
| 60.5 |
$A_5$ |
${}^2A(1,4), {}^2D(2,2)$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
$\SL(2,5)$ |
${}^2A(1,5)$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 216.88 |
$\SU(3,2)$ |
${}^2A(2,2)$ |
$2^{3} \cdot 3^{3}$ |
$2^{2} \cdot 3$ |
$-1$ |
$4$ |
$6$ |
$2$ |
16 |
$138$ |
$22$ |
$8$ |
$C_3$ |
$\PSU(3,2)$ |
$C_3^2:S_3$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{3}$ |
$2 \cdot 3$ |
$27$ |
$27$ |
$3$ |
$6$ |
$6$ |
$3$ |
$6$ |
$6$ |
Solvable - 4 |
| 336.114 |
$\SL(2,7)$ |
${}^2A(1,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
$A_6$ |
${}^2D(2,3)$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
$\SL(2,8)$ |
${}^2A(1,8)$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 720.409 |
$\SL(2,9)$ |
${}^2A(1,9)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 1320.13 |
$\SL(2,11)$ |
${}^2A(1,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 1512.779 |
${}^2G(2,3)$ |
${}^2G(2,3)$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
11 |
$1154$ |
$25$ |
$3$ |
$C_1$ |
${}^2G(2,3)$ |
$\SL(2,8)$ |
$C_{3}$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$1$ |
$9$ |
$9$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 2 |
| 2184.a |
$\SL(2,13)$ |
${}^2A(1,13)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 4080.a |
$\SL(2,16)$ |
${}^2A(1,16), {}^2D(2,4)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
$\SL(2,17)$ |
${}^2A(1,17)$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 6048.a |
$\SU(3,3)$ |
${}^2A(2,3)$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
14 |
$5150$ |
$36$ |
$2$ |
$C_1$ |
$\SU(3,3)$ |
$\SU(3,3)$ |
$C_1$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2$ |
$28$ |
$28$ |
$6$ |
$7$ |
$7$ |
$6$ |
$7$ |
$7$ |
Simple |
| 6840.a |
$\SL(2,19)$ |
${}^2A(1,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 7800.a |
$\PSL(2,25)$ |
${}^2D(2,5)$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 12144.a |
$\SL(2,23)$ |
${}^2A(1,23)$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 15600.a |
$\SL(2,25)$ |
${}^2A(1,25)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
$\SL(2,27)$ |
${}^2A(1,27)$ |
$2^{3} \cdot 3^{3} \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 24360.a |
$\SL(2,29)$ |
${}^2A(1,29)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
$\SU(4,2)$ |
${}^2A(3,2), {}^2D(3,2)$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 29120.a |
${}^2B(2,8)$ |
${}^2B(2,8)$ |
$2^{6} \cdot 5 \cdot 7 \cdot 13$ |
$2^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
11 |
$17295$ |
$22$ |
$2$ |
$C_1$ |
${}^2B(2,8)$ |
${}^2B(2,8)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 13$ |
$3$ |
$65$ |
$65$ |
$14$ |
$28$ |
$28$ |
$14$ |
$28$ |
$28$ |
Simple |
| 29760.a |
$\SL(2,31)$ |
${}^2A(1,31)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2^{5} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
$\SL(2,32)$ |
${}^2A(1,32)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 11 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 58800.a |
$\PSL(2,49)$ |
${}^2D(2,7)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
27 |
$73945$ |
$51$ |
$2$ |
$C_1$ |
$\PSL(2,49)$ |
$\PSL(2,49)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{2}$ |
$50$ |
$50$ |
$25$ |
$25$ |
$25$ |
$25$ |
$25$ |
$25$ |
Simple |
| 62400.a |
$\SU(3,4)$ |
${}^2A(2,4)$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
22 |
$31373$ |
$34$ |
$2$ |
$C_1$ |
$\SU(3,4)$ |
$\SU(3,4)$ |
$C_1$ |
$2^{8} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2}$ |
$65$ |
$65$ |
$12$ |
$24$ |
$24$ |
$12$ |
$24$ |
$24$ |
Simple |
| 262080.a |
$\SL(2,64)$ |
${}^2D(2,8)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
65 |
$360787$ |
$76$ |
$2$ |
$C_1$ |
$\SL(2,64)$ |
$\SL(2,64)$ |
$C_1$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13$ |
$2 \cdot 3$ |
$65$ |
$65$ |
$63$ |
$63$ |
$64$ |
$63$ |
$63$ |
$64$ |
Simple |
| 265680.a |
$\PSL(2,81)$ |
${}^2D(2,9)$ |
$2^{4} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 41$ |
$-1$ |
$0$ |
$1$ |
$2$ |
43 |
$433087$ |
$69$ |
$2$ |
$C_1$ |
$\PSL(2,81)$ |
$\PSL(2,81)$ |
$C_1$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{3}$ |
$82$ |
$82$ |
$41$ |
$41$ |
$41$ |
$41$ |
$41$ |
$41$ |
Simple |
| 378000.a |
$\SU(3,5)$ |
${}^2A(2,5)$ |
$2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
40 |
$388665$ |
$146$ |
$3$ |
$C_3$ |
$\PSU(3,5)$ |
$\SU(3,5)$ |
$C_1$ |
$2^{5} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2 \cdot 3$ |
$378$ |
$378$ |
$21$ |
$42$ |
$42$ |
$21$ |
$42$ |
$42$ |
Non-Solvable - 2 |
| 885720.a |
$\PSL(2,121)$ |
${}^2D(2,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11 \cdot 61$ |
$-1$ |
$0$ |
$1$ |
$2$ |
63 |
$976309$ |
$63$ |
$2$ |
$C_1$ |
$\PSL(2,121)$ |
$\PSL(2,121)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2^{2}$ |
$122$ |
$122$ |
$61$ |
$61$ |
$61$ |
$61$ |
$61$ |
$61$ |
Simple |
| 2413320.a |
$\PSL(2,169)$ |
${}^2D(2,13)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
87 |
$2782197$ |
$71$ |
$2$ |
$C_1$ |
$\PSL(2,169)$ |
$\PSL(2,169)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5 \cdot 7 \cdot 13^{2} \cdot 17$ |
$2^{2}$ |
$170$ |
$170$ |
$85$ |
$85$ |
$85$ |
$85$ |
$85$ |
$85$ |
Simple |
| 5663616.a |
$\SU(3,7)$ |
${}^2A(2,7)$ |
$2^{7} \cdot 3 \cdot 7^{3} \cdot 43$ |
$2^{4} \cdot 3 \cdot 7 \cdot 43$ |
$-1$ |
$0$ |
$1$ |
$2$ |
58 |
$3639825$ |
$95$ |
$2$ |
$C_1$ |
$\SU(3,7)$ |
$\SU(3,7)$ |
$C_1$ |
$2^{8} \cdot 3 \cdot 7^{3} \cdot 43$ |
$2$ |
$344$ |
$344$ |
$42$ |
$43$ |
$43$ |
$42$ |
$43$ |
$43$ |
Simple |
| 6531840.a |
$\OmegaMinus(6,3)$ |
${}^2D(3,3)$ |
$2^{8} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
39 |
|
|
|
$C_2$ |
$\PSU(4,3)$ |
$\OmegaMinus(6,3)$ |
$C_1$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3}$ |
|
$224$ |
$20$ |
$40$ |
$40$ |
? |
? |
? |
Non-Solvable - 2 |
| 13063680.b |
$\SU(4,3)$ |
${}^2A(3,3)$ |
$2^{9} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$3$ |
$2$ |
71 |
|
|
|
$C_4$ |
$\PSU(4,3)$ |
$\SU(4,3)$ |
$C_1$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3}$ |
|
$2160$ |
$20$ |
$40$ |
$40$ |
? |
? |
? |
Non-Solvable - 3 |
| 13685760.a |
$\SU(5,2)$ |
${}^2A(4,2)$ |
$2^{10} \cdot 3^{5} \cdot 5 \cdot 11$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$1$ |
$2$ |
47 |
$25308805$ |
$556$ |
$2$ |
$C_1$ |
$\SU(5,2)$ |
$\SU(5,2)$ |
$C_1$ |
$2^{11} \cdot 3^{5} \cdot 5 \cdot 11$ |
$2$ |
$165$ |
$165$ |
$10$ |
$20$ |
$20$ |
? |
? |
? |
Simple |
| 16547328.a |
$\SU(3,8)$ |
${}^2A(2,8)$ |
$2^{9} \cdot 3^{5} \cdot 7 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 7 \cdot 19$ |
$-1$ |
$0$ |
$2$ |
$2$ |
82 |
|
|
|
$C_3$ |
$\PSU(3,8)$ |
$\SU(3,8)$ |
$C_1$ |
$2^{10} \cdot 3^{6} \cdot 7 \cdot 19$ |
$2 \cdot 3^{2}$ |
|
$4617$ |
$57$ |
$114$ |
$342$ |
? |
? |
? |
Non-Solvable - 2 |
| 16776960.a |
$\SL(2,256)$ |
${}^2D(2,16)$ |
$2^{8} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$2 \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$-1$ |
$0$ |
$1$ |
$2$ |
257 |
|
|
$2$ |
$C_1$ |
$\SL(2,256)$ |
$\SL(2,256)$ |
$C_1$ |
$2^{11} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$2^{3}$ |
$257$ |
$257$ |
$255$ |
$255$ |
$256$ |
? |
? |
? |
Simple |
| 17971200.a |
${}^2F(4,2)$ |
${}^2F(4,2)$ |
$2^{11} \cdot 3^{3} \cdot 5^{2} \cdot 13$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
22 |
|
|
|
$C_1$ |
${}^2F(4,2)$ |
${}^2F(4,2)$ |
$C_1$ |
$2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13$ |
$2$ |
|
$1600$ |
$26$ |
$52$ |
$52$ |
? |
? |
? |
Simple |
| 32537600.a |
${}^2B(2,32)$ |
${}^2B(2,32)$ |
$2^{10} \cdot 5^{2} \cdot 31 \cdot 41$ |
$2^{2} \cdot 5^{2} \cdot 31 \cdot 41$ |
$-1$ |
$0$ |
$1$ |
$2$ |
35 |
|
|
|
$C_1$ |
${}^2B(2,32)$ |
${}^2B(2,32)$ |
$C_1$ |
$2^{10} \cdot 5^{3} \cdot 31 \cdot 41$ |
$5$ |
|
$1025$ |
$124$ |
$248$ |
$248$ |
? |
? |
? |
Simple |
| 35942400.a |
${}^2F(4,2)$ |
${}^2F(4,2)$ |
$2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
29 |
|
|
|
$C_1$ |
${}^2F(4,2)$ |
${}^2F(4,2)$ |
$C_{2}$ |
$2^{12} \cdot 3^{3} \cdot 5^{2} \cdot 13$ |
$1$ |
|
$1755$ |
$27$ |
$54$ |
$54$ |
? |
? |
? |
Non-Solvable - 2 |
| 42573600.a |
$\SU(3,9)$ |
${}^2A(2,9)$ |
$2^{5} \cdot 3^{6} \cdot 5^{2} \cdot 73$ |
$2^{4} \cdot 3 \cdot 5 \cdot 73$ |
$-1$ |
$0$ |
$1$ |
$2$ |
92 |
$29208545$ |
$127$ |
$2$ |
$C_1$ |
$\SU(3,9)$ |
$\SU(3,9)$ |
$C_1$ |
$2^{7} \cdot 3^{6} \cdot 5^{2} \cdot 73$ |
$2^{2}$ |
$730$ |
$730$ |
$72$ |
$73$ |
$73$ |
? |
? |
? |
Simple |
| 197406720.a |
$\OmegaMinus(8,2)$ |
${}^2D(4,2)$ |
$2^{12} \cdot 3^{4} \cdot 5 \cdot 7 \cdot 17$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
39 |
|
|
|
$C_1$ |
$\OmegaMinus(8,2)$ |
$\OmegaMinus(8,2)$ |
$C_1$ |
$2^{13} \cdot 3^{4} \cdot 5 \cdot 7 \cdot 17$ |
$2$ |
|
$119$ |
$34$ |
$34$ |
$34$ |
? |
? |
? |
Simple |
| 211341312.a |
${}^3D(4,2)$ |
${}^3D(4,2)$ |
$2^{12} \cdot 3^{4} \cdot 7^{2} \cdot 13$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
35 |
|
|
|
$C_1$ |
${}^3D(4,2)$ |
${}^3D(4,2)$ |
$C_1$ |
$2^{12} \cdot 3^{5} \cdot 7^{2} \cdot 13$ |
$3$ |
|
$819$ |
$26$ |
$26$ |
$26$ |
? |
? |
? |
Simple |
| 212747040.a |
$\SU(3,11)$ |
${}^2A(2,11)$ |
$2^{5} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 37$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 37$ |
$-1$ |
$0$ |
$2$ |
$2$ |
142 |
|
|
|
$C_3$ |
$\PSU(3,11)$ |
$\SU(3,11)$ |
$C_1$ |
$2^{6} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 37$ |
$2 \cdot 3$ |
|
$3996$ |
$111$ |
$222$ |
$222$ |
? |
? |
? |
Non-Solvable - 2 |
| 811273008.a |
$\SU(3,13)$ |
${}^2A(2,13)$ |
$2^{4} \cdot 3 \cdot 7^{2} \cdot 13^{3} \cdot 157$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13 \cdot 157$ |
$-1$ |
$0$ |
$1$ |
$2$ |
184 |
$335083691$ |
$121$ |
$2$ |
$C_1$ |
$\SU(3,13)$ |
$\SU(3,13)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 7^{2} \cdot 13^{3} \cdot 157$ |
$2$ |
$2198$ |
$2198$ |
$156$ |
$157$ |
$157$ |
? |
? |
? |
Simple |
| 1018368000.a |
$\SU(4,4)$ |
${}^2A(3,4), {}^2D(3,4)$ |
$2^{12} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
94 |
|
|
$2$ |
$C_1$ |
$\SU(4,4)$ |
$\SU(4,4)$ |
$C_1$ |
$2^{14} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$2^{2}$ |
$325$ |
$325$ |
$51$ |
$52$ |
$52$ |
? |
? |
? |
Simple |
| 4279234560.a |
$\SU(3,16)$ |
${}^2A(2,16)$ |
$2^{12} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 241$ |
$-1$ |
$0$ |
$1$ |
$2$ |
274 |
|
|
$2$ |
$C_1$ |
$\SU(3,16)$ |
$\SU(3,16)$ |
$C_1$ |
$2^{15} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$ |
$2^{3}$ |
$4097$ |
$4097$ |
$240$ |
? |
? |
? |
? |
? |
Simple |
| 6953034816.a |
$\SU(3,17)$ |
${}^2A(2,17)$ |
$2^{6} \cdot 3^{5} \cdot 7 \cdot 13 \cdot 17^{3}$ |
$2^{5} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$2$ |
$2$ |
316 |
|
|
|
$C_3$ |
|
|
$C_1$ |
$2^{7} \cdot 3^{5} \cdot 7 \cdot 13 \cdot 17^{3}$ |
$2 \cdot 3$ |
|
|
$273$ |
$546$ |
$1638$ |
? |
? |
? |
Non-Solvable - 2 |
| 10073444472.a |
${}^2G(2,27)$ |
${}^2G(2,27)$ |
$2^{3} \cdot 3^{9} \cdot 7 \cdot 13 \cdot 19 \cdot 37$ |
$2 \cdot 3^{2} \cdot 7 \cdot 13 \cdot 19 \cdot 37$ |
$-1$ |
$0$ |
$1$ |
$2$ |
not computed |
|
|
|
$C_1$ |
|
|
$C_1$ |
|
|
|
|
? |
? |
? |
? |
? |
? |
Simple |
