The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)
| Label |
Name |
Degree |
Order |
Parity |
Solvable |
Nil. class |
$\#\Aut(F/K)$ |
Transitivity |
Conj. classes |
Subfields |
Low Degree Siblings |
| 24T4 |
$C_3\times Q_8$ |
$24$ |
$24$ |
$1$ |
✓ |
$2$ |
$24$ |
$1$ |
$15$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8$, $C_6\times C_2$ |
|
| 24T15 |
$C_3\times D_4$ |
$24$ |
$24$ |
$1$ |
✓ |
$2$ |
$24$ |
$1$ |
$15$ |
$C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4$, $C_6\times C_2$, $D_4 \times C_3$ x 2 |
12T14 x 2 |
| 24T16 |
$C_3\times \OD_{16}$ |
$24$ |
$48$ |
$-1$ |
✓ |
$2$ |
$12$ |
$1$ |
$30$ |
$C_2$, $C_3$, $C_4$, $C_6$, $C_8:C_2$, $C_{12}$ |
|
| 24T17 |
$D_4:C_6$ |
$24$ |
$48$ |
$1$ |
✓ |
$2$ |
$12$ |
$1$ |
$30$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8:C_2$, $C_6\times C_2$ |
24T17 x 2 |
| 24T38 |
$C_6\times D_4$ |
$24$ |
$48$ |
$1$ |
✓ |
$2$ |
$12$ |
$1$ |
$30$ |
$C_2$ x 3, $C_3$, $C_2^2$, $D_{4}$ x 2, $C_6$ x 3, $D_4\times C_2$, $C_6\times C_2$, $D_4 \times C_3$ x 2 |
24T38 x 3 |
| 24T39 |
$C_2^2:C_{12}$ |
$24$ |
$48$ |
$1$ |
✓ |
$2$ |
$12$ |
$1$ |
$30$ |
$C_2$, $C_3$, $C_4$, $D_{4}$ x 2, $C_6$, $C_2^2:C_4$, $C_{12}$, $D_4 \times C_3$ x 2 |
24T39 |
| 24T92 |
$C_6.C_2^4$ |
$24$ |
$96$ |
$1$ |
✓ |
$2$ |
$6$ |
$1$ |
$51$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $Q_8:C_2^2$, $C_6\times C_2$ |
24T92 x 5 |
| 24T112 |
$C_2^4:C_6$ |
$24$ |
$96$ |
$1$ |
✓ |
$2$ |
$12$ |
$1$ |
$42$ |
$C_2$, $C_3$, $D_{4}$ x 3, $C_6$, $C_2^2 \wr C_2$, $D_4 \times C_3$ x 3 |
24T112 x 7 |
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