| 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 |
$S_3$ |
$\PGammaU(2,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
| 24.12 |
$S_4$ |
$\PGammaU(2,3)$ |
$2^{3} \cdot 3$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$4$ |
$2$ |
5 |
$30$ |
$11$ |
$4$ |
$C_1$ |
$S_4$ |
$A_4$ |
$C_{2}$ |
$2^{3} \cdot 3$ |
$1$ |
$4$ |
$4$ |
$3$ |
$3$ |
$3$ |
$3$ |
$3$ |
$3$ |
Solvable - 3 |
| 120.34 |
$S_5$ |
$\PGammaU(2,4), \PGammaU(2,5)$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
7 |
$156$ |
$19$ |
$3$ |
$C_1$ |
$S_5$ |
$A_5$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$1$ |
$5$ |
$5$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Non-Solvable - 2 |
| 336.208 |
$\PGL(2,7)$ |
$\PGammaU(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
9 |
$413$ |
$23$ |
$3$ |
$C_1$ |
$\PGL(2,7)$ |
$\PSL(2,7)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 7$ |
$1$ |
$8$ |
$8$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Non-Solvable - 2 |
| 432.734 |
$C_3^2:\GL(2,3)$ |
$\PGammaU(3,2)$ |
$2^{4} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$7$ |
$2$ |
11 |
$646$ |
$46$ |
$6$ |
$C_1$ |
$C_3^2:\GL(2,3)$ |
$\PU(3,2)$ |
$C_{2}$ |
$2^{4} \cdot 3^{3}$ |
$1$ |
$9$ |
$9$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 5 |
| 1320.133 |
$\PGL(2,11)$ |
$\PGammaU(2,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$2$ |
$2$ |
13 |
$1624$ |
$29$ |
$3$ |
$C_1$ |
$\PGL(2,11)$ |
$\PSL(2,11)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$1$ |
$12$ |
$12$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
Non-Solvable - 2 |
| 1440.5841 |
$S_6:C_2$ |
$\PGammaU(2,9)$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
13 |
$2579$ |
$65$ |
$6$ |
$C_1$ |
$S_6:C_2$ |
$A_6$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$1$ |
$10$ |
$10$ |
$9$ |
$9$ |
$9$ |
$9$ |
$9$ |
$9$ |
Non-Solvable - 3 |
| 1512.779 |
${}^2G(2,3)$ |
$\PGammaU(2,8)$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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.b |
$\PGL(2,13)$ |
$\PGammaU(2,13)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
15 |
$2466$ |
$30$ |
$3$ |
$C_1$ |
$\PGL(2,13)$ |
$\PSL(2,13)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$1$ |
$14$ |
$14$ |
$12$ |
$12$ |
$13$ |
$12$ |
$12$ |
$13$ |
Non-Solvable - 2 |
| 4896.b |
$\PGL(2,17)$ |
$\PGammaU(2,17)$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
19 |
$5312$ |
$32$ |
$3$ |
$C_1$ |
$\PGL(2,17)$ |
$\PSL(2,17)$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$1$ |
$18$ |
$18$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Non-Solvable - 2 |
| 6840.b |
$\PGL(2,19)$ |
$\PGammaU(2,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$1$ |
$2$ |
$2$ |
21 |
$8084$ |
$36$ |
$3$ |
$C_1$ |
$\PGL(2,19)$ |
$\PSL(2,19)$ |
$C_{2}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$1$ |
$20$ |
$20$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Non-Solvable - 2 |
| 12096.a |
$G(2,2)$ |
$\PGammaU(3,3)$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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.b |
$\PGL(2,23)$ |
$\PGammaU(2,23)$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$1$ |
$2$ |
$2$ |
25 |
$12634$ |
$34$ |
$3$ |
$C_1$ |
$\PGL(2,23)$ |
$\PSL(2,23)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$1$ |
$24$ |
$24$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
Non-Solvable - 2 |
| 16320.a |
$\SL(2,16).C_4$ |
$\PGammaU(2,16)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 17$ |
$2^{3} \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$1$ |
$3$ |
$2$ |
17 |
|
|
|
$C_1$ |
$\SL(2,16).C_4$ |
$\SL(2,16)$ |
$C_{4}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 17$ |
$1$ |
|
$17$ |
$16$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 24360.b |
$\PGL(2,29)$ |
$\PGammaU(2,29)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$1$ |
$2$ |
$2$ |
31 |
$28748$ |
$41$ |
$3$ |
$C_1$ |
$\PGL(2,29)$ |
$\PSL(2,29)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$1$ |
$30$ |
$30$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
Non-Solvable - 2 |
| 29760.b |
$\PGL(2,31)$ |
$\PGammaU(2,31)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2^{5} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$2$ |
$2$ |
33 |
$34359$ |
$44$ |
$3$ |
$C_1$ |
$\PGL(2,31)$ |
$\PSL(2,31)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$1$ |
$32$ |
$32$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
Non-Solvable - 2 |
| 31200.c |
$\PSL(2,25).C_2^2$ |
$\PGammaU(2,25)$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
24 |
|
|
|
$C_1$ |
$\PSL(2,25).C_2^2$ |
$\PSL(2,25)$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$1$ |
|
$26$ |
$25$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 50616.b |
$\PGL(2,37)$ |
$\PGammaU(2,37)$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$2^{2} \cdot 3^{2} \cdot 19 \cdot 37$ |
$-1$ |
$1$ |
$2$ |
$2$ |
39 |
$48630$ |
$41$ |
$3$ |
$C_1$ |
$\PGL(2,37)$ |
$\PSL(2,37)$ |
$C_{2}$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$1$ |
$38$ |
$38$ |
$36$ |
$36$ |
$37$ |
$36$ |
$36$ |
$37$ |
Non-Solvable - 2 |
| 51840.b |
$\SO(5,3)$ |
$\PGammaU(4,2)$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$2^{3} \cdot 3^{2} \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
25 |
|
|
|
$C_1$ |
$\SO(5,3)$ |
$\SU(4,2)$ |
$C_{2}$ |
$2^{7} \cdot 3^{4} \cdot 5$ |
$1$ |
|
$27$ |
$6$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 58968.a |
$\PSL(2,27).C_6$ |
$\PGammaU(2,27)$ |
$2^{3} \cdot 3^{4} \cdot 7 \cdot 13$ |
$2^{2} \cdot 3^{2} \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
23 |
|
|
|
$C_1$ |
$\PSL(2,27).C_6$ |
$\PSL(2,27)$ |
$C_{6}$ |
$2^{3} \cdot 3^{4} \cdot 7 \cdot 13$ |
$1$ |
|
$28$ |
$26$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 68880.b |
$\PGL(2,41)$ |
$\PGammaU(2,41)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$-1$ |
$1$ |
$2$ |
$2$ |
43 |
$83364$ |
$49$ |
$3$ |
$C_1$ |
$\PGL(2,41)$ |
$\PSL(2,41)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$1$ |
$42$ |
$42$ |
$40$ |
$40$ |
$40$ |
$40$ |
$40$ |
$40$ |
Non-Solvable - 2 |
| 79464.b |
$\PGL(2,43)$ |
$\PGammaU(2,43)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
45 |
$78830$ |
$42$ |
$3$ |
$C_1$ |
$\PGL(2,43)$ |
$\PSL(2,43)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$1$ |
$44$ |
$44$ |
$42$ |
$42$ |
$42$ |
$42$ |
$42$ |
$42$ |
Non-Solvable - 2 |
| 103776.b |
$\PGL(2,47)$ |
$\PGammaU(2,47)$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$2^{4} \cdot 3 \cdot 23 \cdot 47$ |
$-1$ |
$1$ |
$2$ |
$2$ |
49 |
$98848$ |
$40$ |
$3$ |
$C_1$ |
$\PGL(2,47)$ |
$\PSL(2,47)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$1$ |
$48$ |
$48$ |
$46$ |
$46$ |
$46$ |
$46$ |
$46$ |
$46$ |
Non-Solvable - 2 |
| 163680.a |
$\SL(2,32).C_5$ |
$\PGammaU(2,32)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 5 \cdot 11 \cdot 31$ |
$-1$ |
$1$ |
$2$ |
$2$ |
21 |
|
|
|
$C_1$ |
$\SL(2,32).C_5$ |
$\SL(2,32)$ |
$C_{5}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 11 \cdot 31$ |
$1$ |
|
$33$ |
$31$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 249600.a |
$\PGammaU(3,4)$ |
$\PGammaU(3,4)$ |
$2^{8} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
22 |
|
|
|
$C_1$ |
$\PGammaU(3,4)$ |
$\SU(3,4)$ |
$C_{4}$ |
$2^{8} \cdot 3 \cdot 5^{2} \cdot 13$ |
$1$ |
|
$65$ |
$12$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 756000.a |
$\PGammaU(3,5)$ |
$\PGammaU(3,5)$ |
$2^{5} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$3$ |
$2$ |
29 |
|
|
|
$C_1$ |
$\PGammaU(3,5)$ |
$\PU(3,5)$ |
$C_{2}$ |
$2^{5} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$1$ |
|
$126$ |
$20$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 11327232.a |
$\PGammaU(3,7)$ |
$\PGammaU(3,7)$ |
$2^{8} \cdot 3 \cdot 7^{3} \cdot 43$ |
$2^{4} \cdot 3 \cdot 7 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
44 |
|
|
|
$C_1$ |
$\PGammaU(3,7)$ |
$\SU(3,7)$ |
$C_{2}$ |
$2^{8} \cdot 3 \cdot 7^{3} \cdot 43$ |
$1$ |
|
$344$ |
$42$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 26127360.d |
$\PGammaU(4,3)$ |
$\PGammaU(4,3)$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
61 |
|
|
|
$C_1$ |
$\PGammaU(4,3)$ |
$\PSOMinus(6,3)$ |
$C_{2}^{2}$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 7$ |
$1$ |
|
$112$ |
$21$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 27371520.a |
$\PGammaU(5,2)$ |
$\PGammaU(5,2)$ |
$2^{11} \cdot 3^{5} \cdot 5 \cdot 11$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$2$ |
$2$ |
43 |
|
|
|
$C_1$ |
$\PGammaU(5,2)$ |
$\SU(5,2)$ |
$C_{2}$ |
$2^{11} \cdot 3^{5} \cdot 5 \cdot 11$ |
$1$ |
|
$165$ |
$10$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 99283968.a |
$\PGammaU(3,8)$ |
$\PGammaU(3,8)$ |
$2^{10} \cdot 3^{6} \cdot 7 \cdot 19$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
47 |
|
|
|
$C_1$ |
$\PGammaU(3,8)$ |
$\PU(3,8)$ |
$C_{6}$ |
$2^{10} \cdot 3^{6} \cdot 7 \cdot 19$ |
$1$ |
|
$513$ |
$56$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 170294400.a |
$\PGammaU(3,9)$ |
$\PGammaU(3,9)$ |
$2^{7} \cdot 3^{6} \cdot 5^{2} \cdot 73$ |
$2^{4} \cdot 3 \cdot 5 \cdot 73$ |
$-1$ |
$1$ |
$3$ |
$2$ |
50 |
|
|
|
$C_1$ |
$\PGammaU(3,9)$ |
$\SU(3,9)$ |
$C_{4}$ |
$2^{7} \cdot 3^{6} \cdot 5^{2} \cdot 73$ |
$1$ |
|
$730$ |
$72$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 425494080.a |
$\PGammaU(3,11)$ |
$\PGammaU(3,11)$ |
$2^{6} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 37$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 37$ |
$-1$ |
$2$ |
$3$ |
$2$ |
89 |
|
|
|
$C_1$ |
$\PGammaU(3,11)$ |
$\PU(3,11)$ |
$C_{2}$ |
$2^{6} \cdot 3^{3} \cdot 5 \cdot 11^{3} \cdot 37$ |
$1$ |
|
$1332$ |
$110$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 1622546016.a |
$\PGammaU(3,13)$ |
$\PGammaU(3,13)$ |
$2^{5} \cdot 3 \cdot 7^{2} \cdot 13^{3} \cdot 157$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13 \cdot 157$ |
$-1$ |
$1$ |
$2$ |
$2$ |
116 |
|
|
|
$C_1$ |
$\PGammaU(3,13)$ |
$\SU(3,13)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 7^{2} \cdot 13^{3} \cdot 157$ |
$1$ |
|
$2198$ |
$156$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 4073472000.a |
$\PGammaU(4,4)$ |
$\PGammaU(4,4)$ |
$2^{14} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 17$ |
$-1$ |
$1$ |
$3$ |
$2$ |
73 |
|
|
|
$C_1$ |
$\PGammaU(4,4)$ |
$\SU(4,4)$ |
$C_{4}$ |
$2^{14} \cdot 3^{2} \cdot 5^{3} \cdot 13 \cdot 17$ |
$1$ |
|
$325$ |
$52$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 13906069632.a |
$\PGammaU(3,17)$ |
$\PGammaU(3,17)$ |
$2^{7} \cdot 3^{5} \cdot 7 \cdot 13 \cdot 17^{3}$ |
$2^{5} \cdot 3^{2} \cdot 7 \cdot 13 \cdot 17$ |
$-1$ |
$2$ |
$3$ |
$2$ |
185 |
|
|
|
$C_1$ |
$\PGammaU(3,17)$ |
$\PU(3,17)$ |
$C_{2}$ |
$2^{7} \cdot 3^{5} \cdot 7 \cdot 13 \cdot 17^{3}$ |
$1$ |
|
$4914$ |
$272$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 33877972800.a |
$\PGammaU(3,19)$ |
$\PGammaU(3,19)$ |
$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 19^{3}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{3} \cdot 19$ |
$-1$ |
$1$ |
$2$ |
$2$ |
224 |
|
|
|
$C_1$ |
$\PGammaU(3,19)$ |
$\SU(3,19)$ |
$C_{2}$ |
$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 7^{3} \cdot 19^{3}$ |
$1$ |
|
$6860$ |
$342$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 34233876480.a |
$\PGammaU(3,16)$ |
$\PGammaU(3,16)$ |
$2^{15} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$ |
$2^{5} \cdot 3 \cdot 5 \cdot 17 \cdot 241$ |
$-1$ |
$1$ |
$4$ |
$2$ |
74 |
|
|
|
$C_1$ |
$\PGammaU(3,16)$ |
$\SU(3,16)$ |
$C_{8}$ |
$2^{15} \cdot 3 \cdot 5 \cdot 17^{2} \cdot 241$ |
$1$ |
|
$4097$ |
$240$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 55180984320.a |
$\PGammaU(6,2)$ |
$\PGammaU(6,2)$ |
$2^{16} \cdot 3^{7} \cdot 5 \cdot 7 \cdot 11$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ |
$-1$ |
$2$ |
$3$ |
$2$ |
99 |
|
|
|
$C_1$ |
$\PGammaU(6,2)$ |
$\PU(6,2)$ |
$C_{2}$ |
$2^{16} \cdot 3^{7} \cdot 5 \cdot 7 \cdot 11$ |
$1$ |
|
$672$ |
$22$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 58968000000.c |
$\PGammaU(4,5)$ |
$\PGammaU(4,5)$ |
$2^{9} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
154 |
|
|
|
$C_1$ |
$\PGammaU(4,5)$ |
$\PSU(4,5)$ |
$C_{2}^{2}$ |
$2^{9} \cdot 3^{4} \cdot 5^{6} \cdot 7 \cdot 13$ |
$1$ |
|
$756$ |
$105$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 516381143040.a |
$\PGammaU(5,3)$ |
$\PGammaU(5,3)$ |
$2^{12} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 61$ |
$-1$ |
$1$ |
$2$ |
$2$ |
117 |
|
|
|
$C_1$ |
$\PGammaU(5,3)$ |
$\SU(5,3)$ |
$C_{2}$ |
$2^{12} \cdot 3^{10} \cdot 5 \cdot 7 \cdot 61$ |
$1$ |
|
$2440$ |
$60$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 9324577382400.c |
$\PGammaU(4,7)$ |
$\PGammaU(4,7)$ |
$2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
325 |
|
|
|
$C_1$ |
$\PGammaU(4,7)$ |
$\PSOMinus(6,7)$ |
$C_{2}^{2}$ |
$2^{13} \cdot 3^{2} \cdot 5^{2} \cdot 7^{6} \cdot 43$ |
$1$ |
|
|
$301$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 208162738667520.a |
$\PGammaU(4,8)$ |
$\PGammaU(4,8)$ |
$2^{19} \cdot 3^{8} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$ |
$2^{3} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13 \cdot 19$ |
$-1$ |
$1$ |
$3$ |
$2$ |
208 |
|
|
|
$C_1$ |
$\PGammaU(4,8)$ |
$\SU(4,8)$ |
$C_{6}$ |
$2^{19} \cdot 3^{8} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 19$ |
$1$ |
|
|
$456$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 455574206545920.a |
$\PGammaU(7,2)$ |
$\PGammaU(7,2)$ |
$2^{22} \cdot 3^{8} \cdot 5 \cdot 7 \cdot 11 \cdot 43$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
175 |
|
|
|
$C_1$ |
$\PGammaU(7,2)$ |
$\SU(7,2)$ |
$C_{2}$ |
$2^{22} \cdot 3^{8} \cdot 5 \cdot 7 \cdot 11 \cdot 43$ |
$1$ |
|
|
$42$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 1068879052800000.a |
$\PGammaU(5,4)$ |
$\PGammaU(5,4)$ |
$2^{22} \cdot 3^{2} \cdot 5^{5} \cdot 13 \cdot 17 \cdot 41$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 17 \cdot 41$ |
$-1$ |
$2$ |
$4$ |
$2$ |
160 |
|
|
|
$C_1$ |
$\PGammaU(5,4)$ |
$\PU(5,4)$ |
$C_{4}$ |
$2^{22} \cdot 3^{2} \cdot 5^{5} \cdot 13 \cdot 17 \cdot 41$ |
$1$ |
|
|
$204$ |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 91349889728348160.b |
$\PGammaU(6,3)$ |
$\PGammaU(6,3)$ |
$2^{15} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \cdot 61$ |
$-1$ |
$1$ |
$3$ |
$2$ |
378 |
|
|
|
$C_1$ |
$\PGammaU(6,3)$ |
$\PSU(6,3)$ |
$C_{2}^{2}$ |
$2^{15} \cdot 3^{15} \cdot 5 \cdot 7^{2} \cdot 13 \cdot 61$ |
$1$ |
|
|
$183$ |
? |
? |
? |
? |
? |
Non-Solvable - 3 |
| 14869942101658828800.a |
$\PGammaU(8,2)$ |
$\PGammaU(8,2)$ |
$2^{29} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 17 \cdot 43$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 17 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
371 |
|
|
|
$C_1$ |
$\PGammaU(8,2)$ |
$\SU(8,2)$ |
$C_{2}$ |
$2^{29} \cdot 3^{9} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 17 \cdot 43$ |
$1$ |
|
|
$86$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
