| 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 |
| 720.767 |
$S_3\times S_5$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$21$ |
$2088$ |
$121$ |
$10$ |
$C_1$ |
$S_3\times S_5$ |
$\GL(2,4)$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{2} \cdot 5$ |
$1$ |
$15$ |
$8$ |
$8$ |
$8$ |
$8$ |
$6$ |
$6$ |
$6$ |
Non-Solvable - 4 |
| 936.167 |
$S_3\times F_{13}$ |
$2^{3} \cdot 3^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$39$ |
$740$ |
$70$ |
$25$ |
$C_1$ |
$S_3\times F_{13}$ |
$C_{39}$ |
$C_{2} \times C_{12}$ |
$2^{3} \cdot 3^{2} \cdot 13$ |
$1$ |
$39$ |
$16$ |
$24$ |
$24$ |
$24$ |
$14$ |
$14$ |
$14$ |
Solvable - 2 |
| 1008.885 |
$F_8:C_3\times S_3$ |
$2^{4} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$24$ |
$1062$ |
$64$ |
$12$ |
$C_1$ |
$F_8:C_3\times S_3$ |
$C_3\times F_8$ |
$C_{6}$ |
$2^{4} \cdot 3^{2} \cdot 7$ |
$1$ |
$24$ |
$11$ |
$14$ |
$14$ |
$14$ |
$9$ |
$9$ |
$9$ |
Solvable - 3 |
| 1008.886 |
$S_4\times F_7$ |
$2^{4} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$35$ |
$1548$ |
$140$ |
$22$ |
$C_1$ |
$S_4\times F_7$ |
$C_7\times A_4$ |
$C_{2} \times C_{6}$ |
$2^{4} \cdot 3^{2} \cdot 7$ |
$1$ |
$28$ |
$11$ |
$18$ |
$18$ |
$18$ |
$9$ |
$9$ |
$9$ |
Solvable - 3 |
| 1080.271 |
$D_{45}:C_{12}$ |
$2^{3} \cdot 3^{3} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$50$ |
$816$ |
$102$ |
$32$ |
$C_1$ |
$D_{45}:C_{12}$ |
$C_{45}$ |
$C_{2} \times C_{12}$ |
$2^{3} \cdot 3^{3} \cdot 5$ |
$1$ |
$45$ |
$14$ |
$24$ |
$24$ |
$24$ |
$10$ |
$10$ |
$10$ |
Solvable - 2 |
| 1200.946 |
$\AGammaL(1,25)$ |
$2^{4} \cdot 3 \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$20$ |
$984$ |
$48$ |
$14$ |
$C_1$ |
$\AGammaL(1,25)$ |
$C_5^2:C_6$ |
$C_{2} \times C_{4}$ |
$2^{4} \cdot 3 \cdot 5^{2}$ |
$1$ |
$25$ |
$25$ |
$24$ |
$24$ |
$24$ |
$24$ |
$24$ |
$24$ |
Solvable - 3 |
| 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 |
| 2016.cw |
$S_3\times \PGL(2,7)$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$27$ |
$5826$ |
$149$ |
$10$ |
$C_1$ |
$S_3\times \PGL(2,7)$ |
$C_3\times \GL(3,2)$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3^{2} \cdot 7$ |
$1$ |
$24$ |
$11$ |
$12$ |
$12$ |
$12$ |
$8$ |
$8$ |
$8$ |
Non-Solvable - 4 |
| 2052.s |
$S_3\times F_{19}$ |
$2^{2} \cdot 3^{3} \cdot 19$ |
$2 \cdot 3^{2} \cdot 19$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$57$ |
$1012$ |
$68$ |
$24$ |
$C_1$ |
$S_3\times F_{19}$ |
$C_{57}$ |
$C_{2} \times C_{18}$ |
$2^{2} \cdot 3^{3} \cdot 19$ |
$1$ |
$57$ |
$22$ |
$36$ |
$36$ |
$36$ |
$20$ |
$20$ |
$20$ |
Solvable - 2 |
| 2200.be |
$F_5\times F_{11}$ |
$2^{3} \cdot 5^{2} \cdot 11$ |
$2^{2} \cdot 5 \cdot 11$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$55$ |
$916$ |
$68$ |
$24$ |
$C_1$ |
$F_5\times F_{11}$ |
$C_{55}$ |
$C_{2} \times C_{20}$ |
$2^{3} \cdot 5^{2} \cdot 11$ |
$1$ |
$55$ |
$16$ |
$40$ |
$40$ |
$40$ |
$14$ |
$14$ |
$14$ |
Solvable - 2 |
| 2268.o |
$C_{63}:C_6^2$ |
$2^{2} \cdot 3^{4} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$70$ |
$2456$ |
$220$ |
$53$ |
$C_1$ |
$C_{63}:C_6^2$ |
$C_{63}$ |
$C_{6}^{2}$ |
$2^{2} \cdot 3^{4} \cdot 7$ |
$1$ |
$63$ |
$16$ |
$36$ |
$36$ |
$36$ |
$12$ |
$12$ |
$12$ |
Solvable - 2 |
| 2400.db |
$F_5\times S_5$ |
$2^{5} \cdot 3 \cdot 5^{2}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$35$ |
$5376$ |
$199$ |
$14$ |
$C_1$ |
$F_5\times S_5$ |
$C_5\times A_5$ |
$C_{2} \times C_{4}$ |
$2^{5} \cdot 3 \cdot 5^{2}$ |
$1$ |
$25$ |
$10$ |
$16$ |
$16$ |
$16$ |
$8$ |
$8$ |
$8$ |
Non-Solvable - 5 |
| 2400.dc |
$C_5^2:\GU(2,3)$ |
$2^{5} \cdot 3 \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$20$ |
$2064$ |
$63$ |
$9$ |
$C_1$ |
$C_5^2:\GU(2,3)$ |
$C_5^2:\SL(2,3)$ |
$C_{4}$ |
$2^{5} \cdot 3 \cdot 5^{2}$ |
$1$ |
$25$ |
$25$ |
$24$ |
$24$ |
$24$ |
$24$ |
$24$ |
$24$ |
Solvable - 5 |
| 2880.dv |
$S_4\times S_5$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$35$ |
$17070$ |
$467$ |
$13$ |
$C_1$ |
$S_4\times S_5$ |
$A_4\times A_5$ |
$C_{2}^{2}$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$1$ |
$20$ |
$9$ |
$12$ |
$12$ |
$12$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 6 |
| 2880.fk |
$F_5\times F_9:C_2$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$9$ |
$3$ |
$45$ |
$6108$ |
$298$ |
$48$ |
$C_1$ |
$F_5\times F_9:C_2$ |
$C_3^2:C_{20}$ |
$C_{2}^{2} \times C_{4}$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$1$ |
$45$ |
$14$ |
$32$ |
$32$ |
$32$ |
$12$ |
$12$ |
$12$ |
Solvable - 3 |
| 2880.hl |
$S_3\times F_5\times S_4$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$9$ |
$3$ |
$75$ |
$15912$ |
$964$ |
$70$ |
$C_1$ |
$S_3\times F_5\times S_4$ |
$A_4\times C_{15}$ |
$C_{2}^{2} \times C_{4}$ |
$2^{6} \cdot 3^{2} \cdot 5$ |
$1$ |
$60$ |
$12$ |
$24$ |
$24$ |
$24$ |
$9$ |
$9$ |
$9$ |
Solvable - 3 |
| 3000.cl |
$D_{75}:C_{20}$ |
$2^{3} \cdot 3 \cdot 5^{3}$ |
$2^{2} \cdot 3 \cdot 5^{2}$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$78$ |
$1324$ |
$100$ |
$31$ |
$C_1$ |
$D_{75}:C_{20}$ |
$C_{75}$ |
$C_{2} \times C_{20}$ |
$2^{3} \cdot 3 \cdot 5^{3}$ |
$1$ |
$75$ |
$28$ |
$40$ |
$40$ |
$40$ |
$22$ |
$22$ |
$22$ |
Solvable - 2 |
| 3024.r |
$\SL(2,8):C_6$ |
$2^{4} \cdot 3^{3} \cdot 7$ |
$2 \cdot 3^{2} \cdot 7$ |
$-1$ |
$1$ |
$3$ |
$2$ |
$22$ |
$3234$ |
$61$ |
$6$ |
$C_2$ |
${}^2G(2,3)$ |
$\SL(2,8)$ |
$C_{6}$ |
$2^{3} \cdot 3^{3} \cdot 7$ |
$1$ |
$18$ |
$11$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Non-Solvable - 3 |
| 3528.br |
$F_7\wr C_2$ |
$2^{3} \cdot 3^{2} \cdot 7^{2}$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$35$ |
$3668$ |
$114$ |
$19$ |
$C_1$ |
$F_7\wr C_2$ |
$C_7:F_7$ |
$C_{2} \times C_{6}$ |
$2^{3} \cdot 3^{2} \cdot 7^{2}$ |
$1$ |
$14$ |
$14$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Solvable - 3 |
| 3744.q |
$S_4\times F_{13}$ |
$2^{5} \cdot 3^{2} \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$65$ |
$4876$ |
$236$ |
$32$ |
$C_1$ |
$S_4\times F_{13}$ |
$A_4\times C_{13}$ |
$C_{2} \times C_{12}$ |
$2^{5} \cdot 3^{2} \cdot 13$ |
$1$ |
$52$ |
$17$ |
$36$ |
$36$ |
$36$ |
$15$ |
$15$ |
$15$ |
Solvable - 3 |
| 4032.cm |
$F_8:C_3\times S_4$ |
$2^{6} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$9$ |
$2$ |
$40$ |
$7494$ |
$209$ |
$16$ |
$C_1$ |
$F_8:C_3\times S_4$ |
$A_4\times F_8$ |
$C_{6}$ |
$2^{6} \cdot 3^{2} \cdot 7$ |
$1$ |
$32$ |
$12$ |
$21$ |
$21$ |
$21$ |
$10$ |
$10$ |
$10$ |
Solvable - 3 |
| 4320.bx |
$C_3.S_6:C_2$ |
$2^{5} \cdot 3^{3} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$1$ |
$4$ |
$2$ |
$20$ |
$8949$ |
$117$ |
$7$ |
$C_1$ |
$C_3.S_6:C_2$ |
$C_3.A_6$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3^{3} \cdot 5$ |
$1$ |
$36$ |
$36$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Non-Solvable - 4 |
| 4704.cb |
$C_7^2:(C_3\times \SD_{32})$ |
$2^{5} \cdot 3 \cdot 7^{2}$ |
$2^{4} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$35$ |
$2880$ |
$62$ |
$17$ |
$C_1$ |
$C_7^2:(C_3\times \SD_{32})$ |
$C_7^2:C_8$ |
$C_{2} \times C_{6}$ |
$2^{5} \cdot 3 \cdot 7^{2}$ |
$1$ |
$49$ |
$49$ |
$48$ |
$48$ |
$48$ |
$48$ |
$48$ |
$48$ |
Solvable - 3 |
| 4800.bn |
$F_5^2:D_6$ |
$2^{6} \cdot 3 \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$9$ |
$3$ |
$60$ |
$13972$ |
$502$ |
$56$ |
$C_1$ |
$F_5^2:D_6$ |
$C_{15}:F_5$ |
$C_{2}^{2} \times C_{4}$ |
$2^{6} \cdot 3 \cdot 5^{2}$ |
$1$ |
$30$ |
$13$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 3 |
| 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 |
| 5040.x |
$F_7\times S_5$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$49$ |
$8584$ |
$242$ |
$17$ |
$C_1$ |
$F_7\times S_5$ |
$C_7\times A_5$ |
$C_{2} \times C_{6}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$1$ |
$35$ |
$12$ |
$24$ |
$24$ |
$24$ |
$10$ |
$10$ |
$10$ |
Non-Solvable - 5 |
| 5040.bh |
$S_3\times F_5\times F_7$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$8$ |
$3$ |
$105$ |
$7656$ |
$464$ |
$98$ |
$C_1$ |
$S_3\times F_5\times F_7$ |
$C_{105}$ |
$C_{2}^{2} \times C_{12}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ |
$1$ |
$105$ |
$15$ |
$48$ |
$48$ |
$48$ |
$12$ |
$12$ |
$12$ |
Solvable - 2 |
| 5256.b |
$F_{73}$ |
$2^{3} \cdot 3^{2} \cdot 73$ |
$2^{3} \cdot 3^{2} \cdot 73$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$73$ |
$816$ |
$24$ |
$13$ |
$C_1$ |
$F_{73}$ |
$C_{73}$ |
$C_{72}$ |
$2^{3} \cdot 3^{2} \cdot 73$ |
$1$ |
$73$ |
$73$ |
$72$ |
$72$ |
$72$ |
$72$ |
$72$ |
$72$ |
Solvable - 2 |
| 5760.c |
$\AGammaL(2,4)$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$17$ |
$17948$ |
$199$ |
$6$ |
$C_1$ |
$\AGammaL(2,4)$ |
$C_2^4:\GL(2,4)$ |
$C_{2}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$1$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
Non-Solvable - 7 |
| 5760.ie |
$F_{16}:C_4\times S_3$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$10$ |
$2$ |
$39$ |
$14272$ |
$305$ |
$27$ |
$C_1$ |
$F_{16}:C_4\times S_3$ |
$C_3\times F_{16}$ |
$C_{2} \times C_{4}$ |
$2^{7} \cdot 3^{2} \cdot 5$ |
$1$ |
$48$ |
$19$ |
$30$ |
$30$ |
$30$ |
$17$ |
$17$ |
$17$ |
Solvable - 3 |
| 5940.d |
$D_{99}:C_{30}$ |
$2^{2} \cdot 3^{3} \cdot 5 \cdot 11$ |
$2 \cdot 3^{2} \cdot 5 \cdot 11$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$110$ |
$1992$ |
$128$ |
$39$ |
$C_1$ |
$D_{99}:C_{30}$ |
$C_{99}$ |
$C_{2} \times C_{30}$ |
$2^{2} \cdot 3^{3} \cdot 5 \cdot 11$ |
$1$ |
$99$ |
$20$ |
$60$ |
$60$ |
$60$ |
$16$ |
$16$ |
$16$ |
Solvable - 2 |
| 6000.q |
$\He_5:C_{24}:C_2$ |
$2^{4} \cdot 3 \cdot 5^{3}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$4$ |
$8$ |
$2$ |
$26$ |
$4900$ |
$76$ |
$15$ |
$C_1$ |
$\He_5:C_{24}:C_2$ |
$\He_5:C_6$ |
$C_{2} \times C_{4}$ |
$2^{4} \cdot 3 \cdot 5^{3}$ |
$1$ |
$125$ |
$125$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Solvable - 4 |
| 6048.bj |
$S_3\times S_4\times F_7$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$9$ |
$3$ |
$105$ |
$26760$ |
$1210$ |
$83$ |
$C_1$ |
$S_3\times S_4\times F_7$ |
$A_4\times C_{21}$ |
$C_{2}^{2} \times C_{6}$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$1$ |
$84$ |
$14$ |
$36$ |
$36$ |
$36$ |
? |
? |
? |
Solvable - 3 |
| 6048.br |
$F_7\times F_9:C_2$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$9$ |
$3$ |
$63$ |
$9716$ |
$356$ |
$56$ |
$C_1$ |
$F_7\times F_9:C_2$ |
$C_3^2:C_{28}$ |
$C_{2}^{2} \times C_{6}$ |
$2^{5} \cdot 3^{3} \cdot 7$ |
$1$ |
$63$ |
$16$ |
$48$ |
$48$ |
$48$ |
$14$ |
$14$ |
$14$ |
Solvable - 3 |
| 6480.co |
$C_9:C_6\times S_5$ |
$2^{4} \cdot 3^{4} \cdot 5$ |
$2^{2} \cdot 3^{2} \cdot 5$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$70$ |
$14754$ |
$416$ |
$23$ |
$C_1$ |
$C_9:C_6\times S_5$ |
$C_9\times A_5$ |
$C_{2} \times C_{6}$ |
$2^{4} \cdot 3^{4} \cdot 5$ |
$1$ |
$45$ |
$14$ |
$24$ |
$24$ |
$24$ |
$10$ |
$10$ |
$10$ |
Non-Solvable - 6 |
| 6552.m |
$F_7\times F_{13}$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 13$ |
$2^{2} \cdot 3 \cdot 7 \cdot 13$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$91$ |
$4560$ |
$192$ |
$59$ |
$C_1$ |
$F_7\times F_{13}$ |
$C_{91}$ |
$C_{6} \times C_{12}$ |
$2^{3} \cdot 3^{2} \cdot 7 \cdot 13$ |
$1$ |
$91$ |
$20$ |
$72$ |
$72$ |
$72$ |
$18$ |
$18$ |
$18$ |
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 |
| 6840.s |
$F_5\times F_{19}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 5 \cdot 19$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$95$ |
$2148$ |
$96$ |
$34$ |
$C_1$ |
$F_5\times F_{19}$ |
$C_{95}$ |
$C_{2} \times C_{36}$ |
$2^{3} \cdot 3^{2} \cdot 5 \cdot 19$ |
$1$ |
$95$ |
$24$ |
$72$ |
$72$ |
$72$ |
$22$ |
$22$ |
$22$ |
Solvable - 2 |
| 7056.bu |
$F_7\times F_8:C_3$ |
$2^{4} \cdot 3^{2} \cdot 7^{2}$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$56$ |
$7344$ |
$176$ |
$24$ |
$C_1$ |
$F_7\times F_8:C_3$ |
$C_7\times F_8$ |
$C_{3} \times C_{6}$ |
$2^{4} \cdot 3^{2} \cdot 7^{2}$ |
$1$ |
$56$ |
$15$ |
$42$ |
$42$ |
$42$ |
$13$ |
$13$ |
$13$ |
Solvable - 3 |
| 7200.ed |
$S_3\times \AGammaL(1,25)$ |
$2^{5} \cdot 3^{2} \cdot 5^{2}$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$9$ |
$3$ |
$60$ |
$13980$ |
$346$ |
$57$ |
$C_1$ |
$S_3\times \AGammaL(1,25)$ |
$C_3\times C_5^2:C_6$ |
$C_{2}^{2} \times C_{4}$ |
$2^{5} \cdot 3^{2} \cdot 5^{2}$ |
$1$ |
$75$ |
$28$ |
$48$ |
$48$ |
$48$ |
$26$ |
$26$ |
$26$ |
Solvable - 3 |
| 7920.a |
$M_{11}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ |
$2^{3} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$0$ |
$1$ |
$2$ |
$10$ |
$8651$ |
$39$ |
$2$ |
$C_1$ |
$M_{11}$ |
$M_{11}$ |
$C_1$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ |
$1$ |
$11$ |
$11$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
Simple |
| 7920.q |
$S_3\times \PGL(2,11)$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$39$ |
$23352$ |
$186$ |
$10$ |
$C_1$ |
$S_3\times \PGL(2,11)$ |
$C_3\times \PSL(2,11)$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{2} \cdot 5 \cdot 11$ |
$1$ |
$36$ |
$15$ |
$20$ |
$20$ |
$20$ |
$12$ |
$12$ |
$12$ |
Non-Solvable - 4 |
| 7992.e |
$S_3\times F_{37}$ |
$2^{3} \cdot 3^{3} \cdot 37$ |
$2^{2} \cdot 3^{2} \cdot 37$ |
$-1$ |
$2$ |
$7$ |
$2$ |
$111$ |
$3204$ |
$108$ |
$36$ |
$C_1$ |
$S_3\times F_{37}$ |
$C_{111}$ |
$C_{2} \times C_{36}$ |
$2^{3} \cdot 3^{3} \cdot 37$ |
$1$ |
$111$ |
$40$ |
$72$ |
$72$ |
$72$ |
$38$ |
$38$ |
$38$ |
Solvable - 2 |
| 8064.bq |
$C_2^6:C_{21}:C_6$ |
$2^{7} \cdot 3^{2} \cdot 7$ |
$2^{2} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$10$ |
$2$ |
$24$ |
$13698$ |
$148$ |
$10$ |
$C_1$ |
$C_2^6:C_{21}:C_6$ |
$C_2^6:C_{21}$ |
$C_{6}$ |
$2^{7} \cdot 3^{2} \cdot 7$ |
$1$ |
$24$ |
$24$ |
$21$ |
$21$ |
$21$ |
? |
? |
? |
Solvable - 3 |
| 8064.cc |
$S_4\times \PGL(2,7)$ |
$2^{7} \cdot 3^{2} \cdot 7$ |
$2^{3} \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$45$ |
$49386$ |
$584$ |
$13$ |
$C_1$ |
$S_4\times \PGL(2,7)$ |
$A_4\times \GL(3,2)$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3^{2} \cdot 7$ |
$1$ |
$32$ |
$12$ |
$18$ |
$18$ |
$18$ |
$9$ |
$9$ |
$9$ |
Non-Solvable - 6 |
| 8208.e |
$S_4\times F_{19}$ |
$2^{4} \cdot 3^{3} \cdot 19$ |
$2^{2} \cdot 3^{2} \cdot 19$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$95$ |
$6140$ |
$214$ |
$31$ |
$C_1$ |
$S_4\times F_{19}$ |
$A_4\times C_{19}$ |
$C_{2} \times C_{18}$ |
$2^{4} \cdot 3^{3} \cdot 19$ |
$1$ |
$76$ |
$23$ |
$54$ |
$54$ |
$54$ |
$21$ |
$21$ |
$21$ |
Solvable - 3 |
| 8424.a |
$C_9:C_6\times F_{13}$ |
$2^{3} \cdot 3^{4} \cdot 13$ |
$2^{2} \cdot 3^{2} \cdot 13$ |
$-1$ |
$2$ |
$8$ |
$2$ |
$130$ |
$7128$ |
$348$ |
$79$ |
$C_1$ |
$C_9:C_6\times F_{13}$ |
$C_{117}$ |
$C_{6} \times C_{12}$ |
$2^{3} \cdot 3^{4} \cdot 13$ |
$1$ |
$117$ |
$22$ |
$72$ |
$72$ |
$72$ |
$18$ |
$18$ |
$18$ |
Solvable - 2 |
| 8640.q |
$S_6:D_6$ |
$2^{6} \cdot 3^{3} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$3$ |
$39$ |
$42754$ |
$503$ |
$24$ |
$C_1$ |
$S_6:D_6$ |
$C_3\times A_6$ |
$C_{2}^{3}$ |
$2^{6} \cdot 3^{3} \cdot 5$ |
$1$ |
$30$ |
$13$ |
$18$ |
$18$ |
$18$ |
$11$ |
$11$ |
$11$ |
Non-Solvable - 5 |
