| 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 |
$S_3$ |
$\GL(2,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
| 48.29 |
$\GL(2,3)$ |
$\GL(2,3)$ |
$2^{4} \cdot 3$ |
$2^{3} \cdot 3$ |
$-1$ |
$4$ |
$5$ |
$2$ |
8 |
$55$ |
$16$ |
$5$ |
$C_2$ |
$S_4$ |
$\SL(2,3)$ |
$C_{2}$ |
$2^{4} \cdot 3$ |
$2$ |
$8$ |
$8$ |
$2$ |
$4$ |
$4$ |
$2$ |
$4$ |
$4$ |
Solvable - 4 |
| 168.42 |
$\PSL(2,7)$ |
$\GL(3,2)$ |
$2^{3} \cdot 3 \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
6 |
$179$ |
$15$ |
$2$ |
$C_1$ |
$\PSL(2,7)$ |
$\PSL(2,7)$ |
$C_1$ |
$2^{4} \cdot 3 \cdot 7$ |
$2$ |
$7$ |
$7$ |
$3$ |
$6$ |
$6$ |
$3$ |
$6$ |
$6$ |
Simple |
| 180.19 |
$\GL(2,4)$ |
$\GL(2,4)$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
15 |
$148$ |
$21$ |
$4$ |
$C_3$ |
$A_5$ |
$A_5$ |
$C_{3}$ |
$2^{4} \cdot 3 \cdot 5$ |
$2^{2}$ |
$15$ |
$8$ |
$3$ |
$6$ |
$8$ |
$3$ |
$5$ |
$6$ |
Non-Solvable - 2 |
| 480.218 |
$\GL(2,5)$ |
$\GL(2,5)$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$4$ |
$2$ |
24 |
$466$ |
$48$ |
$6$ |
$C_4$ |
$S_5$ |
$\SL(2,5)$ |
$C_{4}$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{2}$ |
$24$ |
$24$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Non-Solvable - 4 |
| 2016.a |
$\GL(2,7)$ |
$\GL(2,7)$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$2^{4} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$4$ |
$2$ |
48 |
|
|
|
$C_6$ |
$\PGL(2,7)$ |
$\SL(2,7)$ |
$C_{6}$ |
$2^{6} \cdot 3 \cdot 7$ |
$2^{2}$ |
|
$19$ |
$6$ |
$12$ |
$16$ |
? |
? |
? |
Non-Solvable - 4 |
| 3528.a |
$\GL(2,8)$ |
$\GL(2,8)$ |
$2^{3} \cdot 3^{2} \cdot 7^{2}$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
63 |
|
|
|
$C_7$ |
$\SL(2,8)$ |
$\SL(2,8)$ |
$C_{7}$ |
$2^{4} \cdot 3^{4} \cdot 7$ |
$2 \cdot 3^{2}$ |
|
$16$ |
$7$ |
$14$ |
$42$ |
? |
? |
? |
Non-Solvable - 2 |
| 5760.a |
$\GL(2,9)$ |
$\GL(2,9)$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{4} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$5$ |
$2$ |
80 |
|
|
|
$C_8$ |
$\PGL(2,9)$ |
$\SL(2,9)$ |
$C_{8}$ |
$2^{8} \cdot 3^{2} \cdot 5$ |
$2^{4}$ |
|
$80$ |
$8$ |
$16$ |
$32$ |
? |
? |
? |
Non-Solvable - 5 |
| 11232.a |
$\GL(3,3)$ |
$\GL(3,3)$ |
$2^{5} \cdot 3^{3} \cdot 13$ |
$2^{3} \cdot 3 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
24 |
$21731$ |
$154$ |
$4$ |
$C_2$ |
$\SL(3,3)$ |
$\SL(3,3)$ |
$C_{2}$ |
$2^{5} \cdot 3^{3} \cdot 13$ |
$2$ |
$26$ |
$15$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Non-Solvable - 2 |
| 13200.a |
$\GL(2,11)$ |
$\GL(2,11)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 11$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$4$ |
$2$ |
120 |
|
|
|
$C_{10}$ |
$\PGL(2,11)$ |
$\SL(2,11)$ |
$C_{10}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 11$ |
$2^{3}$ |
|
$29$ |
$10$ |
$20$ |
$48$ |
? |
? |
? |
Non-Solvable - 4 |
| 20160.a |
$A_8$ |
$\GL(4,2)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
14 |
$48337$ |
$137$ |
$2$ |
$C_1$ |
$A_8$ |
$A_8$ |
$C_1$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2$ |
$8$ |
$8$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Simple |
| 26208.a |
$\GL(2,13)$ |
$\GL(2,13)$ |
$2^{5} \cdot 3^{2} \cdot 7 \cdot 13$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$5$ |
$2$ |
168 |
|
|
|
$C_{12}$ |
$\PGL(2,13)$ |
$\SL(2,13)$ |
$C_{12}$ |
$2^{6} \cdot 3 \cdot 7 \cdot 13$ |
$2^{3}$ |
|
$59$ |
$12$ |
$24$ |
$48$ |
? |
? |
? |
Non-Solvable - 5 |
| 61200.a |
$\GL(2,16)$ |
$\GL(2,16)$ |
$2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$1$ |
$3$ |
$2$ |
255 |
|
|
|
$C_{15}$ |
$\SL(2,16)$ |
$\SL(2,16)$ |
$C_{15}$ |
$2^{9} \cdot 3 \cdot 5 \cdot 17$ |
$2^{5}$ |
|
$25$ |
$15$ |
$30$ |
$128$ |
? |
? |
? |
Non-Solvable - 3 |
| 78336.a |
$\GL(2,17)$ |
$\GL(2,17)$ |
$2^{9} \cdot 3^{2} \cdot 17$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$-1$ |
$1$ |
$6$ |
$2$ |
288 |
|
|
|
$C_{16}$ |
$\PGL(2,17)$ |
$\SL(2,17)$ |
$C_{16}$ |
$2^{9} \cdot 3^{2} \cdot 17$ |
$2^{4}$ |
|
$288$ |
$16$ |
$32$ |
$128$ |
? |
? |
? |
Non-Solvable - 6 |
| 123120.a |
$\GL(2,19)$ |
$\GL(2,19)$ |
$2^{4} \cdot 3^{4} \cdot 5 \cdot 19$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$1$ |
$5$ |
$2$ |
360 |
|
|
|
$C_{18}$ |
$\PGL(2,19)$ |
$\SL(2,19)$ |
$C_{18}$ |
$2^{5} \cdot 3^{3} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3$ |
|
$49$ |
$18$ |
$36$ |
$120$ |
? |
? |
? |
Non-Solvable - 5 |
| 181440.a |
$\GL(3,4)$ |
$\GL(3,4)$ |
$2^{6} \cdot 3^{4} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$3$ |
$2$ |
60 |
$245714$ |
$282$ |
$4$ |
$C_3$ |
$\PGL(3,4)$ |
$\SL(3,4)$ |
$C_{3}$ |
$2^{8} \cdot 3^{4} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3$ |
$63$ |
$63$ |
$21$ |
$42$ |
$42$ |
$21$ |
$42$ |
$42$ |
Non-Solvable - 3 |
| 267168.a |
$\GL(2,23)$ |
$\GL(2,23)$ |
$2^{5} \cdot 3 \cdot 11^{2} \cdot 23$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$1$ |
$4$ |
$2$ |
528 |
|
|
|
$C_{22}$ |
$\PGL(2,23)$ |
$\SL(2,23)$ |
$C_{22}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 23$ |
$2^{2} \cdot 5$ |
|
$59$ |
$22$ |
? |
$240$ |
? |
? |
? |
Non-Solvable - 4 |
| 374400.a |
$\GL(2,25)$ |
$\GL(2,25)$ |
$2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 13$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$6$ |
$2$ |
624 |
|
|
|
$C_{24}$ |
$\PGL(2,25)$ |
$\SL(2,25)$ |
$C_{24}$ |
$2^{9} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{5}$ |
|
$211$ |
$24$ |
? |
$192$ |
? |
? |
? |
Non-Solvable - 6 |
| 511056.a |
$\GL(2,27)$ |
$\GL(2,27)$ |
$2^{4} \cdot 3^{3} \cdot 7 \cdot 13^{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$4$ |
$2$ |
728 |
|
|
|
$C_{26}$ |
$\PGL(2,27)$ |
$\SL(2,27)$ |
$C_{26}$ |
$2^{6} \cdot 3^{5} \cdot 7 \cdot 13$ |
$2^{3} \cdot 3^{2}$ |
|
$69$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 682080.a |
$\GL(2,29)$ |
$\GL(2,29)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 29$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$1$ |
$5$ |
$2$ |
840 |
|
|
|
$C_{28}$ |
$\PGL(2,29)$ |
$\SL(2,29)$ |
$C_{28}$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 29$ |
$2^{3} \cdot 3$ |
|
$127$ |
$28$ |
? |
$336$ |
? |
? |
? |
Non-Solvable - 5 |
| 892800.a |
$\GL(2,31)$ |
$\GL(2,31)$ |
$2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 31$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$5$ |
$2$ |
960 |
|
|
|
$C_{30}$ |
$\PGL(2,31)$ |
$\SL(2,31)$ |
$C_{30}$ |
$2^{10} \cdot 3 \cdot 5 \cdot 31$ |
$2^{4}$ |
|
$72$ |
$30$ |
? |
$256$ |
? |
? |
? |
Non-Solvable - 5 |
| 1014816.a |
$\GL(2,32)$ |
$\GL(2,32)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 31^{2}$ |
$2 \cdot 3 \cdot 11 \cdot 31$ |
$-1$ |
$1$ |
$2$ |
$2$ |
1023 |
|
|
|
$C_{31}$ |
$\SL(2,32)$ |
$\SL(2,32)$ |
$C_{31}$ |
$2^{6} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 5^{2}$ |
|
$64$ |
$31$ |
? |
? |
? |
? |
? |
Non-Solvable - 2 |
| 1488000.a |
$\GL(3,5)$ |
$\GL(3,5)$ |
$2^{7} \cdot 3 \cdot 5^{3} \cdot 31$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$3$ |
$2$ |
120 |
$2756935$ |
$992$ |
$6$ |
$C_4$ |
$\SL(3,5)$ |
$\SL(3,5)$ |
$C_{4}$ |
$2^{7} \cdot 3 \cdot 5^{3} \cdot 31$ |
$2^{2}$ |
$124$ |
$35$ |
$30$ |
$60$ |
$60$ |
? |
? |
? |
Non-Solvable - 3 |
| 1822176.a |
$\GL(2,37)$ |
$\GL(2,37)$ |
$2^{5} \cdot 3^{4} \cdot 19 \cdot 37$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$-1$ |
$1$ |
$6$ |
$2$ |
1368 |
|
|
|
$C_{36}$ |
$\PGL(2,37)$ |
$\SL(2,37)$ |
$C_{36}$ |
$2^{6} \cdot 3^{3} \cdot 19 \cdot 37$ |
$2^{3} \cdot 3$ |
|
$161$ |
$36$ |
? |
? |
? |
? |
? |
Non-Solvable - 6 |
| 2755200.a |
$\GL(2,41)$ |
$\GL(2,41)$ |
$2^{7} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 41$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$-1$ |
$1$ |
$6$ |
$2$ |
1680 |
|
|
|
$C_{40}$ |
$\PGL(2,41)$ |
$\SL(2,41)$ |
$C_{40}$ |
$2^{9} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$2^{5}$ |
|
$341$ |
$40$ |
? |
? |
? |
? |
? |
Non-Solvable - 6 |
| 3337488.a |
$\GL(2,43)$ |
$\GL(2,43)$ |
$2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 11 \cdot 43$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$-1$ |
$1$ |
$5$ |
$2$ |
1848 |
|
|
|
$C_{42}$ |
$\PGL(2,43)$ |
$\SL(2,43)$ |
$C_{42}$ |
$2^{6} \cdot 3^{2} \cdot 7 \cdot 11 \cdot 43$ |
$2^{3} \cdot 3$ |
|
$98$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 5 |
| 4773696.a |
$\GL(2,47)$ |
$\GL(2,47)$ |
$2^{6} \cdot 3 \cdot 23^{2} \cdot 47$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$-1$ |
$1$ |
$4$ |
$2$ |
2208 |
|
|
|
$C_{46}$ |
$\PGL(2,47)$ |
$\SL(2,47)$ |
$C_{46}$ |
$2^{7} \cdot 3 \cdot 11 \cdot 23 \cdot 47$ |
$2^{2} \cdot 11$ |
|
$119$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 5644800.a |
$\GL(2,49)$ |
$\GL(2,49)$ |
$2^{9} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2}$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$1$ |
$7$ |
$2$ |
2400 |
|
|
|
$C_{48}$ |
$\PGL(2,49)$ |
$\SL(2,49)$ |
$C_{48}$ |
$2^{11} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{6}$ |
|
$803$ |
$48$ |
? |
? |
? |
? |
? |
Non-Solvable - 7 |
| 7738848.a |
$\GL(2,53)$ |
$\GL(2,53)$ |
$2^{5} \cdot 3^{3} \cdot 13^{2} \cdot 53$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$-1$ |
$1$ |
$5$ |
$2$ |
2808 |
$862456$ |
$480$ |
$12$ |
$C_{52}$ |
$\PGL(2,53)$ |
$\SL(2,53)$ |
$C_{52}$ |
$2^{7} \cdot 3^{4} \cdot 13 \cdot 53$ |
$2^{4} \cdot 3$ |
$2808$ |
$229$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 5 |
| 9999360.a |
$\GL(5,2)$ |
$\GL(5,2)$ |
$2^{10} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 31$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
27 |
|
|
$2$ |
$C_1$ |
$\GL(5,2)$ |
$\GL(5,2)$ |
$C_1$ |
$2^{11} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 31$ |
$2$ |
$31$ |
$31$ |
$30$ |
$30$ |
$30$ |
? |
? |
? |
Simple |
| 11908560.a |
$\GL(2,59)$ |
$\GL(2,59)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 29^{2} \cdot 59$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$-1$ |
$1$ |
$4$ |
$2$ |
3480 |
$850948$ |
$334$ |
$8$ |
$C_{58}$ |
$\PGL(2,59)$ |
$\SL(2,59)$ |
$C_{58}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 29 \cdot 59$ |
$2^{3} \cdot 7$ |
$3480$ |
$149$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 13615200.a |
$\GL(2,61)$ |
$\GL(2,61)$ |
$2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 31 \cdot 61$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$-1$ |
$1$ |
$6$ |
$2$ |
3720 |
|
|
|
$C_{60}$ |
$\PGL(2,61)$ |
$\SL(2,61)$ |
$C_{60}$ |
$2^{8} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$2^{5}$ |
|
$256$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 6 |
| 16511040.a |
$\GL(2,64)$ |
$\GL(2,64)$ |
$2^{6} \cdot 3^{4} \cdot 5 \cdot 7^{2} \cdot 13$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$4$ |
$2$ |
4095 |
|
|
|
$C_{63}$ |
$\SL(2,64)$ |
$\SL(2,64)$ |
$C_{63}$ |
$2^{9} \cdot 3^{5} \cdot 5 \cdot 7 \cdot 13$ |
$2^{3} \cdot 3^{3}$ |
|
$81$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 19845936.a |
$\GL(2,67)$ |
$\GL(2,67)$ |
$2^{4} \cdot 3^{2} \cdot 11^{2} \cdot 17 \cdot 67$ |
$2^{3} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$-1$ |
$1$ |
$5$ |
$2$ |
4488 |
|
|
|
$C_{66}$ |
$\PGL(2,67)$ |
$\SL(2,67)$ |
$C_{66}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 11 \cdot 17 \cdot 67$ |
$2^{3} \cdot 5$ |
|
$150$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 5 |
| 24261120.a |
$\GL(4,3)$ |
$\GL(4,3)$ |
$2^{9} \cdot 3^{6} \cdot 5 \cdot 13$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$3$ |
$2$ |
78 |
|
|
|
$C_2$ |
$\PGL(4,3)$ |
$\SL(4,3)$ |
$C_{2}$ |
$2^{10} \cdot 3^{6} \cdot 5 \cdot 13$ |
$2^{2}$ |
|
$80$ |
$40$ |
$40$ |
$40$ |
? |
? |
? |
Non-Solvable - 3 |
| 25048800.a |
$\GL(2,71)$ |
$\GL(2,71)$ |
$2^{5} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 71$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$-1$ |
$1$ |
$5$ |
$2$ |
5040 |
|
|
|
$C_{70}$ |
$\PGL(2,71)$ |
$\SL(2,71)$ |
$C_{70}$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 71$ |
$2^{4} \cdot 3$ |
|
$156$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 5 |
| 28003968.a |
$\GL(2,73)$ |
$\GL(2,73)$ |
$2^{7} \cdot 3^{4} \cdot 37 \cdot 73$ |
$2^{4} \cdot 3^{2} \cdot 37 \cdot 73$ |
$-1$ |
$1$ |
$7$ |
$2$ |
5328 |
|
|
|
$C_{72}$ |
$\PGL(2,73)$ |
$\SL(2,73)$ |
$C_{72}$ |
$2^{8} \cdot 3^{3} \cdot 37 \cdot 73$ |
$2^{4} \cdot 3$ |
|
$601$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 7 |
| 33784128.a |
$\GL(3,7)$ |
$\GL(3,7)$ |
$2^{6} \cdot 3^{4} \cdot 7^{3} \cdot 19$ |
$2^{4} \cdot 3^{2} \cdot 7 \cdot 19$ |
$-1$ |
$1$ |
$4$ |
$2$ |
336 |
|
|
|
$C_6$ |
$\PGL(3,7)$ |
$\SL(3,7)$ |
$C_{6}$ |
$2^{6} \cdot 3^{4} \cdot 7^{3} \cdot 19$ |
$2 \cdot 3$ |
|
$173$ |
$57$ |
$114$ |
$114$ |
? |
? |
? |
Non-Solvable - 4 |
| 38450880.a |
$\GL(2,79)$ |
$\GL(2,79)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 13^{2} \cdot 79$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$-1$ |
$1$ |
$5$ |
$2$ |
6240 |
|
|
|
$C_{78}$ |
$\PGL(2,79)$ |
$\SL(2,79)$ |
$C_{78}$ |
$2^{9} \cdot 3^{2} \cdot 5 \cdot 13 \cdot 79$ |
$2^{4} \cdot 3$ |
|
$176$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 5 |
| 42508800.a |
$\GL(2,81)$ |
$\GL(2,81)$ |
$2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 41$ |
$2^{5} \cdot 3 \cdot 5 \cdot 41$ |
$-1$ |
$1$ |
$7$ |
$2$ |
6560 |
|
|
|
$C_{80}$ |
$\PGL(2,81)$ |
$\SL(2,81)$ |
$C_{80}$ |
$2^{13} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{8}$ |
|
$1317$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 7 |
| 46879728.a |
$\GL(2,83)$ |
$\GL(2,83)$ |
$2^{4} \cdot 3 \cdot 7 \cdot 41^{2} \cdot 83$ |
$2^{3} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$-1$ |
$1$ |
$4$ |
$2$ |
6888 |
|
|
|
$C_{82}$ |
$\PGL(2,83)$ |
$\SL(2,83)$ |
$C_{82}$ |
$2^{7} \cdot 3 \cdot 5 \cdot 7 \cdot 41 \cdot 83$ |
$2^{4} \cdot 5$ |
|
$209$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 62029440.a |
$\GL(2,89)$ |
$\GL(2,89)$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 11^{2} \cdot 89$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$-1$ |
$1$ |
$6$ |
$2$ |
7920 |
|
|
|
$C_{88}$ |
$\PGL(2,89)$ |
$\SL(2,89)$ |
$C_{88}$ |
$2^{8} \cdot 3^{2} \cdot 5^{2} \cdot 11 \cdot 89$ |
$2^{4} \cdot 5$ |
|
$731$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 6 |
| 87607296.a |
$\GL(2,97)$ |
$\GL(2,97)$ |
$2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 97$ |
$2^{6} \cdot 3 \cdot 7^{2} \cdot 97$ |
$-1$ |
$1$ |
$8$ |
$2$ |
9408 |
|
|
|
$C_{96}$ |
$\PGL(2,97)$ |
$\SL(2,97)$ |
$C_{96}$ |
$2^{12} \cdot 3 \cdot 7^{2} \cdot 97$ |
$2^{6}$ |
|
$3139$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 8 |
| 103020000.a |
$\GL(2,101)$ |
$\GL(2,101)$ |
$2^{5} \cdot 3 \cdot 5^{4} \cdot 17 \cdot 101$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 17 \cdot 101$ |
$-1$ |
$1$ |
$6$ |
$2$ |
10200 |
|
|
|
$C_{100}$ |
$\PGL(2,101)$ |
$\SL(2,101)$ |
$C_{100}$ |
$2^{7} \cdot 3 \cdot 5^{3} \cdot 17 \cdot 101$ |
$2^{4} \cdot 5$ |
|
$433$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 6 |
| 111447648.a |
$\GL(2,103)$ |
$\GL(2,103)$ |
$2^{5} \cdot 3^{2} \cdot 13 \cdot 17^{2} \cdot 103$ |
$2^{4} \cdot 3 \cdot 13 \cdot 17 \cdot 103$ |
$-1$ |
$1$ |
$5$ |
$2$ |
10608 |
|
|
|
$C_{102}$ |
$\PGL(2,103)$ |
$\SL(2,103)$ |
$C_{102}$ |
$2^{10} \cdot 3 \cdot 13 \cdot 17 \cdot 103$ |
$2^{6}$ |
|
$228$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 5 |
| 115379712.a |
$\GL(3,8)$ |
$\GL(3,8)$ |
$2^{9} \cdot 3^{2} \cdot 7^{3} \cdot 73$ |
$2^{2} \cdot 3^{2} \cdot 7 \cdot 73$ |
$-1$ |
$1$ |
$2$ |
$2$ |
504 |
|
|
|
$C_7$ |
$\SL(3,8)$ |
$\SL(3,8)$ |
$C_{7}$ |
$2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 73$ |
$2^{2} \cdot 3^{2}$ |
|
$80$ |
$72$ |
$144$ |
$432$ |
? |
? |
? |
Non-Solvable - 2 |
| 129843216.a |
$\GL(2,107)$ |
$\GL(2,107)$ |
$2^{4} \cdot 3^{3} \cdot 53^{2} \cdot 107$ |
$2^{3} \cdot 3^{3} \cdot 53 \cdot 107$ |
$-1$ |
$1$ |
$4$ |
$2$ |
11448 |
|
|
|
$C_{106}$ |
$\PGL(2,107)$ |
$\SL(2,107)$ |
$C_{106}$ |
$2^{6} \cdot 3^{3} \cdot 13 \cdot 53 \cdot 107$ |
$2^{3} \cdot 13$ |
|
$269$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 4 |
| 139851360.a |
$\GL(2,109)$ |
$\GL(2,109)$ |
$2^{5} \cdot 3^{6} \cdot 5 \cdot 11 \cdot 109$ |
$2^{3} \cdot 3^{3} \cdot 5 \cdot 11 \cdot 109$ |
$-1$ |
$1$ |
$7$ |
$2$ |
11880 |
|
|
|
$C_{108}$ |
$\PGL(2,109)$ |
$\SL(2,109)$ |
$C_{108}$ |
$2^{6} \cdot 3^{5} \cdot 5 \cdot 11 \cdot 109$ |
$2^{3} \cdot 3^{2}$ |
|
$467$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 7 |
| 161591808.a |
$\GL(2,113)$ |
$\GL(2,113)$ |
$2^{9} \cdot 3 \cdot 7^{2} \cdot 19 \cdot 113$ |
$2^{5} \cdot 3 \cdot 7 \cdot 19 \cdot 113$ |
$-1$ |
$1$ |
$7$ |
$2$ |
12768 |
|
|
|
$C_{112}$ |
$\PGL(2,113)$ |
$\SL(2,113)$ |
$C_{112}$ |
$2^{10} \cdot 3^{2} \cdot 7 \cdot 19 \cdot 113$ |
$2^{5} \cdot 3$ |
|
$1831$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 7 |
| 212572800.a |
$\GL(2,121)$ |
$\GL(2,121)$ |
$2^{7} \cdot 3^{2} \cdot 5^{2} \cdot 11^{2} \cdot 61$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11 \cdot 61$ |
$-1$ |
$1$ |
$7$ |
$2$ |
14640 |
|
|
|
$C_{120}$ |
$\PGL(2,121)$ |
$\SL(2,121)$ |
$C_{120}$ |
$2^{11} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2^{7}$ |
|
$984$ |
? |
? |
? |
? |
? |
? |
Non-Solvable - 7 |
