Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
4T4 |
$A_4$ |
$12$ |
$1$ |
✓ |
$-1$ |
$4$ |
|
6T4, 12T4 |
4T5 |
$S_4$ |
$24$ |
$-1$ |
✓ |
$-1$ |
$5$ |
|
6T7, 6T8, 8T14, 12T8, 12T9, 24T10 |
5T1 |
$C_5$ |
$5$ |
$1$ |
✓ |
$1$ |
$5$ |
|
|
5T2 |
$D_{5}$ |
$10$ |
$1$ |
✓ |
$-1$ |
$4$ |
|
10T2 |
5T3 |
$F_5$ |
$20$ |
$-1$ |
✓ |
$-1$ |
$5$ |
|
10T4, 20T5 |
5T4 |
$A_5$ |
$60$ |
$1$ |
|
$-1$ |
$5$ |
|
6T12, 10T7, 12T33, 15T5, 20T15, 30T9 |
5T5 |
$S_5$ |
$120$ |
$-1$ |
|
$-1$ |
$7$ |
|
6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
6T12 |
$\PSL(2,5)$ |
$60$ |
$1$ |
|
$-1$ |
$5$ |
|
5T4, 10T7, 12T33, 15T5, 20T15, 30T9 |
6T14 |
$\PGL(2,5)$ |
$120$ |
$-1$ |
|
$-1$ |
$7$ |
|
5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62 |
6T15 |
$A_6$ |
$360$ |
$1$ |
|
$-1$ |
$7$ |
|
6T15, 10T26, 15T20 x 2, 20T89, 30T88 x 2, 36T555, 40T304, 45T49 |
6T16 |
$S_6$ |
$720$ |
$-1$ |
|
$-1$ |
$11$ |
|
6T16, 10T32, 12T183 x 2, 15T28 x 2, 20T145, 20T149 x 2, 30T164 x 2, 30T166 x 2, 30T176 x 2, 36T1252, 40T589, 40T592 x 2, 45T96 |
7T1 |
$C_7$ |
$7$ |
$1$ |
✓ |
$1$ |
$7$ |
|
|
7T2 |
$D_{7}$ |
$14$ |
$-1$ |
✓ |
$-1$ |
$5$ |
|
14T2 |
7T3 |
$C_7:C_3$ |
$21$ |
$1$ |
✓ |
$-1$ |
$5$ |
|
21T2 |
7T4 |
$F_7$ |
$42$ |
$-1$ |
✓ |
$-1$ |
$7$ |
|
14T4, 21T4, 42T4 |
7T5 |
$\GL(3,2)$ |
$168$ |
$1$ |
|
$-1$ |
$6$ |
|
7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2 |
7T6 |
$A_7$ |
$2520$ |
$1$ |
|
$-1$ |
$9$ |
|
15T47 x 2, 21T33, 35T28, 42T294, 42T299 |
7T7 |
$S_7$ |
$5040$ |
$-1$ |
|
$-1$ |
$15$ |
|
14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418 |
Results are complete for degrees $\leq 23$.