| 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 |
| 120.34 |
$S_5$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$7$ |
$156$ |
$19$ |
$3$ |
$C_1$ |
$S_5$ |
$A_5$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$1$ |
$5$ |
$5$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Non-Solvable - 2 |
| 336.208 |
$\PGL(2,7)$ |
$2^{4} \cdot 3 \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$9$ |
$413$ |
$23$ |
$3$ |
$C_1$ |
$\PGL(2,7)$ |
$\GL(3,2)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 7$ |
$1$ |
$8$ |
$8$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Non-Solvable - 2 |
| 720.763 |
$S_6$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$11$ |
$1455$ |
$56$ |
$3$ |
$C_1$ |
$S_6$ |
$A_6$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2$ |
$6$ |
$6$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Non-Solvable - 2 |
| 720.764 |
$\PGL(2,9)$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$11$ |
$881$ |
$26$ |
$3$ |
$C_1$ |
$\PGL(2,9)$ |
$A_6$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2$ |
$10$ |
$10$ |
$8$ |
$8$ |
$9$ |
$8$ |
$8$ |
$9$ |
Non-Solvable - 2 |
| 720.765 |
$A_6.C_2$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$8$ |
$793$ |
$25$ |
$3$ |
$C_1$ |
$A_6.C_2$ |
$A_6$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2$ |
$10$ |
$10$ |
$9$ |
$9$ |
$9$ |
$9$ |
$9$ |
$9$ |
Non-Solvable - 2 |
| 1320.133 |
$\PGL(2,11)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$13$ |
$1624$ |
$29$ |
$3$ |
$C_1$ |
$\PGL(2,11)$ |
$\PSL(2,11)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$1$ |
$12$ |
$12$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
Non-Solvable - 2 |
| 1440.5841 |
$S_6:C_2$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$13$ |
$2579$ |
$65$ |
$6$ |
$C_1$ |
$S_6:C_2$ |
$A_6$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3^{2} \cdot 5$ |
$1$ |
$10$ |
$10$ |
$9$ |
$9$ |
$9$ |
$9$ |
$9$ |
$9$ |
Non-Solvable - 3 |
| 1512.779 |
${}^2G(2,3)$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$11$ |
$1154$ |
$25$ |
$3$ |
$C_1$ |
${}^2G(2,3)$ |
$\SL(2,8)$ |
$C_{3}$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$1$ |
$9$ |
$9$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 2 |
| 2184.b |
$\PGL(2,13)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$15$ |
$2466$ |
$30$ |
$3$ |
$C_1$ |
$\PGL(2,13)$ |
$\PSL(2,13)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 13$ |
$1$ |
$14$ |
$14$ |
$12$ |
$12$ |
$13$ |
$12$ |
$12$ |
$13$ |
Non-Solvable - 2 |
| 4896.b |
$\PGL(2,17)$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$2^{4} \cdot 3^{2} \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$19$ |
$5312$ |
$32$ |
$3$ |
$C_1$ |
$\PGL(2,17)$ |
$\PSL(2,17)$ |
$C_{2}$ |
$2^{5} \cdot 3^{2} \cdot 17$ |
$1$ |
$18$ |
$18$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Non-Solvable - 2 |
| 5040.w |
$S_7$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$15$ |
$11300$ |
$96$ |
$3$ |
$C_1$ |
$S_7$ |
$A_7$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$1$ |
$7$ |
$7$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Non-Solvable - 2 |
| 6840.b |
$\PGL(2,19)$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$21$ |
$8084$ |
$36$ |
$3$ |
$C_1$ |
$\PGL(2,19)$ |
$\PSL(2,19)$ |
$C_{2}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$1$ |
$20$ |
$20$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Non-Solvable - 2 |
| 8160.a |
$\SOMinus(4,4)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 17$ |
$2^{2} \cdot 3 \cdot 5 \cdot 17$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$16$ |
$10002$ |
$47$ |
$3$ |
$C_1$ |
$\SOMinus(4,4)$ |
$\SL(2,16)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 17$ |
$2$ |
$17$ |
$17$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Non-Solvable - 2 |
| 11232.b |
$\SL(3,3):C_2$ |
$2^{5} \cdot 3^{3} \cdot 13$ |
$2^{3} \cdot 3 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$15$ |
$19195$ |
$78$ |
$3$ |
$C_1$ |
$\SL(3,3):C_2$ |
$\SL(3,3)$ |
$C_{2}$ |
$2^{5} \cdot 3^{3} \cdot 13$ |
$1$ |
$26$ |
$26$ |
$12$ |
$12$ |
$13$ |
$12$ |
$12$ |
$13$ |
Non-Solvable - 2 |
| 12144.b |
$\PGL(2,23)$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$2^{3} \cdot 3 \cdot 11 \cdot 23$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$25$ |
$12634$ |
$34$ |
$3$ |
$C_1$ |
$\PGL(2,23)$ |
$\PSL(2,23)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 11 \cdot 23$ |
$1$ |
$24$ |
$24$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
Non-Solvable - 2 |
| 15600.b |
$\PGL(2,25)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$27$ |
$17962$ |
$43$ |
$3$ |
$C_1$ |
$\PGL(2,25)$ |
$\PSL(2,25)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2$ |
$26$ |
$26$ |
$24$ |
$24$ |
$25$ |
$24$ |
$24$ |
$25$ |
Non-Solvable - 2 |
| 15600.d |
$\PGOMinus(4,5)$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$18$ |
$31726$ |
$103$ |
$3$ |
$C_1$ |
$\PGOMinus(4,5)$ |
$\PSL(2,25)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2$ |
$26$ |
$26$ |
$13$ |
$13$ |
$13$ |
$13$ |
$13$ |
$13$ |
Non-Solvable - 2 |
| 15600.e |
$\PSL(2,25).C_2$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2^{3} \cdot 3 \cdot 5 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$15$ |
$14514$ |
$39$ |
$3$ |
$C_1$ |
$\PSL(2,25).C_2$ |
$\PSL(2,25)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 13$ |
$2$ |
$26$ |
$26$ |
$25$ |
$25$ |
$25$ |
$25$ |
$25$ |
$25$ |
Non-Solvable - 2 |
| 19656.b |
$\PGL(2,27)$ |
$2^{3} \cdot 3^{3} \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$29$ |
$19062$ |
$32$ |
$3$ |
$C_1$ |
$\PGL(2,27)$ |
$\PSL(2,27)$ |
$C_{2}$ |
$2^{3} \cdot 3^{4} \cdot 7 \cdot 13$ |
$3$ |
$28$ |
$28$ |
$26$ |
$26$ |
$26$ |
$26$ |
$26$ |
$26$ |
Non-Solvable - 2 |
| 24360.b |
$\PGL(2,29)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$31$ |
$28748$ |
$41$ |
$3$ |
$C_1$ |
$\PGL(2,29)$ |
$\PSL(2,29)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 29$ |
$1$ |
$30$ |
$30$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
Non-Solvable - 2 |
| 29760.b |
$\PGL(2,31)$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$2^{5} \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$33$ |
$34359$ |
$44$ |
$3$ |
$C_1$ |
$\PGL(2,31)$ |
$\PSL(2,31)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5 \cdot 31$ |
$1$ |
$32$ |
$32$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
Non-Solvable - 2 |
| 40320.a |
$S_8$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$22$ |
$151221$ |
$296$ |
$3$ |
$C_1$ |
$S_8$ |
$A_8$ |
$C_{2}$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$1$ |
$8$ |
$8$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 2 |
| 40320.n |
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$14$ |
$81694$ |
$102$ |
$3$ |
$C_1$ |
$\PSL(3,4):C_2$ |
$\PSL(3,4)$ |
$C_{2}$ |
$2^{8} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2$ |
$42$ |
$42$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 2 |
| 40320.o |
$\PSL(3,4):C_2$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$14$ |
$100708$ |
$151$ |
$3$ |
$C_1$ |
$\PSL(3,4):C_2$ |
$\PSL(3,4)$ |
$C_{2}$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2 \cdot 3$ |
$42$ |
$42$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 2 |
| 50616.b |
$\PGL(2,37)$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$2^{2} \cdot 3^{2} \cdot 19 \cdot 37$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$39$ |
$48630$ |
$41$ |
$3$ |
$C_1$ |
$\PGL(2,37)$ |
$\PSL(2,37)$ |
$C_{2}$ |
$2^{3} \cdot 3^{2} \cdot 19 \cdot 37$ |
$1$ |
$38$ |
$38$ |
$36$ |
$36$ |
$37$ |
$36$ |
$36$ |
$37$ |
Non-Solvable - 2 |
| 60480.b |
$\PGL(3,4)$ |
$2^{6} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$22$ |
$81220$ |
$100$ |
$3$ |
$C_1$ |
$\PGL(3,4)$ |
$\PSL(3,4)$ |
$C_{3}$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{2}$ |
$21$ |
$21$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 2 |
| 68880.b |
$\PGL(2,41)$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$43$ |
$83364$ |
$49$ |
$3$ |
$C_1$ |
$\PGL(2,41)$ |
$\PSL(2,41)$ |
$C_{2}$ |
$2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 41$ |
$1$ |
$42$ |
$42$ |
$40$ |
$40$ |
$40$ |
$40$ |
$40$ |
$40$ |
Non-Solvable - 2 |
| 79464.b |
$\PGL(2,43)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$2^{2} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$45$ |
$78830$ |
$42$ |
$3$ |
$C_1$ |
$\PGL(2,43)$ |
$\PSL(2,43)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 11 \cdot 43$ |
$1$ |
$44$ |
$44$ |
$42$ |
$42$ |
$42$ |
$42$ |
$42$ |
$42$ |
Non-Solvable - 2 |
| 80640.f |
$\PSL(3,4):C_2^2$ |
$2^{8} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$22$ |
$268959$ |
$288$ |
$6$ |
$C_1$ |
$\PSL(3,4):C_2^2$ |
$\PSL(3,4)$ |
$C_{2}^{2}$ |
$2^{8} \cdot 3^{2} \cdot 5 \cdot 7$ |
$1$ |
$42$ |
$42$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 3 |
| 103776.b |
$\PGL(2,47)$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$2^{4} \cdot 3 \cdot 23 \cdot 47$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$49$ |
$98848$ |
$40$ |
$3$ |
$C_1$ |
$\PGL(2,47)$ |
$\PSL(2,47)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 23 \cdot 47$ |
$1$ |
$48$ |
$48$ |
$46$ |
$46$ |
$46$ |
$46$ |
$46$ |
$46$ |
Non-Solvable - 2 |
| 117600.c |
$\PGL(2,49)$ |
$2^{5} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2^{4} \cdot 3 \cdot 5^{2} \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$51$ |
$143136$ |
$58$ |
$3$ |
$C_1$ |
$\PGL(2,49)$ |
$\PSL(2,49)$ |
$C_{2}$ |
$2^{6} \cdot 3 \cdot 5^{2} \cdot 7^{2}$ |
$2$ |
$50$ |
$50$ |
$48$ |
$48$ |
$49$ |
$48$ |
$48$ |
$49$ |
Non-Solvable - 2 |
| 120960.k |
$\PGL(3,4):C_2$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$20$ |
$247702$ |
$142$ |
$4$ |
$C_1$ |
$\PGL(3,4):C_2$ |
$\PGL(3,4)$ |
$C_{2}$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2$ |
$42$ |
$42$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 3 |
| 120960.l |
$\PSL(3,4):C_6$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$26$ |
$188044$ |
$143$ |
$5$ |
$C_1$ |
$\PSL(3,4):C_6$ |
$\PSL(3,4)$ |
$C_{6}$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2$ |
$42$ |
$42$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 3 |
| 148824.b |
$\PGL(2,53)$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$2^{2} \cdot 3^{3} \cdot 13 \cdot 53$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$55$ |
$136696$ |
$40$ |
$3$ |
$C_1$ |
$\PGL(2,53)$ |
$\PSL(2,53)$ |
$C_{2}$ |
$2^{3} \cdot 3^{3} \cdot 13 \cdot 53$ |
$1$ |
$54$ |
$54$ |
$52$ |
$52$ |
$52$ |
$52$ |
$52$ |
$52$ |
Non-Solvable - 2 |
| 190080.c |
$M_{12}:C_2$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 11$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$21$ |
$538243$ |
$213$ |
$3$ |
$C_1$ |
$M_{12}:C_2$ |
$M_{12}$ |
$C_{2}$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 11$ |
$1$ |
$24$ |
$24$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
Non-Solvable - 2 |
| 205320.b |
$\PGL(2,59)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$2^{2} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$61$ |
$217894$ |
$45$ |
$3$ |
$C_1$ |
$\PGL(2,59)$ |
$\PSL(2,59)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 29 \cdot 59$ |
$1$ |
$60$ |
$60$ |
$58$ |
$58$ |
$58$ |
$58$ |
$58$ |
$58$ |
Non-Solvable - 2 |
| 226920.b |
$\PGL(2,61)$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$2^{2} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$63$ |
$240538$ |
$53$ |
$3$ |
$C_1$ |
$\PGL(2,61)$ |
$\PSL(2,61)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 31 \cdot 61$ |
$1$ |
$62$ |
$62$ |
$60$ |
$60$ |
$61$ |
$60$ |
$60$ |
$61$ |
Non-Solvable - 2 |
| 241920.d |
$\PSL(3,4):D_6$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$28$ |
$898278$ |
$409$ |
$8$ |
$C_1$ |
$\PSL(3,4):D_6$ |
$\PGL(3,4)$ |
$C_{2}^{2}$ |
$2^{8} \cdot 3^{3} \cdot 5 \cdot 7$ |
$1$ |
$42$ |
$42$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Non-Solvable - 4 |
| 300696.b |
$\PGL(2,67)$ |
$2^{3} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$2^{2} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$69$ |
$258296$ |
$42$ |
$3$ |
$C_1$ |
$\PGL(2,67)$ |
$\PSL(2,67)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 11 \cdot 17 \cdot 67$ |
$1$ |
$68$ |
$68$ |
$66$ |
$66$ |
$66$ |
$66$ |
$66$ |
$66$ |
Non-Solvable - 2 |
| 357840.b |
$\PGL(2,71)$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$73$ |
$457109$ |
$60$ |
$3$ |
$C_1$ |
$\PGL(2,71)$ |
$\PSL(2,71)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 71$ |
$1$ |
$72$ |
$72$ |
$70$ |
$70$ |
$70$ |
$70$ |
$70$ |
$70$ |
Non-Solvable - 2 |
| 362880.a |
$S_9$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 7$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$30$ |
$1694723$ |
$554$ |
$3$ |
$C_1$ |
$S_9$ |
$A_9$ |
$C_{2}$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 7$ |
$1$ |
$9$ |
$9$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Non-Solvable - 2 |
| 378000.b |
$\PGU(3,5)$ |
$2^{4} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$34$ |
$367138$ |
$93$ |
$3$ |
$C_1$ |
$\PGU(3,5)$ |
${}^2A(2,5)$ |
$C_{3}$ |
$2^{5} \cdot 3^{3} \cdot 5^{3} \cdot 7$ |
$2$ |
$126$ |
$126$ |
$20$ |
$21$ |
$21$ |
$20$ |
$21$ |
$21$ |
Non-Solvable - 2 |
| 388944.b |
$\PGL(2,73)$ |
$2^{4} \cdot 3^{2} \cdot 37 \cdot 73$ |
$2^{3} \cdot 3^{2} \cdot 37 \cdot 73$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$75$ |
$378593$ |
$53$ |
$3$ |
$C_1$ |
$\PGL(2,73)$ |
$\PSL(2,73)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 37 \cdot 73$ |
$1$ |
$74$ |
$74$ |
$72$ |
$72$ |
$73$ |
$72$ |
$72$ |
$73$ |
Non-Solvable - 2 |
| 492960.b |
$\PGL(2,79)$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$81$ |
$546454$ |
$55$ |
$3$ |
$C_1$ |
$\PGL(2,79)$ |
$\PSL(2,79)$ |
$C_{2}$ |
$2^{5} \cdot 3 \cdot 5 \cdot 13 \cdot 79$ |
$1$ |
$80$ |
$80$ |
$78$ |
$78$ |
$78$ |
$78$ |
$78$ |
$78$ |
Non-Solvable - 2 |
| 524160.a |
$\SOMinus(4,8)$ |
$2^{7} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$46$ |
$885500$ |
$127$ |
$3$ |
$C_1$ |
$\SOMinus(4,8)$ |
$\SL(2,64)$ |
$C_{2}$ |
$2^{7} \cdot 3^{3} \cdot 5 \cdot 7 \cdot 13$ |
$3$ |
$65$ |
$65$ |
$64$ |
$64$ |
$64$ |
$64$ |
$64$ |
$64$ |
Non-Solvable - 2 |
| 531360.c |
$\PGL(2,81)$ |
$2^{5} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{4} \cdot 3 \cdot 5 \cdot 41$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$83$ |
$638830$ |
$63$ |
$3$ |
$C_1$ |
$\PGL(2,81)$ |
$\PSL(2,81)$ |
$C_{2}$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{2}$ |
$82$ |
$82$ |
$80$ |
$80$ |
$81$ |
$80$ |
$80$ |
$81$ |
Non-Solvable - 2 |
| 531360.d |
$\PGOMinus(4,9)$ |
$2^{5} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{3} \cdot 3 \cdot 5 \cdot 41$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$38$ |
$1289128$ |
$187$ |
$3$ |
$C_1$ |
$\PGOMinus(4,9)$ |
$\PSL(2,81)$ |
$C_{2}$ |
$2^{7} \cdot 3^{4} \cdot 5 \cdot 41$ |
$2^{2}$ |
$82$ |
$82$ |
$41$ |
$41$ |
$41$ |
$41$ |
$41$ |
$41$ |
Non-Solvable - 2 |
| 571704.b |
$\PGL(2,83)$ |
$2^{3} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$2^{2} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$85$ |
$535108$ |
$44$ |
$3$ |
$C_1$ |
$\PGL(2,83)$ |
$\PSL(2,83)$ |
$C_{2}$ |
$2^{3} \cdot 3 \cdot 7 \cdot 41 \cdot 83$ |
$1$ |
$84$ |
$84$ |
$82$ |
$82$ |
$82$ |
$82$ |
$82$ |
$82$ |
Non-Solvable - 2 |
| 704880.b |
$\PGL(2,89)$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$91$ |
$839726$ |
$59$ |
$3$ |
$C_1$ |
$\PGL(2,89)$ |
$\PSL(2,89)$ |
$C_{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \cdot 89$ |
$1$ |
$90$ |
$90$ |
$88$ |
$88$ |
$88$ |
$88$ |
$88$ |
$88$ |
Non-Solvable - 2 |
| 887040.a |
$M_{22}:C_2$ |
$2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11$ |
$-1$ |
$1$ |
$2$ |
$2$ |
$21$ |
$3396237$ |
$490$ |
$3$ |
$C_1$ |
$M_{22}:C_2$ |
$M_{22}$ |
$C_{2}$ |
$2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ |
$1$ |
$22$ |
$22$ |
$21$ |
$21$ |
$21$ |
$21$ |
$21$ |
$21$ |
Non-Solvable - 2 |
