| 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 |
$S_3$ |
$B(1,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
| 60.5 |
$A_5$ |
$B(1,4), B(1,5)$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 168.42 |
$\PSL(2,7)$ |
$B(1,7)$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 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 |
$\SL(2,8)$ |
$B(1,8)$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 720.763 |
$S_6$ |
$B(2,2)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 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 |
| 4080.a |
$\SL(2,16)$ |
$B(1,16)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 32736.a |
$\SL(2,32)$ |
$B(1,32)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 11 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 979200.a |
$\Sp(4,4)$ |
$B(2,4)$ |
$2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
27 |
$4045873$ |
$496$ |
$2$ |
$C_1$ |
$\Sp(4,4)$ |
$\Sp(4,4)$ |
$C_1$ |
$2^{10} \cdot 3^{2} \cdot 5^{2} \cdot 17$ |
$2^{2}$ |
$85$ |
$85$ |
$18$ |
$18$ |
$18$ |
? |
? |
? |
Simple |
| 1451520.a |
$\Sp(6,2)$ |
$B(3,2)$ |
$2^{9} \cdot 3^{4} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
30 |
$11094174$ |
$1369$ |
$2$ |
$C_1$ |
$\Sp(6,2)$ |
$\Sp(6,2)$ |
$C_1$ |
$2^{9} \cdot 3^{4} \cdot 5 \cdot 7$ |
$1$ |
$28$ |
$28$ |
$7$ |
$7$ |
$7$ |
? |
? |
? |
Simple |
| 4680000.a |
$\PSp(4,5)$ |
$B(2,5)$ |
$2^{6} \cdot 3^{2} \cdot 5^{4} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
34 |
$10928951$ |
$307$ |
$2$ |
$C_1$ |
$\PSp(4,5)$ |
$\PSp(4,5)$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5^{4} \cdot 13$ |
$2$ |
$156$ |
$156$ |
$13$ |
$13$ |
$26$ |
? |
? |
? |
Simple |
| 138297600.a |
$\PSp(4,7)$ |
$B(2,7)$ |
$2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4}$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
52 |
$371553398$ |
$603$ |
$2$ |
$C_1$ |
$\PSp(4,7)$ |
$\PSp(4,7)$ |
$C_1$ |
$2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 7^{4}$ |
$2$ |
$400$ |
$400$ |
$25$ |
$50$ |
$50$ |
? |
? |
? |
Simple |
| 1056706560.a |
$\Sp(4,8)$ |
$B(2,8)$ |
$2^{12} \cdot 3^{4} \cdot 5 \cdot 7^{2} \cdot 13$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
83 |
|
|
|
$C_1$ |
$\Sp(4,8)$ |
$\Sp(4,8)$ |
$C_1$ |
$2^{13} \cdot 3^{5} \cdot 5 \cdot 7^{2} \cdot 13$ |
$2 \cdot 3$ |
|
$585$ |
$196$ |
$196$ |
$196$ |
? |
? |
? |
Simple |
| 1721606400.a |
$\PSp(4,9)$ |
$B(2,9)$ |
$2^{8} \cdot 3^{8} \cdot 5^{2} \cdot 41$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 41$ |
$-1$ |
$0$ |
$1$ |
$2$ |
74 |
|
|
$2$ |
$C_1$ |
$\PSp(4,9)$ |
$\PSp(4,9)$ |
$C_1$ |
$2^{10} \cdot 3^{8} \cdot 5^{2} \cdot 41$ |
$2^{2}$ |
$820$ |
$820$ |
$41$ |
$41$ |
$41$ |
? |
? |
? |
Simple |
| 4585351680.a |
$\Omega(7,3)$ |
$B(3,3)$ |
$2^{9} \cdot 3^{9} \cdot 5 \cdot 7 \cdot 13$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
58 |
|
|
|
$C_1$ |
$\Omega(7,3)$ |
$\Omega(7,3)$ |
$C_1$ |
$2^{10} \cdot 3^{9} \cdot 5 \cdot 7 \cdot 13$ |
$2$ |
|
$351$ |
$78$ |
$78$ |
$78$ |
? |
? |
? |
Simple |
| 12860654400.a |
$\PSp(4,11)$ |
$B(2,11)$ |
$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11^{4} \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11 \cdot 61$ |
$-1$ |
$0$ |
$1$ |
$2$ |
100 |
$33837674726$ |
$754$ |
$2$ |
$C_1$ |
$\PSp(4,11)$ |
$\PSp(4,11)$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 11^{4} \cdot 61$ |
$2$ |
$1464$ |
$1464$ |
$61$ |
$122$ |
$122$ |
? |
? |
? |
Simple |
| 47377612800.a |
$\Sp(8,2)$ |
$B(4,2)$ |
$2^{16} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
81 |
|
|
$2$ |
$C_1$ |
$\Sp(8,2)$ |
$\Sp(8,2)$ |
$C_1$ |
$2^{16} \cdot 3^{5} \cdot 5^{2} \cdot 7 \cdot 17$ |
$1$ |
$120$ |
$120$ |
$35$ |
$35$ |
$35$ |
? |
? |
? |
Simple |
| 68518981440.a |
$\PSp(4,13)$ |
$B(2,13)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13^{4} \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
130 |
|
|
$2$ |
$C_1$ |
$\PSp(4,13)$ |
$\PSp(4,13)$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 13^{4} \cdot 17$ |
$2$ |
$2380$ |
$2380$ |
$85$ |
$85$ |
$170$ |
? |
? |
? |
Simple |
| 1095199948800.a |
$\Sp(4,16)$ |
$B(2,16)$ |
$2^{16} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \cdot 257$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17 \cdot 257$ |
$-1$ |
$0$ |
$1$ |
$2$ |
291 |
|
|
|
$C_1$ |
$\Sp(4,16)$ |
$\Sp(4,16)$ |
$C_1$ |
$2^{19} \cdot 3^{2} \cdot 5^{2} \cdot 17^{2} \cdot 257$ |
$2^{3}$ |
|
$4369$ |
$1800$ |
? |
? |
? |
? |
? |
Simple |
| 65784756654489600.a |
$\Omega(9,3)$ |
$B(4,3)$ |
$2^{14} \cdot 3^{16} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 41$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 41$ |
$-1$ |
$0$ |
$1$ |
$2$ |
218 |
|
|
|
$C_1$ |
$\Omega(9,3)$ |
$\Omega(9,3)$ |
$C_1$ |
$2^{15} \cdot 3^{16} \cdot 5^{2} \cdot 7 \cdot 13 \cdot 41$ |
$2$ |
|
$3240$ |
$780$ |
? |
? |
? |
? |
? |
Simple |
