| Label |
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 |
| 1.1 |
$C_1$ |
$1$ |
$1$ |
$0$ |
$0$ |
$0$ |
$0$ |
$1$ |
$1$ |
$1$ |
$1$ |
$C_1$ |
$C_1$ |
$C_1$ |
$C_1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$0$ |
$0$ |
$0$ |
Trivial |
| 60.5 |
$A_5$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$5$ |
$59$ |
$9$ |
$2$ |
$C_1$ |
$A_5$ |
$A_5$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$5$ |
$5$ |
$3$ |
$3$ |
$4$ |
$3$ |
$3$ |
$4$ |
Simple |
| 120.5 |
$\SL(2,5)$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$9$ |
$76$ |
$12$ |
$3$ |
$C_2$ |
$A_5$ |
$\SL(2,5)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5$ |
$2$ |
$24$ |
$24$ |
$2$ |
$4$ |
$8$ |
$2$ |
$4$ |
$8$ |
Non-Solvable - 2 |
| 168.42 |
$\GL(3,2)$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$6$ |
$179$ |
$15$ |
$2$ |
$C_1$ |
$\GL(3,2)$ |
$\GL(3,2)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 7$ |
$2$ |
$7$ |
$7$ |
$3$ |
$6$ |
$6$ |
$3$ |
$6$ |
$6$ |
Simple |
| 336.114 |
$\SL(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$11$ |
$224$ |
$19$ |
$3$ |
$C_2$ |
$\GL(3,2)$ |
$\SL(2,7)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 7$ |
$2$ |
$16$ |
$16$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 360.118 |
$A_6$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$7$ |
$501$ |
$22$ |
$2$ |
$C_1$ |
$A_6$ |
$A_6$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$6$ |
$6$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Simple |
| 504.156 |
$\SL(2,8)$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$9$ |
$386$ |
$12$ |
$2$ |
$C_1$ |
$\SL(2,8)$ |
$\SL(2,8)$ |
$C_1$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$3$ |
$9$ |
$9$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Simple |
| 660.13 |
$\PSL(2,11)$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$2 \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$8$ |
$620$ |
$16$ |
$2$ |
$C_1$ |
$\PSL(2,11)$ |
$\PSL(2,11)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2$ |
$11$ |
$11$ |
$5$ |
$10$ |
$10$ |
$5$ |
$10$ |
$10$ |
Simple |
| 720.409 |
$\SL(2,9)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$13$ |
$588$ |
$27$ |
$3$ |
$C_2$ |
$A_6$ |
$\SL(2,9)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$80$ |
$80$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 960.11357 |
$C_2^4:A_5$ |
$2^{6} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$9$ |
$2331$ |
$77$ |
$3$ |
$C_1$ |
$C_2^4:A_5$ |
$C_2^4:A_5$ |
$C_1$ |
$2^{9} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
Non-Solvable - 5 |
| 960.11358 |
$C_2^4:A_5$ |
$2^{6} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$12$ |
$1708$ |
$63$ |
$3$ |
$C_1$ |
$C_2^4:A_5$ |
$C_2^4:A_5$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 5$ |
$2$ |
$10$ |
$10$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Non-Solvable - 5 |
| 1080.260 |
$C_3.A_6$ |
$2^{3} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$17$ |
$1111$ |
$42$ |
$3$ |
$C_3$ |
$A_6$ |
$C_3.A_6$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$18$ |
$18$ |
$3$ |
$6$ |
$12$ |
$3$ |
$6$ |
$12$ |
Non-Solvable - 2 |
| 1092.25 |
$\PSL(2,13)$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$2 \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$9$ |
$942$ |
$16$ |
$2$ |
$C_1$ |
$\PSL(2,13)$ |
$\PSL(2,13)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2$ |
$14$ |
$14$ |
$7$ |
$7$ |
$13$ |
$7$ |
$7$ |
$13$ |
Simple |
| 1320.13 |
$\SL(2,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$15$ |
$766$ |
$21$ |
$3$ |
$C_2$ |
$\PSL(2,11)$ |
$\SL(2,11)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2$ |
$24$ |
$24$ |
$6$ |
$12$ |
$12$ |
$6$ |
$12$ |
$12$ |
Non-Solvable - 2 |
| 1344.814 |
$C_2^3.\GL(3,2)$ |
$2^{6} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$4$ |
$2$ |
$11$ |
$2331$ |
$72$ |
$3$ |
$C_1$ |
$C_2^3.\GL(3,2)$ |
$C_2^3.\GL(3,2)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 7$ |
$2$ |
$14$ |
$14$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 4 |
| 1344.11686 |
$C_2^3:\GL(3,2)$ |
$2^{6} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$4$ |
$2$ |
$11$ |
$3299$ |
$95$ |
$3$ |
$C_1$ |
$C_2^3:\GL(3,2)$ |
$C_2^3:\GL(3,2)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 7$ |
$2$ |
$8$ |
$8$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 4 |
| 1920.240998 |
$C_2^5:A_5$ |
$2^{7} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$16$ |
$7858$ |
$219$ |
$4$ |
$C_2$ |
$C_2^4:A_5$ |
$C_2^5:A_5$ |
$C_1$ |
$2^{9} \cdot 3 \cdot 5$ |
$2^{3}$ |
$12$ |
$12$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Non-Solvable - 6 |
| 1920.240999 |
$C_2^5.A_5$ |
$2^{7} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$16$ |
$3730$ |
$121$ |
$4$ |
$C_2$ |
$C_2^4:A_5$ |
$C_2^5.A_5$ |
$C_1$ |
$2^{9} \cdot 3 \cdot 5$ |
$2^{3}$ |
$24$ |
$24$ |
$6$ |
$12$ |
$12$ |
$6$ |
$12$ |
$12$ |
Non-Solvable - 6 |
| 1920.241001 |
$C_2^5.A_5$ |
$2^{7} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$14$ |
$2846$ |
$73$ |
$4$ |
$C_1$ |
$C_2^5.A_5$ |
$C_2^5.A_5$ |
$C_1$ |
$2^{9} \cdot 3 \cdot 5$ |
$2^{2}$ |
$40$ |
$40$ |
$15$ |
$30$ |
$30$ |
$15$ |
$30$ |
$30$ |
Non-Solvable - 6 |
| 1920.241002 |
$C_2^4:\SL(2,5)$ |
$2^{7} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$22$ |
$3387$ |
$117$ |
$5$ |
$C_2$ |
$C_2^4:A_5$ |
$C_2^4:\SL(2,5)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 5$ |
$2$ |
$40$ |
$34$ |
$10$ |
$20$ |
$20$ |
$7$ |
$9$ |
$13$ |
Non-Solvable - 6 |
| 1920.241003 |
$C_2.C_2^4:A_5$ |
$2^{7} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$17$ |
$2155$ |
$73$ |
$4$ |
$C_2$ |
$C_2^4:A_5$ |
$C_2.C_2^4:A_5$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 5$ |
$2$ |
$80$ |
$80$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 6 |
| 1920.241004 |
$C_2.C_2^4:A_5$ |
$2^{7} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$16$ |
$3243$ |
$86$ |
$4$ |
$C_2$ |
$C_2^4:A_5$ |
$C_2.C_2^4:A_5$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 5$ |
$2$ |
$32$ |
$32$ |
$8$ |
$8$ |
$16$ |
$8$ |
$8$ |
$16$ |
Non-Solvable - 6 |
| 2160.a |
$C_6.A_6$ |
$2^{4} \cdot 3^{3} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$3$ |
$2$ |
$31$ |
$1355$ |
$51$ |
$5$ |
$C_6$ |
$A_6$ |
$C_6.A_6$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$432$ |
$98$ |
$6$ |
$12$ |
$24$ |
$6$ |
$12$ |
$20$ |
Non-Solvable - 3 |
| 2184.a |
$\SL(2,13)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$2$ |
|
$17$ |
|
|
|
$C_2$ |
$\PSL(2,13)$ |
$\SL(2,13)$ |
$C_1$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2$ |
|
$56$ |
$6$ |
$12$ |
$24$ |
? |
? |
? |
Non-Solvable - 2 |
| 2448.a |
$\PSL(2,17)$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$2^{3} \cdot 3^{2} \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$11$ |
$2420$ |
$22$ |
$2$ |
$C_1$ |
$\PSL(2,17)$ |
$\PSL(2,17)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2$ |
$18$ |
$18$ |
$9$ |
$9$ |
$16$ |
$9$ |
$9$ |
$16$ |
Simple |
| 2520.a |
$A_7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$9$ |
$3786$ |
$40$ |
$2$ |
$C_1$ |
$A_7$ |
$A_7$ |
$C_1$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2$ |
$7$ |
$7$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Simple |
| 2688.b |
$C_2^3:\SL(2,7)$ |
$2^{7} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$19$ |
$4194$ |
$116$ |
$5$ |
$C_2$ |
$C_2^3:\GL(3,2)$ |
$C_2^3:\SL(2,7)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 7$ |
$2$ |
$112$ |
$24$ |
$14$ |
$28$ |
$56$ |
$11$ |
$15$ |
$15$ |
Non-Solvable - 5 |
| 2688.c |
$C_2^3.\SL(2,7)$ |
$2^{7} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$19$ |
$3394$ |
$98$ |
$5$ |
$C_2$ |
$C_2^3.\GL(3,2)$ |
$C_2^3.\SL(2,7)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 7$ |
$2$ |
$112$ |
$30$ |
$14$ |
$28$ |
$56$ |
$11$ |
$15$ |
$15$ |
Non-Solvable - 5 |
| 2688.ci |
$C_2^4:\GL(3,2)$ |
$2^{7} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$16$ |
$5770$ |
$129$ |
$4$ |
$C_2$ |
$C_2^3:\GL(3,2)$ |
$C_2^4:\GL(3,2)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 7$ |
$1$ |
$16$ |
$16$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Non-Solvable - 5 |
| 3000.a |
$C_5^2.\SL(2,5)$ |
$2^{3} \cdot 3 \cdot 5^{3}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$4$ |
|
$14$ |
$2228$ |
$32$ |
$4$ |
$C_1$ |
$C_5^2.\SL(2,5)$ |
$C_5^2.\SL(2,5)$ |
$C_1$ |
$2^{5} \cdot 3 \cdot 5^{3}$ |
$2^{2}$ |
$25$ |
$25$ |
$24$ |
$24$ |
$24$ |
? |
? |
? |
Non-Solvable - 4 |
| 3420.a |
$\PSL(2,19)$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2 \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$12$ |
$2912$ |
$19$ |
$2$ |
$C_1$ |
$\PSL(2,19)$ |
$\PSL(2,19)$ |
$C_1$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2$ |
$20$ |
$20$ |
$9$ |
$18$ |
$18$ |
$9$ |
$18$ |
$18$ |
Simple |
| 3600.a |
$A_5^2$ |
$2^{4} \cdot 3^{2} \cdot 5^{2}$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$25$ |
$8381$ |
$113$ |
$4$ |
$C_1$ |
$A_5^2$ |
$A_5^2$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5^{2}$ |
$2^{3}$ |
$25$ |
$10$ |
$9$ |
$9$ |
$16$ |
$6$ |
$6$ |
$8$ |
Non-Solvable - 2 |
| 3840.a |
$C_4.C_2^4:A_5$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
$2$ |
$24$ |
$9989$ |
$246$ |
$5$ |
$C_4$ |
$C_2^4:A_5$ |
$C_4.C_2^4:A_5$ |
$C_1$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{2}$ |
$64$ |
$64$ |
$8$ |
$16$ |
$32$ |
$8$ |
$16$ |
$32$ |
Non-Solvable - 7 |
| 3840.b |
$C_4.C_2^4:A_5$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
$2$ |
$26$ |
$10089$ |
$251$ |
$5$ |
$C_4$ |
$C_2^4:A_5$ |
$C_4.C_2^4:A_5$ |
$C_1$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{2}$ |
$64$ |
$64$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 7 |
| 3840.c |
$C_2^6.A_5$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
|
$30$ |
$14865$ |
$411$ |
$7$ |
$C_2^2$ |
$C_2^4:A_5$ |
$C_2^6.A_5$ |
$C_1$ |
$2^{9} \cdot 3 \cdot 5$ |
$2^{3}$ |
$48$ |
$36$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Non-Solvable - 7 |
| 3840.d |
$C_2^5.\SL(2,5)$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
|
$28$ |
$15045$ |
$408$ |
$8$ |
$C_2^2$ |
$C_2^4:A_5$ |
$C_2^5.\SL(2,5)$ |
$C_1$ |
$2^{9} \cdot 3 \cdot 5$ |
$2^{3}$ |
$48$ |
$36$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Non-Solvable - 7 |
| 3840.e |
$C_2^5.\SL(2,5)$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
$2$ |
$28$ |
$3625$ |
$99$ |
$5$ |
$C_2$ |
$C_2^5.A_5$ |
$C_2^5.\SL(2,5)$ |
$C_1$ |
$2^{9} \cdot 3 \cdot 5$ |
$2^{2}$ |
$48$ |
$48$ |
$6$ |
$12$ |
$24$ |
$6$ |
$12$ |
$24$ |
Non-Solvable - 7 |
| 3840.f |
$C_2^2.C_2^4:A_5$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
$2$ |
$31$ |
$6166$ |
$162$ |
$8$ |
$C_2^2$ |
$C_2^4:A_5$ |
$C_2^2.C_2^4:A_5$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 5$ |
$2$ |
$160$ |
$56$ |
$-$ |
$-$ |
$-$ |
$6$ |
$12$ |
$16$ |
Non-Solvable - 7 |
| 3840.dc |
$C_2^6.A_5$ |
$2^{8} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$7$ |
|
$30$ |
$42433$ |
$1043$ |
$7$ |
$C_2^2$ |
$C_2^4:A_5$ |
$C_2^6.A_5$ |
$C_1$ |
$2^{9} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3$ |
$24$ |
$24$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Non-Solvable - 7 |
| 4080.a |
$\SL(2,16)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$17$ |
$3455$ |
$21$ |
$2$ |
$C_1$ |
$\SL(2,16)$ |
$\SL(2,16)$ |
$C_1$ |
$2^{6} \cdot 3 \cdot 5 \cdot 17$ |
$2^{2}$ |
$17$ |
$17$ |
$15$ |
$15$ |
$16$ |
$15$ |
$15$ |
$16$ |
Simple |
| 4860.j |
$C_3^4:A_5$ |
$2^{2} \cdot 3^{5} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$24$ |
$8100$ |
$118$ |
$3$ |
$C_1$ |
$C_3^4:A_5$ |
$C_3^4:A_5$ |
$C_1$ |
$2^{4} \cdot 3^{6} \cdot 5$ |
$2^{2} \cdot 3$ |
$15$ |
$15$ |
$5$ |
$10$ |
$10$ |
$5$ |
$10$ |
$10$ |
Non-Solvable - 5 |
| 4860.s |
$C_3^4.A_5$ |
$2^{2} \cdot 3^{5} \cdot 5$ |
$2 \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$24$ |
$4557$ |
$70$ |
$3$ |
$C_1$ |
$C_3^4.A_5$ |
$C_3^4.A_5$ |
$C_1$ |
$2^{3} \cdot 3^{6} \cdot 5$ |
$2 \cdot 3$ |
$30$ |
$30$ |
$5$ |
$10$ |
$20$ |
$5$ |
$10$ |
$20$ |
Non-Solvable - 5 |
| 4896.a |
$\SL(2,17)$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$-1$ |
$0$ |
$2$ |
|
$21$ |
|
|
|
$C_2$ |
$\PSL(2,17)$ |
$\SL(2,17)$ |
$C_1$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2$ |
|
$288$ |
$8$ |
$16$ |
$32$ |
? |
? |
? |
Non-Solvable - 2 |
| 5040.a |
$C_2.A_7$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$2$ |
$2$ |
$16$ |
$4398$ |
$47$ |
$3$ |
$C_2$ |
$A_7$ |
$C_2.A_7$ |
$C_1$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2$ |
$240$ |
$240$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 5376.a |
$C_2^4:\SL(2,7)$ |
$2^{8} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$6$ |
$2$ |
$29$ |
$10633$ |
$205$ |
$8$ |
$C_2^2$ |
$C_2^3:\GL(3,2)$ |
$C_2^4:\SL(2,7)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 7$ |
$2$ |
$32$ |
$32$ |
$-$ |
$-$ |
$-$ |
$12$ |
$16$ |
$16$ |
Non-Solvable - 6 |
| 5616.a |
$\SL(3,3)$ |
$2^{4} \cdot 3^{3} \cdot 13$ |
$2^{3} \cdot 3 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$12$ |
$6374$ |
$51$ |
$2$ |
$C_1$ |
$\SL(3,3)$ |
$\SL(3,3)$ |
$C_1$ |
$2^{5} \cdot 3^{3} \cdot 13$ |
$2$ |
$13$ |
$13$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Simple |
| 5760.cg |
$C_2^4:A_6$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$5$ |
$2$ |
$12$ |
$16176$ |
$139$ |
$3$ |
$C_1$ |
$C_2^4:A_6$ |
$C_2^4:A_6$ |
$C_1$ |
$2^{9} \cdot 3^{2} \cdot 5$ |
$2^{2}$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
Non-Solvable - 5 |
| 6048.a |
${}^2A(2,3)$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$14$ |
$5150$ |
$36$ |
$2$ |
$C_1$ |
${}^2A(2,3)$ |
${}^2A(2,3)$ |
$C_1$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2$ |
$28$ |
$28$ |
$6$ |
$7$ |
$7$ |
$6$ |
$7$ |
$7$ |
Simple |
| 6072.a |
$\PSL(2,23)$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$2^{2} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$14$ |
$5915$ |
$23$ |
$2$ |
$C_1$ |
$\PSL(2,23)$ |
$\PSL(2,23)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2$ |
$24$ |
$24$ |
$11$ |
$22$ |
$22$ |
$11$ |
$22$ |
$22$ |
Simple |
| 6840.a |
$\SL(2,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$0$ |
$2$ |
|
$23$ |
|
|
|
$C_2$ |
$\PSL(2,19)$ |
$\SL(2,19)$ |
$C_1$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2$ |
|
$40$ |
$10$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
