| 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 |
| 432.734 |
$C_3^2:\GL(2,3)$ |
$2^{4} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$7$ |
$2$ |
$11$ |
$646$ |
$46$ |
$6$ |
$C_1$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2}$ |
$2^{4} \cdot 3^{3}$ |
$1$ |
$9$ |
$9$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 5 |
| 648.531 |
$\He_3.\SL(2,3)$ |
$2^{3} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$7$ |
$2$ |
$24$ |
$252$ |
$26$ |
$6$ |
$C_3$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}$ |
$2^{4} \cdot 3^{4}$ |
$2 \cdot 3$ |
$81$ |
$81$ |
$3$ |
$6$ |
$18$ |
$3$ |
$6$ |
$18$ |
Solvable - 5 |
| 648.532 |
$\He_3.\SL(2,3)$ |
$2^{3} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$7$ |
$2$ |
$24$ |
$324$ |
$27$ |
$6$ |
$C_3$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}$ |
$2^{4} \cdot 3^{4}$ |
$2 \cdot 3$ |
$81$ |
$81$ |
$3$ |
$6$ |
$18$ |
$3$ |
$6$ |
$18$ |
Solvable - 5 |
| 648.533 |
$\GU(3,2)$ |
$2^{3} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$7$ |
$2$ |
$24$ |
$495$ |
$41$ |
$6$ |
$C_3$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}$ |
$2^{4} \cdot 3^{4}$ |
$2 \cdot 3$ |
$27$ |
$27$ |
$3$ |
$6$ |
$6$ |
$3$ |
$6$ |
$6$ |
Solvable - 5 |
| 864.4053 |
$(C_3\times C_6).\GL(2,3)$ |
$2^{5} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$22$ |
$1022$ |
$78$ |
$12$ |
$C_2$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{4}$ |
$2^{5} \cdot 3^{3}$ |
$2$ |
$36$ |
$13$ |
$8$ |
$16$ |
$16$ |
$8$ |
$10$ |
$10$ |
Solvable - 5 |
| 864.4661 |
$C_2\times C_3^2:\GL(2,3)$ |
$2^{5} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$22$ |
$2306$ |
$144$ |
$14$ |
$C_2$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3^{3}$ |
$2$ |
$18$ |
$11$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 5 |
| 1296.2892 |
$C_3^3.\GL(2,3)$ |
$2^{4} \cdot 3^{4}$ |
$2^{3} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$21$ |
$1720$ |
$73$ |
$10$ |
$C_1$ |
$C_3^3.\GL(2,3)$ |
$C_3^3.\SL(2,3)$ |
$C_{2}$ |
$2^{4} \cdot 3^{5}$ |
$3$ |
$72$ |
$18$ |
$16$ |
$16$ |
$48$ |
$10$ |
$10$ |
$14$ |
Solvable - 5 |
| 1296.2893 |
$\SU(3,2):C_6$ |
$2^{4} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$48$ |
$857$ |
$68$ |
$13$ |
$C_6$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{6}$ |
$2^{4} \cdot 3^{4}$ |
$2 \cdot 3$ |
$162$ |
$83$ |
$3$ |
$6$ |
$18$ |
$3$ |
$6$ |
$18$ |
Solvable - 5 |
| 1296.2894 |
$\SU(3,2).C_6$ |
$2^{4} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$48$ |
$713$ |
$66$ |
$13$ |
$C_6$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{6}$ |
$2^{4} \cdot 3^{4}$ |
$2 \cdot 3$ |
$162$ |
$83$ |
$3$ |
$6$ |
$18$ |
$3$ |
$6$ |
$18$ |
Solvable - 5 |
| 1296.2895 |
$C_2\times \GU(3,2)$ |
$2^{4} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$48$ |
$1343$ |
$102$ |
$13$ |
$C_6$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{6}$ |
$2^{4} \cdot 3^{4}$ |
$2 \cdot 3$ |
$54$ |
$29$ |
$3$ |
$6$ |
$6$ |
$3$ |
$6$ |
$6$ |
Solvable - 5 |
| 1296.3487 |
$C_3^3:\GL(2,3)$ |
$2^{4} \cdot 3^{4}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$33$ |
$1808$ |
$115$ |
$12$ |
$C_3$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{6}$ |
$2^{5} \cdot 3^{3}$ |
$2$ |
$24$ |
$12$ |
$8$ |
$16$ |
$16$ |
$8$ |
$10$ |
$10$ |
Solvable - 5 |
| 1296.3488 |
$C_3^3:\GL(2,3)$ |
$2^{4} \cdot 3^{4}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$8$ |
$3$ |
$21$ |
$3940$ |
$151$ |
$13$ |
$C_1$ |
$C_3^3:\GL(2,3)$ |
$C_3^3:\SL(2,3)$ |
$C_{2}$ |
$2^{5} \cdot 3^{5}$ |
$2 \cdot 3$ |
$24$ |
$12$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 1728.31095 |
$(C_3\times C_{12}).\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$44$ |
$1518$ |
$114$ |
$18$ |
$C_4$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{8}$ |
$2^{6} \cdot 3^{3}$ |
$2^{2}$ |
$72$ |
$17$ |
$8$ |
$16$ |
$32$ |
$8$ |
$10$ |
$12$ |
Solvable - 5 |
| 1728.31096 |
$C_6^2.\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$20$ |
$3866$ |
$133$ |
$9$ |
$C_1$ |
$C_6^2.\GL(2,3)$ |
$C_6^2.\SL(2,3)$ |
$C_{2}$ |
$2^{7} \cdot 3^{3}$ |
$2$ |
$48$ |
$21$ |
$24$ |
$24$ |
$24$ |
$11$ |
$14$ |
$14$ |
Solvable - 5 |
| 1728.46190 |
$(C_3\times C_{12}).\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$32$ |
$2802$ |
$180$ |
$20$ |
$C_2$ |
$C_2\times C_3^2:\GL(2,3)$ |
$C_2\times \PGU(3,2)$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3^{3}$ |
$2^{2}$ |
$72$ |
$17$ |
$16$ |
$32$ |
$32$ |
$10$ |
$12$ |
$12$ |
Solvable - 5 |
| 1728.46191 |
$C_4\times C_3^2:\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$44$ |
$4086$ |
$246$ |
$22$ |
$C_4$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2} \times C_{4}$ |
$2^{6} \cdot 3^{3}$ |
$2^{2}$ |
$36$ |
$13$ |
$8$ |
$16$ |
$16$ |
$8$ |
$10$ |
$10$ |
Solvable - 5 |
| 1728.46192 |
$\PSU(3,2):D_{12}$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$32$ |
$5610$ |
$252$ |
$20$ |
$C_2$ |
$C_2\times C_3^2:\GL(2,3)$ |
$C_2\times \PGU(3,2)$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3^{3}$ |
$2^{2}$ |
$36$ |
$13$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 1728.46193 |
$C_6^2.\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$44$ |
$3822$ |
$264$ |
$34$ |
$C_2^2$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2} \times C_{4}$ |
$2^{7} \cdot 3^{3}$ |
$2^{3}$ |
$72$ |
$15$ |
$-$ |
$-$ |
$-$ |
$9$ |
$10$ |
$10$ |
Solvable - 5 |
| 1728.46194 |
$C_6^2:\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$32$ |
$5106$ |
$260$ |
$20$ |
$C_2$ |
$C_2\times C_3^2:\GL(2,3)$ |
$C_2\times \PGU(3,2)$ |
$C_{2}^{2}$ |
$2^{6} \cdot 3^{3}$ |
$2$ |
$36$ |
$13$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 1728.47845 |
$C_6^2:\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$3$ |
$44$ |
$10622$ |
$592$ |
$42$ |
$C_2^2$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2}^{3}$ |
$2^{7} \cdot 3^{4}$ |
$2^{3} \cdot 3$ |
$36$ |
$13$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Solvable - 5 |
| 1728.47846 |
$C_6^2:\GL(2,3)$ |
$2^{6} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$20$ |
$4746$ |
$187$ |
$11$ |
$C_1$ |
$C_6^2:\GL(2,3)$ |
$C_6^2:\SL(2,3)$ |
$C_{2}$ |
$2^{7} \cdot 3^{3}$ |
$2$ |
$36$ |
$13$ |
$24$ |
$24$ |
$24$ |
$11$ |
$11$ |
$11$ |
Solvable - 5 |
| 1944.2292 |
$\SU(3,2):C_9$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$885$ |
$73$ |
$13$ |
$C_3^2$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{9}$ |
$2^{4} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$243$ |
$36$ |
$-$ |
$-$ |
$-$ |
$4$ |
$8$ |
$12$ |
Solvable - 5 |
| 1944.2293 |
$\SU(3,2).C_9$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{3}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$336$ |
$38$ |
$10$ |
$C_9$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{9}$ |
$2^{4} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$243$ |
$243$ |
$3$ |
$6$ |
$54$ |
$3$ |
$6$ |
$54$ |
Solvable - 5 |
| 1944.2294 |
$\SU(3,2).C_9$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{3}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$336$ |
$38$ |
$10$ |
$C_9$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{9}$ |
$2^{4} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$243$ |
$243$ |
$3$ |
$6$ |
$54$ |
$3$ |
$6$ |
$54$ |
Solvable - 5 |
| 1944.3442 |
$\SU(3,2):C_3^2$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$1440$ |
$99$ |
$16$ |
$C_3^2$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{5} \cdot 3^{6}$ |
$2^{2} \cdot 3^{3}$ |
$243$ |
$84$ |
$-$ |
$-$ |
$-$ |
$4$ |
$8$ |
$20$ |
Solvable - 5 |
| 1944.3443 |
$\SU(3,2):C_3^2$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$40$ |
$1440$ |
$89$ |
$13$ |
$C_3$ |
$C_3^3:\SL(2,3)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{4} \cdot 3^{6}$ |
$2 \cdot 3^{2}$ |
$81$ |
$81$ |
$9$ |
$18$ |
$18$ |
$9$ |
$18$ |
$18$ |
Solvable - 5 |
| 1944.3444 |
$\SU(3,2).C_3^2$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$1008$ |
$93$ |
$16$ |
$C_3^2$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{5} \cdot 3^{6}$ |
$2^{2} \cdot 3^{3}$ |
$243$ |
$84$ |
$-$ |
$-$ |
$-$ |
$4$ |
$8$ |
$20$ |
Solvable - 5 |
| 1944.3445 |
$\SU(3,2).C_3^2$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$40$ |
$1008$ |
$83$ |
$13$ |
$C_3$ |
$C_3^3:\SL(2,3)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{4} \cdot 3^{6}$ |
$2 \cdot 3^{2}$ |
$81$ |
$81$ |
$9$ |
$18$ |
$18$ |
$9$ |
$18$ |
$18$ |
Solvable - 5 |
| 1944.3446 |
$C_3\times \GU(3,2)$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$2682$ |
$192$ |
$16$ |
$C_3^2$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{5} \cdot 3^{6}$ |
$2^{2} \cdot 3^{3}$ |
$81$ |
$30$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Solvable - 5 |
| 1944.3447 |
$\GU(3,2):C_3$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$40$ |
$1737$ |
$98$ |
$13$ |
$C_3$ |
$C_3^3:\SL(2,3)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{4} \cdot 3^{6}$ |
$2 \cdot 3^{2}$ |
$81$ |
$81$ |
$9$ |
$18$ |
$18$ |
$9$ |
$18$ |
$18$ |
Solvable - 5 |
| 1944.3448 |
$\GU(3,2):C_3$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$72$ |
$1089$ |
$90$ |
$13$ |
$C_9$ |
$\PGU(3,2)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{4} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$81$ |
$81$ |
$3$ |
$6$ |
$18$ |
$3$ |
$6$ |
$18$ |
Solvable - 5 |
| 1944.3449 |
$\GU(3,2):C_3$ |
$2^{3} \cdot 3^{5}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$40$ |
$1089$ |
$80$ |
$13$ |
$C_3$ |
$C_3^3:\SL(2,3)$ |
$\SU(3,2)$ |
$C_{3}^{2}$ |
$2^{3} \cdot 3^{5}$ |
$3$ |
$81$ |
$81$ |
$9$ |
$18$ |
$18$ |
$9$ |
$18$ |
$18$ |
Solvable - 5 |
| 2160.cv |
$C_5\times C_3^2:\GL(2,3)$ |
$2^{4} \cdot 3^{3} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$55$ |
$1292$ |
$92$ |
$12$ |
$C_5$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{10}$ |
$2^{6} \cdot 3^{3}$ |
$2^{2}$ |
$45$ |
$14$ |
$8$ |
$16$ |
$32$ |
$8$ |
$10$ |
$12$ |
Solvable - 5 |
| 2160.cw |
$\PSU(3,2):D_{15}$ |
$2^{4} \cdot 3^{3} \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$5$ |
$8$ |
$2$ |
$31$ |
$3148$ |
$92$ |
$11$ |
$C_1$ |
$\PSU(3,2):D_{15}$ |
$C_5\times \PGU(3,2)$ |
$C_{2}$ |
$2^{6} \cdot 3^{3} \cdot 5$ |
$2^{2}$ |
$45$ |
$14$ |
$16$ |
$16$ |
$32$ |
$10$ |
$10$ |
$12$ |
Solvable - 5 |
| 2304.a |
$\COPlus(4,3)$ |
$2^{8} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$2$ |
$29$ |
$9097$ |
$310$ |
$9$ |
$C_2$ |
$S_4\wr C_2$ |
$\SOPlus(4,3)$ |
$C_{2}^{2}$ |
$2^{9} \cdot 3^{2}$ |
$2^{2}$ |
$32$ |
$32$ |
$4$ |
$8$ |
$8$ |
$4$ |
$8$ |
$8$ |
Solvable - 5 |
| 2304.bey |
$\OmegaPlus(4,3):D_4$ |
$2^{8} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$2$ |
$29$ |
$9129$ |
$301$ |
$9$ |
$C_2$ |
$S_4\wr C_2$ |
$\SOPlus(4,3)$ |
$C_{2}^{2}$ |
$2^{9} \cdot 3^{2}$ |
$2^{2}$ |
$48$ |
$48$ |
$4$ |
$4$ |
$8$ |
$4$ |
$4$ |
$8$ |
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 |
| 2592.fv |
$S_3\times C_3^2:\GL(2,3)$ |
$2^{5} \cdot 3^{4}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$33$ |
$10404$ |
$335$ |
$20$ |
$C_1$ |
$S_3\times C_3^2:\GL(2,3)$ |
$C_3^3:\SL(2,3)$ |
$C_{2}^{2}$ |
$2^{5} \cdot 3^{4}$ |
$1$ |
$24$ |
$12$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 2592.nv |
$C_6\times C_3^2:\GL(2,3)$ |
$2^{5} \cdot 3^{4}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$66$ |
$5924$ |
$343$ |
$28$ |
$C_6$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2} \times C_{6}$ |
$2^{6} \cdot 3^{3}$ |
$2^{2}$ |
$48$ |
$14$ |
$8$ |
$16$ |
$16$ |
$8$ |
$10$ |
$10$ |
Solvable - 5 |
| 2592.nx |
$C_2\times C_3^3:\GL(2,3)$ |
$2^{5} \cdot 3^{4}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$3$ |
$42$ |
$13776$ |
$456$ |
$29$ |
$C_2$ |
$C_3^3:\GL(2,3)$ |
$C_3^3:\SL(2,3)$ |
$C_{2}^{2}$ |
$2^{6} \cdot 3^{5}$ |
$2^{2} \cdot 3$ |
$48$ |
$14$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 3000.ba |
$\He_5:\SL(2,3)$ |
$2^{3} \cdot 3 \cdot 5^{3}$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$5$ |
$7$ |
$2$ |
$36$ |
$873$ |
$27$ |
$6$ |
$C_5$ |
$C_5^2:\SL(2,3)$ |
$\He_5:Q_8$ |
$C_{3}$ |
$2^{5} \cdot 3 \cdot 5^{2}$ |
$2^{2}$ |
$125$ |
$125$ |
$5$ |
$10$ |
$20$ |
$5$ |
$10$ |
$20$ |
Solvable - 5 |
| 3456.cx |
$(C_2\times C_6^2):\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$2$ |
$31$ |
$16920$ |
$491$ |
$15$ |
$C_2$ |
$C_6^2:\GL(2,3)$ |
$(C_2\times C_6^2):\SL(2,3)$ |
$C_{2}$ |
$2^{8} \cdot 3^{3}$ |
$2^{2}$ |
$24$ |
$17$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 5 |
| 3456.in |
$D_4\times C_3^2:\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$3$ |
$55$ |
$26194$ |
$1056$ |
$50$ |
$C_2$ |
$C_6^2:\GL(2,3)$ |
$C_2\times \PGU(3,2)$ |
$C_{2}^{3}$ |
$2^{8} \cdot 3^{3}$ |
$2^{2}$ |
$36$ |
$13$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 3456.kp |
$C_2\times C_6^2:\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$2$ |
$40$ |
$21430$ |
$771$ |
$25$ |
$C_2$ |
$C_6^2:\GL(2,3)$ |
$C_6^2:\SL(2,3)$ |
$C_{2}^{2}$ |
$2^{8} \cdot 3^{3}$ |
$2^{2}$ |
$54$ |
$15$ |
$24$ |
$24$ |
$24$ |
$11$ |
$11$ |
$11$ |
Solvable - 5 |
| 3456.kr |
$C_2\times C_6^2:\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$3$ |
$64$ |
$25290$ |
$1144$ |
$62$ |
$C_2^2$ |
$C_2\times C_3^2:\GL(2,3)$ |
$C_2\times \PGU(3,2)$ |
$C_{2}^{3}$ |
$2^{9} \cdot 3^{3}$ |
$2^{4}$ |
$72$ |
$15$ |
$-$ |
$-$ |
$-$ |
$10$ |
$10$ |
$10$ |
Solvable - 5 |
| 3456.ks |
$C_2\times C_6^2:\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$4$ |
$88$ |
$64138$ |
$3256$ |
$166$ |
$C_2^3$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2}^{4}$ |
$2^{10} \cdot 3^{4} \cdot 7$ |
$2^{6} \cdot 3 \cdot 7$ |
$72$ |
$15$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Solvable - 5 |
| 3456.kt |
$(C_6\times C_{12}):\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$3$ |
$64$ |
$27658$ |
$1088$ |
$62$ |
$C_2^2$ |
$C_2\times C_3^2:\GL(2,3)$ |
$C_2\times \PGU(3,2)$ |
$C_{2}^{3}$ |
$2^{10} \cdot 3^{3}$ |
$2^{5}$ |
$72$ |
$15$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Solvable - 5 |
| 3456.pz |
$(C_6\times C_{12}):\GL(2,3)$ |
$2^{7} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$10$ |
$3$ |
$88$ |
$19418$ |
$1056$ |
$70$ |
$C_2\times C_4$ |
$C_3^2:\GL(2,3)$ |
$\PGU(3,2)$ |
$C_{2}^{2} \times C_{4}$ |
$2^{9} \cdot 3^{3}$ |
$2^{5}$ |
$72$ |
$15$ |
$-$ |
$-$ |
$-$ |
? |
? |
? |
Solvable - 5 |
| 3888.br |
$C_3^4:\GL(2,3)$ |
$2^{4} \cdot 3^{5}$ |
$2^{3} \cdot 3^{2}$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$21$ |
$12418$ |
$214$ |
$7$ |
$C_1$ |
$C_3^4:\GL(2,3)$ |
$C_3^4:\SL(2,3)$ |
$C_{2}$ |
$2^{4} \cdot 3^{5}$ |
$1$ |
$12$ |
$12$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 5 |
| 3888.cc |
$C_3^3:S_3.S_4$ |
$2^{4} \cdot 3^{5}$ |
$2^{3} \cdot 3$ |
$-1$ |
$5$ |
$9$ |
$2$ |
$15$ |
$8346$ |
$128$ |
$6$ |
$C_1$ |
$C_3^3:S_3.S_4$ |
$C_3^4:\SL(2,3)$ |
$C_{2}$ |
$2^{7} \cdot 3^{5}$ |
$2^{3}$ |
$18$ |
$18$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Solvable - 5 |
