| 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 |
| 6.1 |
$S_3$ |
$2 \cdot 3$ |
$2 \cdot 3$ |
$-1$ |
$2$ |
$2$ |
$2$ |
$3$ |
$6$ |
$4$ |
$3$ |
$C_1$ |
$S_3$ |
$C_3$ |
$C_{2}$ |
$2 \cdot 3$ |
$1$ |
$3$ |
$3$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
Solvable - 2 |
| 20.3 |
$F_5$ |
$2^{2} \cdot 5$ |
$2^{2} \cdot 5$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$5$ |
$14$ |
$6$ |
$4$ |
$C_1$ |
$F_5$ |
$C_5$ |
$C_{4}$ |
$2^{2} \cdot 5$ |
$1$ |
$5$ |
$5$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
$4$ |
Solvable - 2 |
| 24.12 |
$S_4$ |
$2^{3} \cdot 3$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$4$ |
$2$ |
$5$ |
$30$ |
$11$ |
$4$ |
$C_1$ |
$S_4$ |
$A_4$ |
$C_{2}$ |
$2^{3} \cdot 3$ |
$1$ |
$4$ |
$4$ |
$3$ |
$3$ |
$3$ |
$3$ |
$3$ |
$3$ |
Solvable - 3 |
| 42.1 |
$F_7$ |
$2 \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$7$ |
$26$ |
$8$ |
$5$ |
$C_1$ |
$F_7$ |
$C_7$ |
$C_{6}$ |
$2 \cdot 3 \cdot 7$ |
$1$ |
$7$ |
$7$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 2 |
| 54.6 |
$C_9:C_6$ |
$2 \cdot 3^{3}$ |
$2 \cdot 3^{2}$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$10$ |
$36$ |
$13$ |
$7$ |
$C_1$ |
$C_9:C_6$ |
$C_9$ |
$C_{6}$ |
$2 \cdot 3^{3}$ |
$1$ |
$9$ |
$9$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 2 |
| 110.1 |
$F_{11}$ |
$2 \cdot 5 \cdot 11$ |
$2 \cdot 5 \cdot 11$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$11$ |
$38$ |
$8$ |
$5$ |
$C_1$ |
$F_{11}$ |
$C_{11}$ |
$C_{10}$ |
$2 \cdot 5 \cdot 11$ |
$1$ |
$11$ |
$11$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
$10$ |
Solvable - 2 |
| 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 |
| 120.36 |
$S_3\times F_5$ |
$2^{3} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$15$ |
$132$ |
$32$ |
$14$ |
$C_1$ |
$S_3\times F_5$ |
$C_{15}$ |
$C_{2} \times C_{4}$ |
$2^{3} \cdot 3 \cdot 5$ |
$1$ |
$15$ |
$8$ |
$8$ |
$8$ |
$8$ |
$6$ |
$6$ |
$6$ |
Solvable - 2 |
| 144.182 |
$F_9:C_2$ |
$2^{4} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$9$ |
$162$ |
$25$ |
$8$ |
$C_1$ |
$F_9:C_2$ |
$C_3^2:C_4$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{2}$ |
$1$ |
$9$ |
$9$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 3 |
| 144.183 |
$S_3\times S_4$ |
$2^{4} \cdot 3^{2}$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$15$ |
$372$ |
$70$ |
$13$ |
$C_1$ |
$S_3\times S_4$ |
$C_3\times A_4$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{2}$ |
$1$ |
$12$ |
$7$ |
$6$ |
$6$ |
$6$ |
$5$ |
$5$ |
$5$ |
Solvable - 3 |
| 156.7 |
$F_{13}$ |
$2^{2} \cdot 3 \cdot 13$ |
$2^{2} \cdot 3 \cdot 13$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$13$ |
$72$ |
$12$ |
$7$ |
$C_1$ |
$F_{13}$ |
$C_{13}$ |
$C_{12}$ |
$2^{2} \cdot 3 \cdot 13$ |
$1$ |
$13$ |
$13$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Solvable - 2 |
| 168.43 |
$F_8:C_3$ |
$2^{3} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$5$ |
$2$ |
$8$ |
$104$ |
$12$ |
$4$ |
$C_1$ |
$F_8:C_3$ |
$F_8$ |
$C_{3}$ |
$2^{3} \cdot 3 \cdot 7$ |
$1$ |
$8$ |
$8$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Solvable - 3 |
| 216.90 |
$C_3^2.S_4$ |
$2^{3} \cdot 3^{3}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$19$ |
$180$ |
$39$ |
$10$ |
$C_1$ |
$C_3^2.S_4$ |
$C_2^2:C_9$ |
$C_{6}$ |
$2^{3} \cdot 3^{3}$ |
$1$ |
$18$ |
$13$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 3 |
| 252.26 |
$S_3\times F_7$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$21$ |
$252$ |
$44$ |
$17$ |
$C_1$ |
$S_3\times F_7$ |
$C_{21}$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{2} \cdot 7$ |
$1$ |
$21$ |
$10$ |
$12$ |
$12$ |
$12$ |
$8$ |
$8$ |
$8$ |
Solvable - 2 |
| 272.50 |
$F_{17}$ |
$2^{4} \cdot 17$ |
$2^{4} \cdot 17$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$17$ |
$74$ |
$10$ |
$6$ |
$C_1$ |
$F_{17}$ |
$C_{17}$ |
$C_{16}$ |
$2^{4} \cdot 17$ |
$1$ |
$17$ |
$17$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
$16$ |
Solvable - 2 |
| 320.1635 |
$C_2^4:F_5$ |
$2^{6} \cdot 5$ |
$2^{3} \cdot 5$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$11$ |
$428$ |
$40$ |
$5$ |
$C_1$ |
$C_2^4:F_5$ |
$C_2^4:C_5$ |
$C_{4}$ |
$2^{6} \cdot 5$ |
$1$ |
$10$ |
$10$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
$5$ |
Solvable - 3 |
| 324.118 |
$C_3^2.S_3^2$ |
$2^{2} \cdot 3^{4}$ |
$2 \cdot 3^{2}$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$30$ |
$424$ |
$80$ |
$23$ |
$C_1$ |
$C_3^2.S_3^2$ |
$C_3\times C_9$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{4}$ |
$1$ |
$18$ |
$12$ |
$12$ |
$12$ |
$12$ |
$8$ |
$8$ |
$8$ |
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 |
| 336.210 |
$F_8:C_6$ |
$2^{4} \cdot 3 \cdot 7$ |
$2 \cdot 3 \cdot 7$ |
$-1$ |
$3$ |
$6$ |
$2$ |
$16$ |
$278$ |
$29$ |
$8$ |
$C_2$ |
$F_8:C_3$ |
$F_8$ |
$C_{6}$ |
$2^{3} \cdot 3 \cdot 7$ |
$1$ |
$14$ |
$10$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
$7$ |
Solvable - 3 |
| 342.7 |
$F_{19}$ |
$2 \cdot 3^{2} \cdot 19$ |
$2 \cdot 3^{2} \cdot 19$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$19$ |
$102$ |
$12$ |
$7$ |
$C_1$ |
$F_{19}$ |
$C_{19}$ |
$C_{18}$ |
$2 \cdot 3^{2} \cdot 19$ |
$1$ |
$19$ |
$19$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Solvable - 2 |
| 384.5677 |
$C_2^2.\GL(2,\mathbb{Z}/4)$ |
$2^{7} \cdot 3$ |
$2^{3} \cdot 3$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$16$ |
$960$ |
$117$ |
$13$ |
$C_1$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ |
$C_4^2:C_6$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3$ |
$1$ |
$16$ |
$16$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Solvable - 3 |
| 384.5678 |
$C_2^4:S_4$ |
$2^{7} \cdot 3$ |
$2^{3} \cdot 3$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$16$ |
$1056$ |
$123$ |
$13$ |
$C_1$ |
$C_2^4:S_4$ |
$C_2^3:A_4$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3$ |
$1$ |
$16$ |
$16$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Solvable - 3 |
| 432.520 |
$\He_3:\SD_{16}$ |
$2^{4} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$4$ |
$7$ |
$2$ |
$14$ |
$511$ |
$40$ |
$9$ |
$C_1$ |
$\He_3:\SD_{16}$ |
$\He_3:C_4$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{3}$ |
$1$ |
$27$ |
$27$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 4 |
| 432.523 |
$C_6^2:D_6$ |
$2^{4} \cdot 3^{3}$ |
$2^{2} \cdot 3$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$20$ |
$1289$ |
$134$ |
$15$ |
$C_1$ |
$C_6^2:D_6$ |
$C_3^2:A_4$ |
$C_{2}^{2}$ |
$2^{4} \cdot 3^{3}$ |
$1$ |
$18$ |
$13$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 3 |
| 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 |
| 480.1189 |
$F_5\times S_4$ |
$2^{5} \cdot 3 \cdot 5$ |
$2^{2} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$25$ |
$912$ |
$112$ |
$18$ |
$C_1$ |
$F_5\times S_4$ |
$C_5\times A_4$ |
$C_{2} \times C_{4}$ |
$2^{5} \cdot 3 \cdot 5$ |
$1$ |
$20$ |
$9$ |
$12$ |
$12$ |
$12$ |
$7$ |
$7$ |
$7$ |
Solvable - 3 |
| 486.31 |
$C_{27}:C_{18}$ |
$2 \cdot 3^{5}$ |
$2 \cdot 3^{3}$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$31$ |
$156$ |
$28$ |
$12$ |
$C_1$ |
$C_{27}:C_{18}$ |
$C_{27}$ |
$C_{18}$ |
$2 \cdot 3^{5}$ |
$1$ |
$27$ |
$27$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Solvable - 2 |
| 500.18 |
$C_{25}:C_{20}$ |
$2^{2} \cdot 5^{3}$ |
$2^{2} \cdot 5^{2}$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$26$ |
$138$ |
$19$ |
$9$ |
$C_1$ |
$C_{25}:C_{20}$ |
$C_{25}$ |
$C_{20}$ |
$2^{2} \cdot 5^{3}$ |
$1$ |
$25$ |
$25$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
$20$ |
Solvable - 2 |
| 506.1 |
$F_{23}$ |
$2 \cdot 11 \cdot 23$ |
$2 \cdot 11 \cdot 23$ |
$-1$ |
$2$ |
$3$ |
$2$ |
$23$ |
$74$ |
$8$ |
$5$ |
$C_1$ |
$F_{23}$ |
$C_{23}$ |
$C_{22}$ |
$2 \cdot 11 \cdot 23$ |
$1$ |
$23$ |
$23$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
$22$ |
Solvable - 2 |
| 660.15 |
$S_3\times F_{11}$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$2 \cdot 3 \cdot 5 \cdot 11$ |
$-1$ |
$2$ |
$5$ |
$2$ |
$33$ |
$324$ |
$40$ |
$17$ |
$C_1$ |
$S_3\times F_{11}$ |
$C_{33}$ |
$C_{2} \times C_{10}$ |
$2^{2} \cdot 3 \cdot 5 \cdot 11$ |
$1$ |
$33$ |
$14$ |
$20$ |
$20$ |
$20$ |
$12$ |
$12$ |
$12$ |
Solvable - 2 |
| 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 |
| 800.1191 |
$F_5\wr C_2$ |
$2^{5} \cdot 5^{2}$ |
$2^{3} \cdot 5$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$20$ |
$954$ |
$67$ |
$13$ |
$C_1$ |
$F_5\wr C_2$ |
$C_5:F_5$ |
$C_{2} \times C_{4}$ |
$2^{5} \cdot 5^{2}$ |
$1$ |
$10$ |
$10$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 3 |
| 812.7 |
$F_{29}$ |
$2^{2} \cdot 7 \cdot 29$ |
$2^{2} \cdot 7 \cdot 29$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$29$ |
$152$ |
$12$ |
$7$ |
$C_1$ |
$F_{29}$ |
$C_{29}$ |
$C_{28}$ |
$2^{2} \cdot 7 \cdot 29$ |
$1$ |
$29$ |
$29$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
$28$ |
Solvable - 2 |
| 840.139 |
$F_5\times F_7$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$2^{2} \cdot 3 \cdot 5 \cdot 7$ |
$-1$ |
$2$ |
$6$ |
$2$ |
$35$ |
$556$ |
$64$ |
$24$ |
$C_1$ |
$F_5\times F_7$ |
$C_{35}$ |
$C_{2} \times C_{12}$ |
$2^{3} \cdot 3 \cdot 5 \cdot 7$ |
$1$ |
$35$ |
$12$ |
$24$ |
$24$ |
$24$ |
$10$ |
$10$ |
$10$ |
Solvable - 2 |
| 864.4662 |
$F_9:D_6$ |
$2^{5} \cdot 3^{3}$ |
$2^{3} \cdot 3$ |
$-1$ |
$3$ |
$8$ |
$3$ |
$27$ |
$2380$ |
$178$ |
$32$ |
$C_1$ |
$F_9:D_6$ |
$C_3^2:C_{12}$ |
$C_{2}^{3}$ |
$2^{5} \cdot 3^{3}$ |
$1$ |
$24$ |
$12$ |
$16$ |
$16$ |
$16$ |
$10$ |
$10$ |
$10$ |
Solvable - 3 |
| 896.564 |
$C_2^4.F_8$ |
$2^{7} \cdot 7$ |
$2^{2} \cdot 7$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$17$ |
$409$ |
$22$ |
$5$ |
$C_2$ |
$C_2^3.F_8$ |
$C_2^4.C_2^3$ |
$C_{7}$ |
$2^{6} \cdot 7$ |
$1$ |
$16$ |
$16$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
$8$ |
Solvable - 3 |
| 930.1 |
$F_{31}$ |
$2 \cdot 3 \cdot 5 \cdot 31$ |
$2 \cdot 3 \cdot 5 \cdot 31$ |
$-1$ |
$2$ |
$4$ |
$2$ |
$31$ |
$226$ |
$16$ |
$9$ |
$C_1$ |
$F_{31}$ |
$C_{31}$ |
$C_{30}$ |
$2 \cdot 3 \cdot 5 \cdot 31$ |
$1$ |
$31$ |
$31$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
$30$ |
Solvable - 2 |
| 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 |
| 960.11359 |
$F_{16}:C_4$ |
$2^{6} \cdot 3 \cdot 5$ |
$2^{3} \cdot 3 \cdot 5$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$13$ |
$990$ |
$44$ |
$8$ |
$C_1$ |
$F_{16}:C_4$ |
$F_{16}$ |
$C_{4}$ |
$2^{6} \cdot 3 \cdot 5$ |
$1$ |
$16$ |
$16$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
$15$ |
Solvable - 3 |
| 972.429 |
$C_3^3.S_3^2$ |
$2^{2} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$39$ |
$1754$ |
$184$ |
$26$ |
$C_1$ |
$C_3^3.S_3^2$ |
$C_3^2:C_9$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{5}$ |
$1$ |
$18$ |
$18$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
$12$ |
Solvable - 3 |
| 972.445 |
$C_3^3.S_3^2$ |
$2^{2} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$35$ |
$1840$ |
$153$ |
$23$ |
$C_1$ |
$C_3^3.S_3^2$ |
$C_3\wr C_3$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{5}$ |
$1$ |
$27$ |
$27$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Solvable - 3 |
| 972.446 |
$C_3^3.S_3^2$ |
$2^{2} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$35$ |
$1408$ |
$139$ |
$23$ |
$C_1$ |
$C_3^3.S_3^2$ |
$C_3.\He_3$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{5}$ |
$1$ |
$27$ |
$27$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Solvable - 3 |
| 972.447 |
$C_3^3.S_3^2$ |
$2^{2} \cdot 3^{5}$ |
$2 \cdot 3^{2}$ |
$-1$ |
$3$ |
$7$ |
$2$ |
$35$ |
$1624$ |
$145$ |
$23$ |
$C_1$ |
$C_3^3.S_3^2$ |
$\He_3:C_3$ |
$C_{2} \times C_{6}$ |
$2^{2} \cdot 3^{5}$ |
$1$ |
$27$ |
$27$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
$18$ |
Solvable - 3 |
| 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 |
| 1152.157849 |
$S_4\wr C_2$ |
$2^{7} \cdot 3^{2}$ |
$2^{3} \cdot 3$ |
$-1$ |
$4$ |
$9$ |
$2$ |
$20$ |
$4586$ |
$221$ |
$8$ |
$C_1$ |
$S_4\wr C_2$ |
$\PSOPlus(4,3)$ |
$C_{2}^{2}$ |
$2^{7} \cdot 3^{2}$ |
$1$ |
$8$ |
$8$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
$6$ |
Solvable - 4 |
| 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 |
| 1296.2920 |
$C_6^2.S_3^2$ |
$2^{4} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$50$ |
$2588$ |
$241$ |
$30$ |
$C_1$ |
$C_6^2.S_3^2$ |
$C_9\times A_4$ |
$C_{2} \times C_{6}$ |
$2^{4} \cdot 3^{4}$ |
$1$ |
$36$ |
$13$ |
$18$ |
$18$ |
$18$ |
$9$ |
$9$ |
$9$ |
Solvable - 3 |
| 1296.2922 |
$C_6^2.S_3^2$ |
$2^{4} \cdot 3^{4}$ |
$2^{2} \cdot 3^{2}$ |
$-1$ |
$3$ |
$8$ |
$2$ |
$57$ |
$2648$ |
$286$ |
$32$ |
$C_1$ |
$C_6^2.S_3^2$ |
$C_3^2.A_4$ |
$C_{2} \times C_{6}$ |
$2^{4} \cdot 3^{4}$ |
$1$ |
$36$ |
$16$ |
$12$ |
$12$ |
$12$ |
$8$ |
$8$ |
$8$ |
Solvable - 3 |
