| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 41T9 |
$A_{41}$ |
$16726263306581903554085031026720375832576000000000$ |
$1$ |
|
$-1$ |
$22365$ |
|
|
| 41T10 |
$S_{41}$ |
$33452526613163807108170062053440751665152000000000$ |
$-1$ |
|
$-1$ |
$44583$ |
|
|
| 42T37 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T38 x 2 |
| 42T38 |
$\PSL(2,7)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$, $\PSL(2,7)$ |
7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 |
| 42T78 |
$C_2\times \GL(3,2)$ |
$336$ |
$-1$ |
|
$-1$ |
$12$ |
$C_2$, $\GL(3,2)$ x 2, $\GL(3,2) \times C_2$ x 2, $\PSL(2,7)$ |
14T17 x 2, 14T19 x 2, 16T714, 28T43 x 2, 42T79, 42T80 x 2 |
| 42T79 |
$C_2\times \GL(3,2)$ |
$336$ |
$-1$ |
|
$-1$ |
$12$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
14T17 x 2, 14T19 x 2, 16T714, 28T43 x 2, 42T78, 42T80 x 2 |
| 42T80 |
$C_2\times \GL(3,2)$ |
$336$ |
$-1$ |
|
$-1$ |
$12$ |
$\GL(3,2)$ x 2, $C_2\times \GL(3,2)$, $\PSL(2,7)$ |
14T17 x 2, 14T19 x 2, 16T714, 28T43 x 2, 42T78, 42T79, 42T80 |
| 42T81 |
$\PGL(2,7)$ |
$336$ |
$-1$ |
|
$-1$ |
$9$ |
$C_2$, $\PGL(2,7)$, $\PGL(2,7)$ |
8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T82, 42T83 |
| 42T82 |
$\PGL(2,7)$ |
$336$ |
$1$ |
|
$-1$ |
$9$ |
$\PGL(2,7)$ |
8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T83 |
| 42T83 |
$\PGL(2,7)$ |
$336$ |
$-1$ |
|
$-1$ |
$9$ |
$\PGL(2,7)$ |
8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82 |
| 42T86 |
$C_7\times A_5$ |
$420$ |
$1$ |
|
$-1$ |
$35$ |
$\PSL(2,5)$, $C_7$ |
35T13 |
| 42T96 |
$C_3\times \GL(3,2)$ |
$504$ |
$1$ |
|
$-1$ |
$18$ |
$C_3$, $\GL(3,2)$, $\PSL(2,7)$, $C_3\times \GL(3,2)$ |
21T22 x 2, 24T1355 x 2, 24T1356, 42T96, 42T103 x 2 |
| 42T103 |
$C_3\times \GL(3,2)$ |
$504$ |
$1$ |
|
$-1$ |
$18$ |
$\GL(3,2)$, $\PSL(2,7)$ |
21T22 x 2, 24T1355 x 2, 24T1356, 42T96 x 2, 42T103 |
| 42T130 |
$C_2\times \PGL(2,7)$ |
$672$ |
$-1$ |
|
$-1$ |
$18$ |
$C_2$, $\PGL(2,7)$ |
16T1035 x 2, 28T80, 28T81, 32T34612, 42T130, 42T131 x 2 |
| 42T131 |
$C_2\times \PGL(2,7)$ |
$672$ |
$-1$ |
|
$-1$ |
$18$ |
$\PGL(2,7)$ |
16T1035 x 2, 28T80, 28T81, 32T34612, 42T130 x 2, 42T131 |
| 42T138 |
$C_7\times S_5$ |
$840$ |
$-1$ |
|
$-1$ |
$49$ |
$\PGL(2,5)$, $C_7$ |
35T17 |
| 42T139 |
$D_7\times A_5$ |
$840$ |
$1$ |
|
$-1$ |
$25$ |
$\PSL(2,5)$, $D_{7}$ |
35T18 |
| 42T140 |
$C_7:S_5$ |
$840$ |
$-1$ |
|
$-1$ |
$22$ |
$\PGL(2,5)$, $D_{7}$ |
35T19 |
| 42T167 |
$C_6\times \GL(3,2)$ |
$1008$ |
$-1$ |
|
$-1$ |
$36$ |
$C_2$, $C_3$, $C_6$, $\GL(3,2)$, $\GL(3,2) \times C_2$, $C_3\times \GL(3,2)$ |
42T167, 42T168 x 2 |
| 42T168 |
$C_6\times \GL(3,2)$ |
$1008$ |
$-1$ |
|
$-1$ |
$36$ |
$C_3$, $\GL(3,2)$, $C_2\times \GL(3,2)$, $C_3\times \GL(3,2)$ |
42T167 x 2, 42T168 |
| 42T169 |
$S_3\times \GL(3,2)$ |
$1008$ |
$1$ |
|
$-1$ |
$18$ |
$S_3$, $\GL(3,2)$, $\PSL(2,7)$, $S_3\times \GL(3,2)$ |
21T27 x 2, 24T2671, 42T169, 42T170 x 2, 42T171 x 2, 42T175 x 2 |
| 42T170 |
$S_3\times \GL(3,2)$ |
$1008$ |
$-1$ |
|
$-1$ |
$18$ |
$S_3$, $\GL(3,2)$, $C_2\times \GL(3,2)$, $S_3\times \GL(3,2)$ |
21T27 x 2, 24T2671, 42T169 x 2, 42T170, 42T171 x 2, 42T175 x 2 |
| 42T171 |
$S_3\times \GL(3,2)$ |
$1008$ |
$-1$ |
|
$-1$ |
$18$ |
$C_2$, $S_3$, $S_3$, $\GL(3,2)$, $\GL(3,2) \times C_2$, $S_3\times \GL(3,2)$ |
21T27 x 2, 24T2671, 42T169 x 2, 42T170 x 2, 42T171, 42T175 x 2 |
| 42T173 |
$C_3\times \PGL(2,7)$ |
$1008$ |
$-1$ |
|
$-1$ |
$27$ |
$C_2$, $C_3$, $C_6$, $\PGL(2,7)$ |
24T2668 x 2, 24T2669 |
| 42T174 |
$C_3:\PGL(2,7)$ |
$1008$ |
$-1$ |
|
$-1$ |
$15$ |
$C_2$, $S_3$, $S_3$, $\PGL(2,7)$ |
24T2667 |
| 42T175 |
$S_3\times \GL(3,2)$ |
$1008$ |
$-1$ |
|
$-1$ |
$18$ |
$\GL(3,2)$, $C_2\times \GL(3,2)$ |
21T27 x 2, 24T2671, 42T169 x 2, 42T170 x 2, 42T171 x 2, 42T175 |
| 42T176 |
$\PSL(2,13)$ |
$1092$ |
$1$ |
|
$-1$ |
$9$ |
$\PSL(2,13)$ |
14T30, 28T120 |
| 42T197 |
$C_7:\GL(2,4)$ |
$1260$ |
$1$ |
|
$-1$ |
$25$ |
$\PSL(2,5)$, $C_7:C_3$ |
35T22 |
| 42T208 |
$C_2^3.\GL(3,2)$ |
$1344$ |
$1$ |
|
$-1$ |
$11$ |
$\GL(3,2)$ x 2, $C_2^3.\GL(3,2)$, $\PSL(2,7)$ |
14T33 x 2, 28T152, 28T158 x 2, 42T208, 42T209 x 2 |
| 42T209 |
$C_2^3.\GL(3,2)$ |
$1344$ |
$1$ |
|
$-1$ |
$11$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
14T33 x 2, 28T152, 28T158 x 2, 42T208 x 2, 42T209 |
| 42T210 |
$C_2^3:\GL(3,2)$ |
$1344$ |
$1$ |
|
$-1$ |
$11$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
8T48 x 2, 14T34 x 2, 28T153, 28T159 x 2, 42T210, 42T211 x 2 |
| 42T211 |
$C_2^3:\GL(3,2)$ |
$1344$ |
$1$ |
|
$-1$ |
$11$ |
$\GL(3,2)$ x 2, $C_2^3:\GL(3,2)$, $\PSL(2,7)$ |
8T48 x 2, 14T34 x 2, 28T153, 28T159 x 2, 42T210 x 2, 42T211 |
| 42T218 |
$D_7\times S_5$ |
$1680$ |
$-1$ |
|
$-1$ |
$35$ |
$\PGL(2,5)$, $D_{7}$ |
35T23 |
| 42T261 |
$A_4\times \GL(3,2)$ |
$2016$ |
$1$ |
|
$-1$ |
$24$ |
$C_3$, $A_4$, $\GL(3,2)$, $C_3\times \GL(3,2)$ |
28T198 x 2, 32T97744, 42T261, 42T262 x 2 |
| 42T262 |
$A_4\times \GL(3,2)$ |
$2016$ |
$1$ |
|
$-1$ |
$24$ |
$C_3$, $\GL(3,2)$, $C_3\times \GL(3,2)$ |
28T198 x 2, 32T97744, 42T261 x 2, 42T262 |
| 42T263 |
$D_6\times \GL(3,2)$ |
$2016$ |
$-1$ |
|
$-1$ |
$36$ |
$C_2$, $S_3$, $D_{6}$, $\GL(3,2)$, $\GL(3,2) \times C_2$, $S_3\times \GL(3,2)$ |
42T263 x 3, 42T264 x 4 |
| 42T264 |
$D_6\times \GL(3,2)$ |
$2016$ |
$-1$ |
|
$-1$ |
$36$ |
$S_3$, $\GL(3,2)$, $C_2\times \GL(3,2)$, $S_3\times \GL(3,2)$ |
42T263 x 4, 42T264 x 3 |
| 42T265 |
$S_3\times \PGL(2,7)$ |
$2016$ |
$-1$ |
|
$-1$ |
$27$ |
$C_2$, $S_3$, $D_{6}$, $\PGL(2,7)$ |
24T4986 |
| 42T284 |
$\PGL(2,13)$ |
$2184$ |
$-1$ |
|
$-1$ |
$15$ |
$\PGL(2,13)$ |
14T39, 28T201 |
| 42T294 |
$A_7$ |
$2520$ |
$1$ |
|
$-1$ |
$9$ |
$A_7$, $A_7$ |
7T6, 15T47 x 2, 21T33, 35T28, 42T299 |
| 42T295 |
$C_7\times A_6$ |
$2520$ |
$1$ |
|
$-1$ |
$49$ |
$A_6$, $C_7$ |
42T295 |
| 42T296 |
$C_7:C_3\times S_5$ |
$2520$ |
$-1$ |
|
$-1$ |
$35$ |
$\PGL(2,5)$, $C_7:C_3$ |
35T25 |
| 42T297 |
$F_7\times A_5$ |
$2520$ |
$1$ |
|
$-1$ |
$35$ |
$\PSL(2,5)$, $F_7$ |
35T27 |
| 42T298 |
$A_5:F_7$ |
$2520$ |
$-1$ |
|
$-1$ |
$26$ |
$\PGL(2,5)$, $F_7$ |
35T26 |
| 42T299 |
$A_7$ |
$2520$ |
$1$ |
|
$-1$ |
$9$ |
$A_7$ |
7T6, 15T47 x 2, 21T33, 35T28, 42T294 |
| 42T327 |
$C_2^4.\GL(3,2)$ |
$2688$ |
$-1$ |
|
$-1$ |
$22$ |
$\GL(3,2)$ x 2, $C_2^4.\GL(3,2)$, $\PSL(2,7)$ |
14T42 x 2, 28T229 x 2, 28T230, 28T231 x 2, 42T327, 42T330 x 2 |
| 42T328 |
$C_2^4:\GL(3,2)$ |
$2688$ |
$-1$ |
|
$-1$ |
$22$ |
$\GL(3,2)$ x 2, $C_2^4:\GL(3,2)$, $\PSL(2,7)$ |
14T43 x 2, 16T1504 x 2, 28T232 x 2, 28T233, 28T234 x 2, 42T328, 42T329 x 2 |
| 42T329 |
$C_2^4:\GL(3,2)$ |
$2688$ |
$-1$ |
|
$-1$ |
$22$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
14T43 x 2, 16T1504 x 2, 28T232 x 2, 28T233, 28T234 x 2, 42T328 x 2, 42T329 |
| 42T330 |
$C_2^4.\GL(3,2)$ |
$2688$ |
$-1$ |
|
$-1$ |
$22$ |
$\GL(3,2)$ x 2, $\PSL(2,7)$ |
14T42 x 2, 28T229 x 2, 28T230, 28T231 x 2, 42T327 x 2, 42T330 |
| 42T332 |
$C_3^2:\PGL(2,7)$ |
$3024$ |
$-1$ |
|
$-1$ |
$45$ |
$C_2$, $S_3\times C_3$, $\PGL(2,7)$ |
42T332 |
Results are complete for degrees $\leq 23$.
