| 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 |
$S_3$ |
$\GSU(2,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
| 48.28 |
$C_2.S_4$ |
$\GSU(2,3)$ |
$2^{4} \cdot 3$ |
$2^{3} \cdot 3$ |
$-1$ |
$4$ |
$5$ |
$2$ |
8 |
$35$ |
$13$ |
$5$ |
$C_2$ |
$S_4$ |
$\SL(2,3)$ |
$C_{2}$ |
$2^{4} \cdot 3$ |
$2$ |
$16$ |
$16$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Solvable - 4 |
| 60.5 |
$A_5$ |
$\GSU(2,4)$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 216.88 |
$\SU(3,2)$ |
$\GSU(3,2)$ |
$2^{3} \cdot 3^{3}$ |
$2^{2} \cdot 3$ |
$-1$ |
$4$ |
$6$ |
$2$ |
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 |
| 240.89 |
$C_2.S_5$ |
$\GSU(2,5)$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
12 |
$173$ |
$22$ |
$4$ |
$C_2$ |
$S_5$ |
$\SL(2,5)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2$ |
$48$ |
$48$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 3 |
| 504.156 |
$\SL(2,8)$ |
$\GSU(2,8)$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 672.1045 |
$C_2.\PGL(2,7)$ |
$\GSU(2,7)$ |
$2^{5} \cdot 3 \cdot 7$ |
$2^{4} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$3$ |
$2$ |
16 |
$458$ |
$27$ |
$4$ |
$C_2$ |
$\PGL(2,7)$ |
$\SL(2,7)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 7$ |
$2$ |
$32$ |
$32$ |
$6$ |
$12$ |
$16$ |
$6$ |
$12$ |
$16$ |
Non-Solvable - 3 |
| 1440.4594 |
$C_2.\PGL(2,9)$ |
$\GSU(2,9)$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{4} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
20 |
$968$ |
$30$ |
$4$ |
$C_2$ |
$\PGL(2,9)$ |
$\SL(2,9)$ |
$C_{2}$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$160$ |
$160$ |
$8$ |
$16$ |
$16$ |
$8$ |
$16$ |
$16$ |
Non-Solvable - 3 |
| 2640.b |
$C_2.\PGL(2,11)$ |
$\GSU(2,11)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$3$ |
$2$ |
24 |
$1770$ |
$34$ |
$4$ |
$C_2$ |
$\PGL(2,11)$ |
$\SL(2,11)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11$ |
$2$ |
$48$ |
$48$ |
$10$ |
$20$ |
$24$ |
$10$ |
$20$ |
$24$ |
Non-Solvable - 3 |
| 4080.a |
$\SL(2,16)$ |
$\GSU(2,16)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 4368.b |
$C_2.\PGL(2,13)$ |
$\GSU(2,13)$ |
$2^{4} \cdot 3 \cdot 7 \cdot 13$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
28 |
$2664$ |
$35$ |
$4$ |
$C_2$ |
$\PGL(2,13)$ |
$\SL(2,13)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 7 \cdot 13$ |
$2$ |
$112$ |
$112$ |
$12$ |
$24$ |
$24$ |
$12$ |
$24$ |
$24$ |
Non-Solvable - 3 |
| 6048.a |
$\SU(3,3)$ |
$\GSU(3,3)$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 9792.b |
$C_2.\PGL(2,17)$ |
$\GSU(2,17)$ |
$2^{6} \cdot 3^{2} \cdot 17$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$-1$ |
$1$ |
$3$ |
$2$ |
36 |
$5603$ |
$36$ |
$4$ |
$C_2$ |
$\PGL(2,17)$ |
$\SL(2,17)$ |
$C_{2}$ |
$2^{6} \cdot 3^{2} \cdot 17$ |
$2$ |
$576$ |
$576$ |
$16$ |
$32$ |
$32$ |
$16$ |
$32$ |
$32$ |
Non-Solvable - 3 |
| 13680.b |
$C_2.\PGL(2,19)$ |
$\GSU(2,19)$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$1$ |
$3$ |
$2$ |
40 |
$8696$ |
$43$ |
$4$ |
$C_2$ |
$\PGL(2,19)$ |
$\SL(2,19)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2$ |
$80$ |
$80$ |
$18$ |
$36$ |
$40$ |
$18$ |
$36$ |
$40$ |
Non-Solvable - 3 |
| 24288.b |
$C_2.\PGL(2,23)$ |
$\GSU(2,23)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 23$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$1$ |
$3$ |
$2$ |
48 |
$13212$ |
$39$ |
$4$ |
$C_2$ |
$\PGL(2,23)$ |
$\SL(2,23)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 11 \cdot 23$ |
$2$ |
$96$ |
$96$ |
$22$ |
$44$ |
$48$ |
$22$ |
$44$ |
$48$ |
Non-Solvable - 3 |
| 25920.a |
$\SU(4,2)$ |
$\GSU(4,2)$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 31200.b |
$C_2.\PGL(2,25)$ |
$\GSU(2,25)$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
52 |
$18796$ |
$49$ |
$4$ |
$C_2$ |
$\PGL(2,25)$ |
$\SL(2,25)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2}$ |
$416$ |
$416$ |
$24$ |
$48$ |
$48$ |
$24$ |
$48$ |
$48$ |
Non-Solvable - 3 |
| 32736.a |
$\SL(2,32)$ |
$\GSU(2,32)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 11 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 39312.a |
$\GSU(2,27)$ |
$\GSU(2,27)$ |
$2^{4} \cdot 3^{3} \cdot 7 \cdot 13$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
56 |
$20576$ |
$39$ |
$4$ |
$C_2$ |
|
|
$C_{2}$ |
$2^{4} \cdot 3^{4} \cdot 7 \cdot 13$ |
$2 \cdot 3$ |
$112$ |
$112$ |
$26$ |
$52$ |
$56$ |
$26$ |
$52$ |
$56$ |
Non-Solvable - 3 |
| 48720.a |
$C_2.\PGL(2,29)$ |
$\GSU(2,29)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$1$ |
$3$ |
$2$ |
60 |
$30462$ |
$48$ |
$4$ |
$C_2$ |
$\PGL(2,29)$ |
$\SL(2,29)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2$ |
$240$ |
$240$ |
$28$ |
$56$ |
$56$ |
$28$ |
$56$ |
$56$ |
Non-Solvable - 3 |
| 59520.a |
$C_2.\PGL(2,31)$ |
$\GSU(2,31)$ |
$2^{7} \cdot 3 \cdot 5 \cdot 31$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$3$ |
$2$ |
64 |
$35976$ |
$52$ |
$4$ |
$C_2$ |
$\PGL(2,31)$ |
$\SL(2,31)$ |
$C_{2}$ |
$2^{7} \cdot 3 \cdot 5 \cdot 31$ |
$2$ |
$128$ |
$128$ |
$30$ |
$60$ |
$64$ |
$30$ |
$60$ |
$64$ |
Non-Solvable - 3 |
| 187200.a |
$C_3\times \SU(3,4)$ |
$\GSU(3,4)$ |
$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
66 |
$82118$ |
$83$ |
$4$ |
$C_3$ |
$\SU(3,4)$ |
$\SU(3,4)$ |
$C_{3}$ |
$2^{9} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3}$ |
$195$ |
$68$ |
$12$ |
$24$ |
$24$ |
$12$ |
$24$ |
$24$ |
Non-Solvable - 2 |
| 378000.a |
$\SU(3,5)$ |
$\GSU(3,5)$ |
$2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 13685760.a |
$\SU(5,2)$ |
$\GSU(5,2)$ |
$2^{10} \cdot 3^{5} \cdot 5 \cdot 11$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
$\SU(3,8)$ |
$\GSU(3,8)$ |
$2^{9} \cdot 3^{5} \cdot 7 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 7 \cdot 19$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 16990848.a |
$C_3\times \SU(3,7)$ |
$\GSU(3,7)$ |
$2^{7} \cdot 3^{2} \cdot 7^{3} \cdot 43$ |
$2^{4} \cdot 3 \cdot 7 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
174 |
$9542312$ |
$231$ |
$4$ |
$C_3$ |
$\SU(3,7)$ |
$\SU(3,7)$ |
$C_{3}$ |
$2^{9} \cdot 3 \cdot 7^{3} \cdot 43$ |
$2^{2}$ |
$1032$ |
$347$ |
$42$ |
$84$ |
$86$ |
? |
? |
? |
Non-Solvable - 2 |
| 26127360.c |
$\GSU(4,3)$ |
$\GSU(4,3)$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$4$ |
$2$ |
118 |
|
|
$5$ |
$C_4$ |
$\PSOMinus(6,3)$ |
$\SU(4,3)$ |
$C_{2}$ |
$2^{11} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3}$ |
$2240$ |
$2240$ |
$20$ |
$40$ |
$80$ |
? |
? |
? |
Non-Solvable - 4 |
| 42573600.a |
$\SU(3,9)$ |
$\GSU(3,9)$ |
$2^{5} \cdot 3^{6} \cdot 5^{2} \cdot 73$ |
$2^{4} \cdot 3 \cdot 5 \cdot 73$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 212747040.a |
$\SU(3,11)$ |
$\GSU(3,11)$ |
$2^{5} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 37$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 37$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 1018368000.a |
$\SU(4,4)$ |
$\GSU(4,4)$ |
$2^{12} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 2433819024.a |
$C_3\times \SU(3,13)$ |
$\GSU(3,13)$ |
$2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 13^{3} \cdot 157$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13 \cdot 157$ |
$-1$ |
$1$ |
$2$ |
$2$ |
552 |
|
|
|
$C_3$ |
|
|
$C_{3}$ |
$2^{6} \cdot 3 \cdot 7^{2} \cdot 13^{3} \cdot 157$ |
$2^{2}$ |
|
$2201$ |
$156$ |
? |
$314$ |
? |
? |
? |
Non-Solvable - 2 |
| 6953034816.a |
$\SU(3,17)$ |
$\GSU(3,17)$ |
$2^{6} \cdot 3^{5} \cdot 7 \cdot 13 \cdot 17^{3}$ |
$2^{5} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$2$ |
$2$ |
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 |
| 12837703680.a |
$\GSU(3,16)$ |
$\GSU(3,16)$ |
$2^{12} \cdot 3^{2} \cdot 5 \cdot 17^{2} \cdot 241$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 241$ |
$-1$ |
$1$ |
$2$ |
$2$ |
822 |
|
|
|
$C_3$ |
$\SU(3,16)$ |
$\SU(3,16)$ |
$C_{3}$ |
$2^{16} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$ |
$2^{4}$ |
|
$4100$ |
$240$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 27590492160.a |
$\SU(6,2)$ |
$\GSU(6,2)$ |
$2^{15} \cdot 3^{7} \cdot 5 \cdot 7 \cdot 11$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ |
$-1$ |
$0$ |
$2$ |
$2$ |
132 |
|
|
|
$C_3$ |
$\PSU(6,2)$ |
$\SU(6,2)$ |
$C_1$ |
$2^{16} \cdot 3^{7} \cdot 5 \cdot 7 \cdot 11$ |
$2 \cdot 3$ |
|
$2016$ |
$21$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 50816959200.a |
$\GSU(3,19)$ |
$\GSU(3,19)$ |
$2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7^{3} \cdot 19^{3}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{3} \cdot 19$ |
$-1$ |
$1$ |
$2$ |
$2$ |
1146 |
|
|
|
$C_3$ |
|
|
$C_{3}$ |
$2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 19^{3}$ |
$2^{2}$ |
|
|
$342$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 117936000000.a |
$\GSU(4,5)$ |
$\GSU(4,5)$ |
$2^{10} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$4$ |
$2$ |
668 |
|
|
|
$C_4$ |
|
|
$C_{4}$ |
$2^{11} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$ |
$2^{3}$ |
|
|
$104$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 258190571520.a |
$\SU(5,3)$ |
$\GSU(5,3)$ |
$2^{11} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 61$ |
$-1$ |
$0$ |
$1$ |
$2$ |
150 |
|
|
$2$ |
$C_1$ |
$\SU(5,3)$ |
$\SU(5,3)$ |
$C_1$ |
$2^{12} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$ |
$2$ |
$2440$ |
$2440$ |
$60$ |
$61$ |
$61$ |
? |
? |
? |
Simple |
| 9324577382400.b |
$\GSU(4,7)$ |
$\GSU(4,7)$ |
$2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 43$ |
$-1$ |
$1$ |
$4$ |
$2$ |
878 |
|
|
|
$C_4$ |
|
|
$C_{2}$ |
$2^{14} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$ |
$2^{3}$ |
|
|
$300$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 34693789777920.a |
$\SU(4,8)$ |
$\GSU(4,8)$ |
$2^{18} \cdot 3^{7} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$ |
$2^{2} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 19$ |
$-1$ |
$0$ |
$1$ |
$2$ |
602 |
|
|
$2$ |
$C_1$ |
$\SU(4,8)$ |
$\SU(4,8)$ |
$C_1$ |
$2^{19} \cdot 3^{8} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$ |
$2 \cdot 3$ |
|
$4617$ |
$455$ |
? |
? |
? |
? |
? |
Simple |
| 267219763200000.a |
$\SU(5,4)$ |
$\GSU(5,4)$ |
$2^{20} \cdot 3^{2} \cdot 5^{5} \cdot 13 \cdot 17 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 41$ |
$-1$ |
$0$ |
$2$ |
$2$ |
411 |
|
|
|
$C_5$ |
|
|
$C_1$ |
$2^{22} \cdot 3^{2} \cdot 5^{5} \cdot 13 \cdot 17 \cdot 41$ |
$2^{2} \cdot 5$ |
|
|
$205$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 91349889728348160.a |
$\GSU(6,3)$ |
$\GSU(6,3)$ |
$2^{15} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 61$ |
$-1$ |
$1$ |
$3$ |
$2$ |
not computed |
|
|
|
$C_2$ |
|
|
$C_{2}$ |
|
|
|
|
? |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
