The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
$\#\Aut(F/K)$ Transitivity
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Results (1-50 of 115 matches)

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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
34T1 $C_{34}$ $34$ $-1$ ✓ $34$ $C_2$, $C_{17}$
34T2 $D_{17}$ $34$ $-1$ ✓ $34$ $C_2$, $D_{17}$ 17T2
34T3 $D_{34}$ $68$ $-1$ ✓ $2$ $C_2$, $D_{17}$ 34T3
34T4 $C_{17}:C_4$ $68$ $-1$ ✓ $2$ $C_2$, $C_{17}:C_{4}$ 17T3
34T5 $C_{34}:C_4$ $136$ $-1$ ✓ $2$ $C_2$, $C_{17}:C_{4}$ 34T5
34T6 $C_{17}:C_8$ $136$ $-1$ ✓ $2$ $C_2$, $C_{17}:C_{8}$ 17T4
34T7 $C_{34}:C_8$ $272$ $-1$ ✓ $2$ $C_2$, $C_{17}:C_{8}$ 34T7
34T8 $F_{17}$ $272$ $-1$ ✓ $2$ $C_2$, $F_{17}$ 17T5
34T9 $C_2\times F_{17}$ $544$ $-1$ ✓ $2$ $C_2$, $F_{17}$ 34T9
34T10 $C_{17}\times D_{17}$ $578$ $-1$ ✓ $17$ $C_2$ 34T10 x 7
34T11 $D_{17}^2$ $1156$ $-1$ ✓ $1$ $C_2$ 34T11 x 7
34T12 $C_{17}^2:C_4$ $1156$ $-1$ ✓ $1$ $C_2$ 34T12 x 7
34T13 $D_{17}\wr C_2$ $2312$ $-1$ ✓ $1$ $C_2$ 34T15 x 2
34T14 $C_{17}^2:Q_8$ $2312$ $-1$ ✓ $1$ $C_2$ 34T14 x 2
34T15 $D_{17}\wr C_2$ $2312$ $-1$ ✓ $1$ $C_2$ 34T13, 34T15
34T16 $D_{17}^2.C_2$ $2312$ $-1$ ✓ $1$ $C_2$ 34T16 x 7
34T17 $C_{17}^2:C_8$ $2312$ $-1$ ✓ $1$ $C_2$ 34T17 x 7
34T18 $C_2^8:C_{17}$ $4352$ $1$ ✓ $2$ $C_{17}$ 34T18 x 14
34T19 $C_{17}^2:D_8$ $4624$ $-1$ ✓ $1$ $C_2$
34T20 $C_{17}^2:Q_{16}$ $4624$ $-1$ ✓ $1$ $C_2$
34T21 $D_{17}^2.C_4$ $4624$ $-1$ ✓ $1$ $C_2$ 34T21 x 7
34T22 $C_{17}:F_{17}$ $4624$ $-1$ ✓ $1$ $C_2$ 34T22 x 7
34T23 $C_{17}^2:\SD_{16}$ $4624$ $-1$ ✓ $1$ $C_2$
34T24 $D_{17}^2.C_2^2$ $4624$ $-1$ ✓ $1$ $C_2$ 34T24 x 2
34T25 $C_{17}^2:\OD_{16}$ $4624$ $-1$ ✓ $1$ $C_2$ 34T26 x 2
34T26 $C_{17}^2:\OD_{16}$ $4624$ $-1$ ✓ $1$ $C_2$ 34T25, 34T26
34T27 $C_2\times \SL(2,16)$ $8160$ $-1$ $2$ $C_2$, $\PSL(2,16)$
34T28 $\SOMinus(4,4)$ $8160$ $-1$ $2$ $C_2$, $\PSL(2,16):C_2$ 17T7
34T29 $C_2^9:C_{17}$ $8704$ $-1$ ✓ $2$ $C_{17}$ 34T29 x 14
34T30 $C_2^8.D_{17}$ $8704$ $1$ ✓ $2$ $D_{17}$ 34T30 x 14, 34T31 x 15
34T31 $C_2^8.D_{17}$ $8704$ $-1$ ✓ $2$ $D_{17}$ 34T30 x 15, 34T31 x 14
34T32 $C_{17}^2:D_{16}$ $9248$ $-1$ ✓ $1$ $C_2$
34T33 $C_{17}^2:Q_{32}$ $9248$ $-1$ ✓ $1$ $C_2$
34T34 $C_{17}^2:\OD_{32}$ $9248$ $-1$ ✓ $1$ $C_2$ 34T34, 34T36
34T35 $D_{17}^2.(C_2\times C_4)$ $9248$ $-1$ ✓ $1$ $C_2$ 34T35 x 2
34T36 $C_{17}^2:\OD_{32}$ $9248$ $-1$ ✓ $1$ $C_2$ 34T34 x 2
34T37 $C_{17}^2:\SD_{32}$ $9248$ $-1$ ✓ $1$ $C_2$
34T38 $D_{17}^2.D_4$ $9248$ $-1$ ✓ $1$ $C_2$
34T39 $D_{17}^2.Q_8$ $9248$ $-1$ ✓ $1$ $C_2$
34T40 $D_{17}^2.D_4$ $9248$ $-1$ ✓ $1$ $C_2$
34T41 $D_{17}:F_{17}$ $9248$ $-1$ ✓ $1$ $C_2$ 34T41 x 7
34T42 $C_{17}^2:C_{32}$ $9248$ $1$ ✓ $1$ $C_2$ 34T42 x 8
34T43 $C_2\times \SOMinus(4,4)$ $16320$ $-1$ $2$ $C_2$, $\PSL(2,16):C_2$ 34T43
34T44 $\SL(2,16).C_4$ $16320$ $-1$ $2$ $C_2$, $\PSL(2,16):C_4$ 17T8
34T45 $C_2^8.D_{34}$ $17408$ $-1$ ✓ $2$ $D_{17}$ 34T45 x 29
34T46 $C_2^8.C_{17}:C_4$ $17408$ $1$ ✓ $2$ $C_{17}:C_{4}$ 34T46 x 2, 34T47 x 3
34T47 $C_2^8.C_{17}:C_4$ $17408$ $-1$ ✓ $2$ $C_{17}:C_{4}$ 34T46 x 3, 34T47 x 2
34T48 $D_{17}^2.D_8$ $18496$ $-1$ ✓ $1$ $C_2$
34T49 $D_{17}^2.Q_{16}$ $18496$ $-1$ ✓ $1$ $C_2$
34T50 $D_{17}^2.\OD_{16}$ $18496$ $-1$ ✓ $1$ $C_2$
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