| 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 |
| 2.1 |
$C_2$ |
$\AGammaL(1,2)$ |
$2$ |
$2$ |
$1$ |
$1$ |
$1$ |
$1$ |
2 |
$2$ |
$2$ |
$2$ |
$C_2$ |
$C_1$ |
$C_1$ |
$C_{2}$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
Cyclic |
| 6.1 |
$S_3$ |
$\AGammaL(1,3)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
| 20.3 |
$F_5$ |
$\AGammaL(1,5)$ |
$2^{2} \cdot 5$ |
$2^{2} \cdot 5$ |
$-1$ |
$2$ |
$3$ |
$2$ |
5 |
$14$ |
$6$ |
$4$ |
$C_1$ |
$F_5$ |
$C_5$ |
$C_{4}$ |
$2^{2} \cdot 5$ |
$1$ |
$5$ |
$5$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Solvable - 2 |
| 24.12 |
$S_4$ |
$\AGammaL(1,4), \AGammaL(2,2)$ |
$2^{3} \cdot 3$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$4$ |
$2$ |
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 |
| 42.1 |
$F_7$ |
$\AGammaL(1,7)$ |
$2 \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$3$ |
$2$ |
7 |
$26$ |
$8$ |
$5$ |
$C_1$ |
$F_7$ |
$C_7$ |
$C_{6}$ |
$2 \cdot 3 \cdot 7$ |
$1$ |
$7$ |
$7$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 2 |
| 110.1 |
$F_{11}$ |
$\AGammaL(1,11)$ |
$2 \cdot 5 \cdot 11$ |
$2 \cdot 5 \cdot 11$ |
$-1$ |
$2$ |
$3$ |
$2$ |
11 |
$38$ |
$8$ |
$5$ |
$C_1$ |
$F_{11}$ |
$C_{11}$ |
$C_{10}$ |
$2 \cdot 5 \cdot 11$ |
$1$ |
$11$ |
$11$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
Solvable - 2 |
| 144.182 |
$F_9:C_2$ |
$\AGammaL(1,9)$ |
$2^{4} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$-1$ |
$3$ |
$6$ |
$2$ |
9 |
$162$ |
$25$ |
$8$ |
$C_1$ |
$F_9:C_2$ |
$C_3^2:C_4$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{2}$ |
$1$ |
$9$ |
$9$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 3 |
| 156.7 |
$F_{13}$ |
$\AGammaL(1,13)$ |
$2^{2} \cdot 3 \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$4$ |
$2$ |
13 |
$72$ |
$12$ |
$7$ |
$C_1$ |
$F_{13}$ |
$C_{13}$ |
$C_{12}$ |
$2^{2} \cdot 3 \cdot 13$ |
$1$ |
$13$ |
$13$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Solvable - 2 |
| 168.43 |
$F_8:C_3$ |
$\AGammaL(1,8)$ |
$2^{3} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$5$ |
$2$ |
8 |
$104$ |
$12$ |
$4$ |
$C_1$ |
$F_8:C_3$ |
$F_8$ |
$C_{3}$ |
$2^{3} \cdot 3 \cdot 7$ |
$1$ |
$8$ |
$8$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Solvable - 3 |
| 272.50 |
$F_{17}$ |
$\AGammaL(1,17)$ |
$2^{4} \cdot 17$ |
$2^{4} \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$2$ |
17 |
$74$ |
$10$ |
$6$ |
$C_1$ |
$F_{17}$ |
$C_{17}$ |
$C_{16}$ |
$2^{4} \cdot 17$ |
$1$ |
$17$ |
$17$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Solvable - 2 |
| 342.7 |
$F_{19}$ |
$\AGammaL(1,19)$ |
$2 \cdot 3^{2} \cdot 19$ |
$2 \cdot 3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
19 |
$102$ |
$12$ |
$7$ |
$C_1$ |
$F_{19}$ |
$C_{19}$ |
$C_{18}$ |
$2 \cdot 3^{2} \cdot 19$ |
$1$ |
$19$ |
$19$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Solvable - 2 |
| 432.734 |
$C_3^2:\GL(2,3)$ |
$\AGammaL(2,3)$ |
$2^{4} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$7$ |
$2$ |
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 |
| 506.1 |
$F_{23}$ |
$\AGammaL(1,23)$ |
$2 \cdot 11 \cdot 23$ |
$2 \cdot 11 \cdot 23$ |
$-1$ |
$2$ |
$3$ |
$2$ |
23 |
$74$ |
$8$ |
$5$ |
$C_1$ |
$F_{23}$ |
$C_{23}$ |
$C_{22}$ |
$2 \cdot 11 \cdot 23$ |
$1$ |
$23$ |
$23$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
Solvable - 2 |
| 812.7 |
$F_{29}$ |
$\AGammaL(1,29)$ |
$2^{2} \cdot 7 \cdot 29$ |
$2^{2} \cdot 7 \cdot 29$ |
$-1$ |
$2$ |
$4$ |
$2$ |
29 |
$152$ |
$12$ |
$7$ |
$C_1$ |
$F_{29}$ |
$C_{29}$ |
$C_{28}$ |
$2^{2} \cdot 7 \cdot 29$ |
$1$ |
$29$ |
$29$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
Solvable - 2 |
| 930.1 |
$F_{31}$ |
$\AGammaL(1,31)$ |
$2 \cdot 3 \cdot 5 \cdot 31$ |
$2 \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$2$ |
$4$ |
$2$ |
31 |
$226$ |
$16$ |
$9$ |
$C_1$ |
$F_{31}$ |
$C_{31}$ |
$C_{30}$ |
$2 \cdot 3 \cdot 5 \cdot 31$ |
$1$ |
$31$ |
$31$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
Solvable - 2 |
| 960.11359 |
$F_{16}:C_4$ |
$\AGammaL(1,16)$ |
$2^{6} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$8$ |
$2$ |
13 |
$990$ |
$44$ |
$8$ |
$C_1$ |
$F_{16}:C_4$ |
$F_{16}$ |
$C_{4}$ |
$2^{6} \cdot 3 \cdot 5$ |
$1$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
Solvable - 3 |
| 1200.946 |
$F_{25}:C_2$ |
$\AGammaL(1,25)$ |
$2^{4} \cdot 3 \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$7$ |
$2$ |
20 |
$984$ |
$48$ |
$14$ |
$C_1$ |
$F_{25}:C_2$ |
$C_5^2:C_6$ |
$C_{2} \times C_{4}$ |
$2^{4} \cdot 3 \cdot 5^{2}$ |
$1$ |
$25$ |
$25$ |
$24$ |
$24$ |
$24$ |
$24$ |
$24$ |
$24$ |
Solvable - 3 |
| 1332.31 |
$F_{37}$ |
$\AGammaL(1,37)$ |
$2^{2} \cdot 3^{2} \cdot 37$ |
$2^{2} \cdot 3^{2} \cdot 37$ |
$-1$ |
$2$ |
$5$ |
$2$ |
37 |
$306$ |
$18$ |
$10$ |
$C_1$ |
$F_{37}$ |
$C_{37}$ |
$C_{36}$ |
$2^{2} \cdot 3^{2} \cdot 37$ |
$1$ |
$37$ |
$37$ |
$36$ |
$36$ |
$36$ |
$36$ |
$36$ |
$36$ |
Solvable - 2 |
| 1344.11686 |
$C_2^3:\GL(3,2)$ |
$\AGammaL(3,2)$ |
$2^{6} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$4$ |
$2$ |
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 |
| 1640.47 |
$F_{41}$ |
$\AGammaL(1,41)$ |
$2^{3} \cdot 5 \cdot 41$ |
$2^{3} \cdot 5 \cdot 41$ |
$-1$ |
$2$ |
$5$ |
$2$ |
41 |
$296$ |
$16$ |
$9$ |
$C_1$ |
$F_{41}$ |
$C_{41}$ |
$C_{40}$ |
$2^{3} \cdot 5 \cdot 41$ |
$1$ |
$41$ |
$41$ |
$40$ |
$40$ |
$40$ |
$40$ |
$40$ |
$40$ |
Solvable - 2 |
| 1806.1 |
$F_{43}$ |
$\AGammaL(1,43)$ |
$2 \cdot 3 \cdot 7 \cdot 43$ |
$2 \cdot 3 \cdot 7 \cdot 43$ |
$-1$ |
$2$ |
$4$ |
$2$ |
43 |
$310$ |
$16$ |
$9$ |
$C_1$ |
$F_{43}$ |
$C_{43}$ |
$C_{42}$ |
$2 \cdot 3 \cdot 7 \cdot 43$ |
$1$ |
$43$ |
$43$ |
$42$ |
$42$ |
$42$ |
$42$ |
$42$ |
$42$ |
Solvable - 2 |
| 2106.a |
$F_{27}:C_3$ |
$\AGammaL(1,27)$ |
$2 \cdot 3^{4} \cdot 13$ |
$2 \cdot 3^{2} \cdot 13$ |
$-1$ |
$3$ |
$6$ |
$2$ |
17 |
$1130$ |
$26$ |
$7$ |
$C_1$ |
$F_{27}:C_3$ |
$C_3^3:C_{13}$ |
$C_{6}$ |
$2 \cdot 3^{4} \cdot 13$ |
$1$ |
$27$ |
$27$ |
$26$ |
$26$ |
$26$ |
$26$ |
$26$ |
$26$ |
Solvable - 3 |
| 3660.a |
$F_{61}$ |
$\AGammaL(1,61)$ |
$2^{2} \cdot 3 \cdot 5 \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 61$ |
$-1$ |
$2$ |
$5$ |
$2$ |
61 |
$684$ |
$24$ |
$13$ |
$C_1$ |
$F_{61}$ |
$C_{61}$ |
$C_{60}$ |
$2^{2} \cdot 3 \cdot 5 \cdot 61$ |
$1$ |
$61$ |
$61$ |
$60$ |
$60$ |
$60$ |
$60$ |
$60$ |
$60$ |
Solvable - 2 |
| 4704.cb |
$F_{49}:C_2$ |
$\AGammaL(1,49)$ |
$2^{5} \cdot 3 \cdot 7^{2}$ |
$2^{4} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$8$ |
$2$ |
35 |
$2880$ |
$62$ |
$17$ |
$C_1$ |
$F_{49}:C_2$ |
$C_7^2:C_8$ |
$C_{2} \times C_{6}$ |
$2^{5} \cdot 3 \cdot 7^{2}$ |
$1$ |
$49$ |
$49$ |
$48$ |
$48$ |
$48$ |
$48$ |
$48$ |
$48$ |
Solvable - 3 |
| 4960.a |
$F_{32}:C_5$ |
$\AGammaL(1,32)$ |
$2^{5} \cdot 5 \cdot 31$ |
$2 \cdot 5 \cdot 31$ |
$-1$ |
$3$ |
$7$ |
$2$ |
16 |
$1494$ |
$14$ |
$4$ |
$C_1$ |
$F_{32}:C_5$ |
$F_{32}$ |
$C_{5}$ |
$2^{5} \cdot 5 \cdot 31$ |
$1$ |
$32$ |
$32$ |
$31$ |
$31$ |
$31$ |
$31$ |
$31$ |
$31$ |
Solvable - 3 |
| 5256.b |
$F_{73}$ |
$\AGammaL(1,73)$ |
$2^{3} \cdot 3^{2} \cdot 73$ |
$2^{3} \cdot 3^{2} \cdot 73$ |
$-1$ |
$2$ |
$6$ |
$2$ |
73 |
$816$ |
$24$ |
$13$ |
$C_1$ |
$F_{73}$ |
$C_{73}$ |
$C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 73$ |
$1$ |
$73$ |
$73$ |
$72$ |
$72$ |
$72$ |
$72$ |
$72$ |
$72$ |
Solvable - 2 |
| 5760.c |
$\AGammaL(2,4)$ |
$\AGammaL(2,4)$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$7$ |
$2$ |
17 |
$17948$ |
$199$ |
$6$ |
$C_1$ |
$\AGammaL(2,4)$ |
$C_2^4:\GL(2,4)$ |
$C_{2}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$1$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
Non-Solvable - 7 |
| 7832.b |
$F_{89}$ |
$\AGammaL(1,89)$ |
$2^{3} \cdot 11 \cdot 89$ |
$2^{3} \cdot 11 \cdot 89$ |
$-1$ |
$2$ |
$5$ |
$2$ |
89 |
$632$ |
$16$ |
$9$ |
$C_1$ |
$F_{89}$ |
$C_{89}$ |
$C_{88}$ |
$2^{3} \cdot 11 \cdot 89$ |
$1$ |
$89$ |
$89$ |
$88$ |
$88$ |
$88$ |
$88$ |
$88$ |
$88$ |
Solvable - 2 |
| 9312.a |
$F_{97}$ |
$\AGammaL(1,97)$ |
$2^{5} \cdot 3 \cdot 97$ |
$2^{5} \cdot 3 \cdot 97$ |
$-1$ |
$2$ |
$7$ |
$2$ |
97 |
$1080$ |
$24$ |
$13$ |
$C_1$ |
$F_{97}$ |
$C_{97}$ |
$C_{96}$ |
$2^{5} \cdot 3 \cdot 97$ |
$1$ |
$97$ |
$97$ |
$96$ |
$96$ |
$96$ |
$96$ |
$96$ |
$96$ |
Solvable - 2 |
| 10100.a |
$F_{101}$ |
$\AGammaL(1,101)$ |
$2^{2} \cdot 5^{2} \cdot 101$ |
$2^{2} \cdot 5^{2} \cdot 101$ |
$-1$ |
$2$ |
$5$ |
$2$ |
101 |
$818$ |
$18$ |
$10$ |
$C_1$ |
$F_{101}$ |
$C_{101}$ |
$C_{100}$ |
$2^{2} \cdot 5^{2} \cdot 101$ |
$1$ |
$101$ |
$101$ |
$100$ |
$100$ |
$100$ |
$100$ |
$100$ |
$100$ |
Solvable - 2 |
| 11772.b |
$F_{109}$ |
$\AGammaL(1,109)$ |
$2^{2} \cdot 3^{3} \cdot 109$ |
$2^{2} \cdot 3^{3} \cdot 109$ |
$-1$ |
$2$ |
$6$ |
$2$ |
109 |
$1212$ |
$24$ |
$13$ |
$C_1$ |
$F_{109}$ |
$C_{109}$ |
$C_{108}$ |
$2^{2} \cdot 3^{3} \cdot 109$ |
$1$ |
$109$ |
$109$ |
$108$ |
$108$ |
$108$ |
$108$ |
$108$ |
$108$ |
Solvable - 2 |
| 12000.a |
$C_5^2.\GL(2,5)$ |
$\AGammaL(2,5)$ |
$2^{5} \cdot 3 \cdot 5^{3}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$6$ |
$2$ |
29 |
$13640$ |
$132$ |
$7$ |
$C_1$ |
$C_5^2.\GL(2,5)$ |
$C_5^2.\SL(2,5)$ |
$C_{4}$ |
$2^{5} \cdot 3 \cdot 5^{3}$ |
$1$ |
$25$ |
$25$ |
$24$ |
$24$ |
$24$ |
? |
? |
? |
Non-Solvable - 6 |
| 12656.c |
$F_{113}$ |
$\AGammaL(1,113)$ |
$2^{4} \cdot 7 \cdot 113$ |
$2^{4} \cdot 7 \cdot 113$ |
$-1$ |
$2$ |
$6$ |
$2$ |
113 |
$1028$ |
$20$ |
$11$ |
$C_1$ |
$F_{113}$ |
$C_{113}$ |
$C_{112}$ |
$2^{4} \cdot 7 \cdot 113$ |
$1$ |
$113$ |
$113$ |
$112$ |
$112$ |
$112$ |
$112$ |
$112$ |
$112$ |
Solvable - 2 |
| 24192.bb |
$F_{64}:C_6$ |
$\AGammaL(1,64)$ |
$2^{7} \cdot 3^{3} \cdot 7$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$-1$ |
$3$ |
$11$ |
$2$ |
28 |
$26226$ |
$120$ |
$12$ |
$C_1$ |
$F_{64}:C_6$ |
$F_{64}$ |
$C_{6}$ |
$2^{7} \cdot 3^{3} \cdot 7$ |
$1$ |
$64$ |
$64$ |
$63$ |
$63$ |
$63$ |
? |
? |
? |
Solvable - 3 |
| 25920.dn |
$F_{81}:C_4$ |
$\AGammaL(1,81)$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$2^{4} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$11$ |
$2$ |
36 |
$24584$ |
$127$ |
$21$ |
$C_1$ |
$F_{81}:C_4$ |
$C_3^4:C_{40}$ |
$C_{2} \times C_{4}$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$1$ |
$81$ |
$81$ |
$80$ |
$80$ |
$80$ |
$80$ |
$80$ |
$80$ |
Solvable - 3 |
| 29040.bc |
$F_{121}:C_2$ |
$\AGammaL(1,121)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11^{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$3$ |
$8$ |
$2$ |
77 |
$12328$ |
$90$ |
$23$ |
$C_1$ |
$F_{121}:C_2$ |
$C_{11}^2:C_{12}$ |
$C_{2} \times C_{10}$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11^{2}$ |
$1$ |
$121$ |
$121$ |
$120$ |
$120$ |
$120$ |
$120$ |
$120$ |
$120$ |
Solvable - 3 |
| 98784.a |
$C_7^2.\GL(2,7)$ |
$\AGammaL(2,7)$ |
$2^{5} \cdot 3^{2} \cdot 7^{3}$ |
$2^{4} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$6$ |
$2$ |
55 |
$94032$ |
$236$ |
$9$ |
$C_1$ |
$C_7^2.\GL(2,7)$ |
$C_7^2.\SL(2,7)$ |
$C_{6}$ |
$2^{5} \cdot 3^{2} \cdot 7^{3}$ |
$1$ |
$49$ |
$49$ |
$48$ |
$48$ |
$48$ |
? |
? |
? |
Non-Solvable - 6 |
| 303264.a |
$C_3^3:\GL(3,3)$ |
$\AGammaL(3,3)$ |
$2^{5} \cdot 3^{6} \cdot 13$ |
$2^{3} \cdot 3^{2} \cdot 13$ |
$-1$ |
$1$ |
$5$ |
$2$ |
35 |
$1158888$ |
$821$ |
$5$ |
$C_1$ |
$C_3^3:\GL(3,3)$ |
$C_3^3.\SL(3,3)$ |
$C_{2}$ |
$2^{5} \cdot 3^{6} \cdot 13$ |
$1$ |
$27$ |
$27$ |
$26$ |
$26$ |
$26$ |
? |
? |
? |
Non-Solvable - 5 |
| 322560.a |
$C_2^4.A_8$ |
$\AGammaL(4,2)$ |
$2^{10} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$5$ |
$2$ |
25 |
|
|
$3$ |
$C_1$ |
$C_2^4.A_8$ |
$C_2^4.A_8$ |
$C_1$ |
$2^{10} \cdot 3^{2} \cdot 5 \cdot 7$ |
$1$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
? |
? |
? |
Non-Solvable - 5 |
| 677376.a |
$\AGammaL(2,8)$ |
$\AGammaL(2,8)$ |
$2^{9} \cdot 3^{3} \cdot 7^{2}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$9$ |
$2$ |
37 |
$1092031$ |
$345$ |
$6$ |
$C_1$ |
$\AGammaL(2,8)$ |
|
$C_{3}$ |
$2^{9} \cdot 3^{3} \cdot 7^{2}$ |
$1$ |
$64$ |
$64$ |
$63$ |
$63$ |
$63$ |
? |
? |
? |
Non-Solvable - 9 |
| 933120.a |
$\AGammaL(2,9)$ |
$\AGammaL(2,9)$ |
$2^{8} \cdot 3^{6} \cdot 5$ |
$2^{4} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$10$ |
$2$ |
61 |
$3384384$ |
$1284$ |
$12$ |
$C_1$ |
$\AGammaL(2,9)$ |
|
$C_{2}^{2}$ |
$2^{8} \cdot 3^{6} \cdot 5$ |
$1$ |
$81$ |
$81$ |
$80$ |
$80$ |
$80$ |
? |
? |
? |
Non-Solvable - 10 |
| 1597200.a |
$C_{11}^2.\GL(2,11)$ |
$\AGammaL(2,11)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 11^{3}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$6$ |
$2$ |
131 |
$824536$ |
$316$ |
$9$ |
$C_1$ |
$C_{11}^2.\GL(2,11)$ |
$C_{11}^2.\SL(2,11)$ |
$C_{10}$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 11^{3}$ |
$1$ |
$121$ |
$121$ |
$120$ |
$120$ |
$120$ |
? |
? |
? |
Non-Solvable - 6 |
| 4429152.a |
$C_{13}^2.\GL(2,13)$ |
$\AGammaL(2,13)$ |
$2^{5} \cdot 3^{2} \cdot 7 \cdot 13^{3}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$7$ |
$2$ |
181 |
$3094772$ |
$626$ |
$13$ |
$C_1$ |
$C_{13}^2.\GL(2,13)$ |
$C_{13}^2.\SL(2,13)$ |
$C_{12}$ |
$2^{5} \cdot 3^{2} \cdot 7 \cdot 13^{3}$ |
$1$ |
$169$ |
$169$ |
$168$ |
$168$ |
$168$ |
? |
? |
? |
Non-Solvable - 7 |
| 22639104.a |
$C_{17}^2.\GL(2,17)$ |
$\AGammaL(2,17)$ |
$2^{9} \cdot 3^{2} \cdot 17^{3}$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$-1$ |
$1$ |
$8$ |
$2$ |
305 |
$9983366$ |
$612$ |
$11$ |
$C_1$ |
|
|
$C_{16}$ |
$2^{9} \cdot 3^{2} \cdot 17^{3}$ |
$1$ |
$289$ |
$289$ |
$288$ |
$288$ |
$288$ |
? |
? |
? |
Non-Solvable - 8 |
| 23224320.a |
$\AGammaL(3,4)$ |
$\AGammaL(3,4)$ |
$2^{13} \cdot 3^{4} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$10$ |
$2$ |
56 |
|
|
$6$ |
$C_1$ |
$\AGammaL(3,4)$ |
$C_2^6.\GL(3,4)$ |
$C_{2}$ |
$2^{13} \cdot 3^{4} \cdot 5 \cdot 7$ |
$1$ |
$64$ |
$64$ |
$63$ |
$63$ |
$63$ |
? |
? |
? |
Non-Solvable - 10 |
| 44446320.a |
$C_{19}^2.\GL(2,19)$ |
$\AGammaL(2,19)$ |
$2^{4} \cdot 3^{4} \cdot 5 \cdot 19^{3}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$1$ |
$7$ |
$2$ |
379 |
$19612960$ |
$786$ |
$13$ |
$C_1$ |
$C_{19}^2.\GL(2,19)$ |
$C_{19}^2.\SL(2,19)$ |
$C_{18}$ |
$2^{4} \cdot 3^{4} \cdot 5 \cdot 19^{3}$ |
$1$ |
$361$ |
$361$ |
$360$ |
$360$ |
$360$ |
? |
? |
? |
Non-Solvable - 7 |
| 62668800.a |
$\AGammaL(2,16)$ |
$\AGammaL(2,16)$ |
$2^{14} \cdot 3^{2} \cdot 5^{2} \cdot 17$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$2$ |
$13$ |
$2$ |
97 |
|
|
$12$ |
$C_1$ |
$\AGammaL(2,16)$ |
$C_2^8.\GL(2,16)$ |
$C_{4}$ |
$2^{14} \cdot 3^{2} \cdot 5^{2} \cdot 17$ |
$1$ |
$256$ |
$256$ |
$255$ |
$255$ |
$255$ |
? |
? |
? |
Non-Solvable - 13 |
| 186000000.a |
$\AGL(3,5)$ |
$\AGammaL(3,5)$ |
$2^{7} \cdot 3 \cdot 5^{6} \cdot 31$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$6$ |
$2$ |
149 |
|
|
|
$C_1$ |
|
|
$C_{4}$ |
$2^{7} \cdot 3 \cdot 5^{6} \cdot 31$ |
$1$ |
|
$125$ |
$124$ |
$124$ |
$124$ |
? |
? |
? |
Non-Solvable - 6 |
| 1965150720.a |
$\AGL(4,3)$ |
$\AGammaL(4,3)$ |
$2^{9} \cdot 3^{10} \cdot 5 \cdot 13$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$7$ |
$2$ |
113 |
|
|
|
$C_1$ |
$\AGL(4,3)$ |
$\ASL(4,3)$ |
$C_{2}$ |
$2^{9} \cdot 3^{10} \cdot 5 \cdot 13$ |
$1$ |
|
$81$ |
$80$ |
$80$ |
$80$ |
? |
? |
? |
Non-Solvable - 7 |
| 11587955904.a |
$C_7^3.\GL(3,7)$ |
$\AGammaL(3,7)$ |
$2^{6} \cdot 3^{4} \cdot 7^{6} \cdot 19$ |
$2^{4} \cdot 3^{2} \cdot 7 \cdot 19$ |
$-1$ |
$1$ |
$7$ |
$2$ |
391 |
|
|
$9$ |
$C_1$ |
|
|
$C_{6}$ |
$2^{6} \cdot 3^{4} \cdot 7^{6} \cdot 19$ |
$1$ |
$343$ |
$343$ |
$342$ |
$342$ |
$342$ |
? |
? |
? |
Non-Solvable - 7 |
