| 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 |
$S_3$ |
$\PU(2,2)$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
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 |
$S_4$ |
$\PU(2,3)$ |
$2^{3} \cdot 3$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$4$ |
$2$ |
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 |
| 60.5 |
$A_5$ |
$\PU(2,4)$ |
$2^{2} \cdot 3 \cdot 5$ |
$2 \cdot 3 \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 120.34 |
$S_5$ |
$\PU(2,5)$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 216.153 |
$\PU(3,2)$ |
$\PU(3,2)$ |
$2^{3} \cdot 3^{3}$ |
$2^{2} \cdot 3$ |
$-1$ |
$4$ |
$6$ |
$2$ |
10 |
$182$ |
$20$ |
$5$ |
$C_1$ |
$\PU(3,2)$ |
$\PSU(3,2)$ |
$C_{3}$ |
$2^{4} \cdot 3^{3}$ |
$2$ |
$9$ |
$9$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 4 |
| 336.208 |
$\PGL(2,7)$ |
$\PU(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 504.156 |
$\SL(2,8)$ |
$\PU(2,8)$ |
$2^{3} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 720.764 |
$\PGL(2,9)$ |
$\PU(2,9)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
11 |
$881$ |
$26$ |
$3$ |
$C_1$ |
$\PGL(2,9)$ |
$A_6$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2$ |
$10$ |
$10$ |
$8$ |
$8$ |
$9$ |
$8$ |
$8$ |
$9$ |
Non-Solvable - 2 |
| 1320.133 |
$\PGL(2,11)$ |
$\PU(2,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 2184.b |
$\PGL(2,13)$ |
$\PU(2,13)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 4080.a |
$\SL(2,16)$ |
$\PU(2,16)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 17$ |
$2 \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 4896.b |
$\PGL(2,17)$ |
$\PU(2,17)$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 6048.a |
$\SU(3,3)$ |
$\PU(3,3)$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$0$ |
$1$ |
$2$ |
14 |
$5150$ |
$36$ |
$2$ |
$C_1$ |
$\SU(3,3)$ |
$\SU(3,3)$ |
$C_1$ |
$2^{6} \cdot 3^{3} \cdot 7$ |
$2$ |
$28$ |
$28$ |
$6$ |
$7$ |
$7$ |
$6$ |
$7$ |
$7$ |
Simple |
| 6840.b |
$\PGL(2,19)$ |
$\PU(2,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 12144.b |
$\PGL(2,23)$ |
$\PU(2,23)$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 15600.b |
$\PGL(2,25)$ |
$\PU(2,25)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
27 |
$17962$ |
$43$ |
$3$ |
$C_1$ |
$\PGL(2,25)$ |
$\PSL(2,25)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2$ |
$26$ |
$26$ |
$24$ |
$24$ |
$25$ |
$24$ |
$24$ |
$25$ |
Non-Solvable - 2 |
| 19656.b |
$\PGL(2,27)$ |
$\PU(2,27)$ |
$2^{3} \cdot 3^{3} \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
29 |
$19062$ |
$32$ |
$3$ |
$C_1$ |
$\PGL(2,27)$ |
$\PSL(2,27)$ |
$C_{2}$ |
$2^{3} \cdot 3^{4} \cdot 7 \cdot 13$ |
$3$ |
$28$ |
$28$ |
$26$ |
$26$ |
$26$ |
$26$ |
$26$ |
$26$ |
Non-Solvable - 2 |
| 24360.b |
$\PGL(2,29)$ |
$\PU(2,29)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 25920.a |
$\SU(4,2)$ |
$\PU(4,2)$ |
$2^{6} \cdot 3^{4} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 29760.b |
$\PGL(2,31)$ |
$\PU(2,31)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2^{5} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 32736.a |
$\SL(2,32)$ |
$\PU(2,32)$ |
$2^{5} \cdot 3 \cdot 11 \cdot 31$ |
$2 \cdot 3 \cdot 11 \cdot 31$ |
$-1$ |
$0$ |
$1$ |
$2$ |
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 |
| 50616.b |
$\PGL(2,37)$ |
$\PU(2,37)$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$2^{2} \cdot 3^{2} \cdot 19 \cdot 37$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 62400.a |
$\SU(3,4)$ |
$\PU(3,4)$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
22 |
$31373$ |
$34$ |
$2$ |
$C_1$ |
$\SU(3,4)$ |
$\SU(3,4)$ |
$C_1$ |
$2^{8} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2}$ |
$65$ |
$65$ |
$12$ |
$24$ |
$24$ |
$12$ |
$24$ |
$24$ |
Simple |
| 68880.b |
$\PGL(2,41)$ |
$\PU(2,41)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
$\PGL(2,43)$ |
$\PU(2,43)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
$\PGL(2,47)$ |
$\PU(2,47)$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$2^{4} \cdot 3 \cdot 23 \cdot 47$ |
$-1$ |
$1$ |
$2$ |
$2$ |
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 |
| 117600.c |
$\PGL(2,49)$ |
$\PU(2,49)$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
51 |
$143136$ |
$58$ |
$3$ |
$C_1$ |
$\PGL(2,49)$ |
$\PSL(2,49)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2$ |
$50$ |
$50$ |
$48$ |
$48$ |
$49$ |
$48$ |
$48$ |
$49$ |
Non-Solvable - 2 |
| 148824.b |
$\PGL(2,53)$ |
$\PU(2,53)$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$2^{2} \cdot 3^{3} \cdot 13 \cdot 53$ |
$-1$ |
$1$ |
$2$ |
$2$ |
55 |
$136696$ |
$40$ |
$3$ |
$C_1$ |
$\PGL(2,53)$ |
$\PSL(2,53)$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$1$ |
$54$ |
$54$ |
$52$ |
$52$ |
$52$ |
$52$ |
$52$ |
$52$ |
Non-Solvable - 2 |
| 205320.b |
$\PGL(2,59)$ |
$\PU(2,59)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$2^{2} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$-1$ |
$1$ |
$2$ |
$2$ |
61 |
$217894$ |
$45$ |
$3$ |
$C_1$ |
$\PGL(2,59)$ |
$\PSL(2,59)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$1$ |
$60$ |
$60$ |
$58$ |
$58$ |
$58$ |
$58$ |
$58$ |
$58$ |
Non-Solvable - 2 |
| 226920.b |
$\PGL(2,61)$ |
$\PU(2,61)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$-1$ |
$1$ |
$2$ |
$2$ |
63 |
$240538$ |
$53$ |
$3$ |
$C_1$ |
$\PGL(2,61)$ |
$\PSL(2,61)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$1$ |
$62$ |
$62$ |
$60$ |
$60$ |
$61$ |
$60$ |
$60$ |
$61$ |
Non-Solvable - 2 |
| 262080.a |
$\SL(2,64)$ |
$\PU(2,64)$ |
$2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$0$ |
$1$ |
$2$ |
65 |
$360787$ |
$76$ |
$2$ |
$C_1$ |
$\SL(2,64)$ |
$\SL(2,64)$ |
$C_1$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13$ |
$2 \cdot 3$ |
$65$ |
$65$ |
$63$ |
$63$ |
$64$ |
$63$ |
$63$ |
$64$ |
Simple |
| 300696.b |
$\PGL(2,67)$ |
$\PU(2,67)$ |
$2^{3} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$2^{2} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$-1$ |
$1$ |
$2$ |
$2$ |
69 |
$258296$ |
$42$ |
$3$ |
$C_1$ |
$\PGL(2,67)$ |
$\PSL(2,67)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$1$ |
$68$ |
$68$ |
$66$ |
$66$ |
$66$ |
$66$ |
$66$ |
$66$ |
Non-Solvable - 2 |
| 357840.b |
$\PGL(2,71)$ |
$\PU(2,71)$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$-1$ |
$1$ |
$2$ |
$2$ |
73 |
$457109$ |
$60$ |
$3$ |
$C_1$ |
$\PGL(2,71)$ |
$\PSL(2,71)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$1$ |
$72$ |
$72$ |
$70$ |
$70$ |
$70$ |
$70$ |
$70$ |
$70$ |
Non-Solvable - 2 |
| 378000.b |
$\PU(3,5)$ |
$\PU(3,5)$ |
$2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
34 |
$367138$ |
$93$ |
$3$ |
$C_1$ |
$\PU(3,5)$ |
$\PSU(3,5)$ |
$C_{3}$ |
$2^{5} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2$ |
$126$ |
$126$ |
$20$ |
$21$ |
$21$ |
$20$ |
$21$ |
$21$ |
Non-Solvable - 2 |
| 388944.b |
$\PGL(2,73)$ |
$\PU(2,73)$ |
$2^{4} \cdot 3^{2} \cdot 37 \cdot 73$ |
$2^{3} \cdot 3^{2} \cdot 37 \cdot 73$ |
$-1$ |
$1$ |
$2$ |
$2$ |
75 |
$378593$ |
$53$ |
$3$ |
$C_1$ |
$\PGL(2,73)$ |
$\PSL(2,73)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 37 \cdot 73$ |
$1$ |
$74$ |
$74$ |
$72$ |
$72$ |
$73$ |
$72$ |
$72$ |
$73$ |
Non-Solvable - 2 |
| 492960.b |
$\PGL(2,79)$ |
$\PU(2,79)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$-1$ |
$1$ |
$2$ |
$2$ |
81 |
$546454$ |
$55$ |
$3$ |
$C_1$ |
$\PGL(2,79)$ |
$\PSL(2,79)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$1$ |
$80$ |
$80$ |
$78$ |
$78$ |
$78$ |
$78$ |
$78$ |
$78$ |
Non-Solvable - 2 |
| 531360.c |
$\PGL(2,81)$ |
$\PU(2,81)$ |
$2^{5} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{4} \cdot 3 \cdot 5 \cdot 41$ |
$-1$ |
$1$ |
$2$ |
$2$ |
83 |
$638830$ |
$63$ |
$3$ |
$C_1$ |
$\PGL(2,81)$ |
$\PSL(2,81)$ |
$C_{2}$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{2}$ |
$82$ |
$82$ |
$80$ |
$80$ |
$81$ |
$80$ |
$80$ |
$81$ |
Non-Solvable - 2 |
| 571704.b |
$\PGL(2,83)$ |
$\PU(2,83)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$2^{2} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$-1$ |
$1$ |
$2$ |
$2$ |
85 |
$535108$ |
$44$ |
$3$ |
$C_1$ |
$\PGL(2,83)$ |
$\PSL(2,83)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$1$ |
$84$ |
$84$ |
$82$ |
$82$ |
$82$ |
$82$ |
$82$ |
$82$ |
Non-Solvable - 2 |
| 704880.b |
$\PGL(2,89)$ |
$\PU(2,89)$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$-1$ |
$1$ |
$2$ |
$2$ |
91 |
$839726$ |
$59$ |
$3$ |
$C_1$ |
$\PGL(2,89)$ |
$\PSL(2,89)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$1$ |
$90$ |
$90$ |
$88$ |
$88$ |
$88$ |
$88$ |
$88$ |
$88$ |
Non-Solvable - 2 |
| 912576.b |
$\PGL(2,97)$ |
$\PU(2,97)$ |
$2^{6} \cdot 3 \cdot 7^{2} \cdot 97$ |
$2^{5} \cdot 3 \cdot 7^{2} \cdot 97$ |
$-1$ |
$1$ |
$2$ |
$2$ |
99 |
$929954$ |
$59$ |
$3$ |
$C_1$ |
$\PGL(2,97)$ |
$\PSL(2,97)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 7^{2} \cdot 97$ |
$1$ |
$98$ |
$98$ |
$96$ |
$96$ |
$97$ |
$96$ |
$96$ |
$97$ |
Non-Solvable - 2 |
| 1030200.b |
$\PGL(2,101)$ |
$\PU(2,101)$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 17 \cdot 101$ |
$2^{2} \cdot 3 \cdot 5^{2} \cdot 17 \cdot 101$ |
$-1$ |
$1$ |
$2$ |
$2$ |
103 |
$1015466$ |
$52$ |
$3$ |
$C_1$ |
$\PGL(2,101)$ |
$\PSL(2,101)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5^{2} \cdot 17 \cdot 101$ |
$1$ |
$102$ |
$102$ |
$100$ |
$100$ |
$100$ |
$100$ |
$100$ |
$100$ |
Non-Solvable - 2 |
| 1092624.b |
$\PGL(2,103)$ |
$\PU(2,103)$ |
$2^{4} \cdot 3 \cdot 13 \cdot 17 \cdot 103$ |
$2^{3} \cdot 3 \cdot 13 \cdot 17 \cdot 103$ |
$-1$ |
$1$ |
$2$ |
$2$ |
105 |
$969344$ |
$48$ |
$3$ |
$C_1$ |
$\PGL(2,103)$ |
$\PSL(2,103)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 13 \cdot 17 \cdot 103$ |
$1$ |
$104$ |
$104$ |
$102$ |
$102$ |
$102$ |
$102$ |
$102$ |
$102$ |
Non-Solvable - 2 |
| 1224936.b |
$\PGL(2,107)$ |
$\PU(2,107)$ |
$2^{3} \cdot 3^{3} \cdot 53 \cdot 107$ |
$2^{2} \cdot 3^{3} \cdot 53 \cdot 107$ |
$-1$ |
$1$ |
$2$ |
$2$ |
109 |
$1072896$ |
$44$ |
$3$ |
$C_1$ |
$\PGL(2,107)$ |
$\PSL(2,107)$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 53 \cdot 107$ |
$1$ |
$108$ |
$108$ |
$106$ |
$106$ |
$106$ |
$106$ |
$106$ |
$106$ |
Non-Solvable - 2 |
| 1294920.b |
$\PGL(2,109)$ |
$\PU(2,109)$ |
$2^{3} \cdot 3^{3} \cdot 5 \cdot 11 \cdot 109$ |
$2^{2} \cdot 3^{3} \cdot 5 \cdot 11 \cdot 109$ |
$-1$ |
$1$ |
$2$ |
$2$ |
111 |
$1461378$ |
$63$ |
$3$ |
$C_1$ |
$\PGL(2,109)$ |
$\PSL(2,109)$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 5 \cdot 11 \cdot 109$ |
$1$ |
$110$ |
$110$ |
$108$ |
$108$ |
$109$ |
$108$ |
$108$ |
$109$ |
Non-Solvable - 2 |
| 1442784.b |
$\PGL(2,113)$ |
$\PU(2,113)$ |
$2^{5} \cdot 3 \cdot 7 \cdot 19 \cdot 113$ |
$2^{4} \cdot 3 \cdot 7 \cdot 19 \cdot 113$ |
$-1$ |
$1$ |
$2$ |
$2$ |
115 |
$1416016$ |
$56$ |
$3$ |
$C_1$ |
$\PGL(2,113)$ |
$\PSL(2,113)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 7 \cdot 19 \cdot 113$ |
$1$ |
$114$ |
$114$ |
$112$ |
$112$ |
$112$ |
$112$ |
$112$ |
$112$ |
Non-Solvable - 2 |
| 1771440.c |
$\PGL(2,121)$ |
$\PU(2,121)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 61$ |
$-1$ |
$1$ |
$2$ |
$2$ |
123 |
$2009654$ |
$75$ |
$3$ |
$C_1$ |
$\PGL(2,121)$ |
$\PSL(2,121)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 11^{2} \cdot 61$ |
$2$ |
$122$ |
$122$ |
$120$ |
$120$ |
$121$ |
$120$ |
$120$ |
$121$ |
Non-Solvable - 2 |
| 1953000.b |
$\PGL(2,125)$ |
$\PU(2,125)$ |
$2^{3} \cdot 3^{2} \cdot 5^{3} \cdot 7 \cdot 31$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 31$ |
$-1$ |
$1$ |
$2$ |
$2$ |
127 |
$2140856$ |
$58$ |
$3$ |
$C_1$ |
$\PGL(2,125)$ |
$\PSL(2,125)$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 5^{3} \cdot 7 \cdot 31$ |
$3$ |
$126$ |
$126$ |
$124$ |
$124$ |
$124$ |
$124$ |
$124$ |
$124$ |
Non-Solvable - 2 |
| 2048256.b |
$\PGL(2,127)$ |
$\PU(2,127)$ |
$2^{8} \cdot 3^{2} \cdot 7 \cdot 127$ |
$2^{7} \cdot 3^{2} \cdot 7 \cdot 127$ |
$-1$ |
$1$ |
$2$ |
$2$ |
129 |
$2162825$ |
$63$ |
$3$ |
$C_1$ |
$\PGL(2,127)$ |
$\PSL(2,127)$ |
$C_{2}$ |
$2^{8} \cdot 3^{2} \cdot 7 \cdot 127$ |
$1$ |
$128$ |
$128$ |
$126$ |
$126$ |
$126$ |
$126$ |
$126$ |
$126$ |
Non-Solvable - 2 |
| 2097024.a |
$\SL(2,128)$ |
$\PU(2,128)$ |
$2^{7} \cdot 3 \cdot 43 \cdot 127$ |
$2 \cdot 3 \cdot 43 \cdot 127$ |
$-1$ |
$0$ |
$1$ |
$2$ |
129 |
$4191262$ |
$242$ |
$2$ |
$C_1$ |
$\SL(2,128)$ |
$\SL(2,128)$ |
$C_1$ |
$2^{7} \cdot 3 \cdot 7 \cdot 43 \cdot 127$ |
$7$ |
$129$ |
$129$ |
$127$ |
$127$ |
$127$ |
? |
? |
? |
Simple |
| 2247960.b |
$\PGL(2,131)$ |
$\PU(2,131)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \cdot 131$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \cdot 131$ |
$-1$ |
$1$ |
$2$ |
$2$ |
133 |
$2422594$ |
$59$ |
$3$ |
$C_1$ |
$\PGL(2,131)$ |
$\PSL(2,131)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11 \cdot 13 \cdot 131$ |
$1$ |
$132$ |
$132$ |
$130$ |
$130$ |
$130$ |
$130$ |
$130$ |
$130$ |
Non-Solvable - 2 |
