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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 306 matches)

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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
39T1 $C_{39}$ $39$ $1$ ✓ $39$ $C_3$, $C_{13}$
39T2 $C_{13}:C_3$ $39$ $1$ ✓ $39$ $C_3$, $C_{13}:C_3$ 13T3
39T3 $S_3\times C_{13}$ $78$ $-1$ ✓ $13$ $S_3$, $C_{13}$
39T4 $D_{39}$ $78$ $-1$ ✓ $1$ $S_3$, $D_{13}$
39T5 $C_3\times D_{13}$ $78$ $1$ ✓ $3$ $C_3$, $D_{13}$
39T6 $C_{13}:C_6$ $78$ $1$ ✓ $3$ $C_3$, $C_{13}:C_6$ 13T5, 26T6
39T7 $C_{39}:C_3$ $117$ $1$ ✓ $3$ $C_3$, $C_{13}:C_3$ 39T7 x 2
39T8 $S_3\times D_{13}$ $156$ $-1$ ✓ $1$ $S_3$, $D_{13}$
39T9 $C_{39}:C_4$ $156$ $1$ ✓ $1$ $S_3$, $C_{13}:C_4$
39T10 $C_{13}:C_{12}$ $156$ $-1$ ✓ $3$ $C_3$, $C_{13}:C_4$
39T11 $F_{13}$ $156$ $-1$ ✓ $3$ $C_3$, $F_{13}$ 13T6, 26T8
39T12 $C_{39}:C_6$ $234$ $-1$ ✓ $1$ $S_3$, $C_{13}:C_3$
39T13 $C_{39}:C_6$ $234$ $1$ ✓ $3$ $C_3$, $C_{13}:C_6$ 39T13 x 2
39T14 $C_{39}:C_6$ $234$ $-1$ ✓ $1$ $S_3$, $C_{13}:C_6$
39T15 $D_{39}:C_4$ $312$ $-1$ ✓ $1$ $S_3$, $C_{13}:C_4$
39T16 $C_3^3:C_{13}$ $351$ $1$ ✓ $3$ $C_{13}$ 27T134
39T17 $D_{39}:C_6$ $468$ $-1$ ✓ $1$ $S_3$, $C_{13}:C_6$
39T18 $C_{39}:C_{12}$ $468$ $1$ ✓ $1$ $S_3$, $F_{13}$
39T19 $C_3\times F_{13}$ $468$ $-1$ ✓ $3$ $C_3$, $F_{13}$ 39T19 x 2
39T20 $C_{13}^2:C_3$ $507$ $1$ ✓ $13$ $C_3$ 39T20 x 3
39T21 $C_{13}:C_{39}$ $507$ $1$ ✓ $13$ $C_3$ 39T21 x 3
39T22 $F_{27}$ $702$ $-1$ ✓ $1$ $C_{13}$ 27T219
39T23 $S_3\times F_{13}$ $936$ $-1$ ✓ $1$ $S_3$, $F_{13}$
39T24 $C_{13}^2:C_6$ $1014$ $1$ ✓ $1$ $C_3$ 39T24 x 3
39T25 $C_{13}^2:C_6$ $1014$ $1$ ✓ $1$ $C_3$ 39T25 x 3
39T26 $C_{13}^2:S_3$ $1014$ $-1$ ✓ $13$ $S_3$ 26T14, 39T27
39T27 $C_{13}^2:S_3$ $1014$ $-1$ ✓ $1$ $S_3$ 26T14, 39T26
39T28 $C_3^3:C_{39}$ $1053$ $1$ ✓ $3$ $C_{13}$ 39T28
39T29 $C_3^3:C_{13}:C_3$ $1053$ $1$ ✓ $3$ $C_{13}:C_3$ 27T292, 39T30 x 2
39T30 $C_3^3:C_{13}:C_3$ $1053$ $1$ ✓ $3$ $C_{13}:C_3$ 27T292, 39T29, 39T30
39T31 $C_{13}^2:C_3^2$ $1521$ $1$ ✓ $1$ $C_3$ 39T31 x 3
39T32 $C_{13}:F_{13}$ $2028$ $-1$ ✓ $1$ $C_3$ 39T32 x 3
39T33 $C_{13}:F_{13}$ $2028$ $-1$ ✓ $1$ $C_3$ 39T33 x 3
39T34 $C_{13}^2:D_6$ $2028$ $-1$ ✓ $1$ $S_3$ 26T23, 39T34
39T35 $C_{13}^2:C_3:C_4$ $2028$ $1$ ✓ $1$ $S_3$ 26T24, 39T35
39T36 $C_3:F_{27}$ $2106$ $-1$ ✓ $1$ $C_{13}$ 39T36
39T37 $F_{27}:C_3$ $2106$ $-1$ ✓ $1$ $C_{13}:C_3$ 27T422
39T38 $C_{13}^2:(C_3\times C_6)$ $3042$ $1$ ✓ $1$ $C_3$ 39T38 x 3
39T39 $C_{13}^2:(C_3\times S_3)$ $3042$ $-1$ ✓ $1$ $S_3$ 26T27, 39T40
39T40 $C_{13}^2:(C_3\times S_3)$ $3042$ $-1$ ✓ $1$ $S_3$ 26T27, 39T39
39T41 $C_3^3:C_{39}:C_3$ $3159$ $1$ ✓ $3$ $C_{13}:C_3$ 39T41 x 5
39T42 $C_{13}^2:(C_4\times S_3)$ $4056$ $-1$ ✓ $1$ $S_3$ 26T30, 39T42
39T43 $\PSL(3,3)$ $5616$ $1$ $1$ $\PSL(3,3)$ 13T7 x 2, 26T39 x 2, 39T43
39T44 $C_{13}:(C_3\times F_{13})$ $6084$ $-1$ ✓ $1$ $C_3$ 39T44 x 3
39T45 $C_{13}^2:C_3:C_{12}$ $6084$ $1$ ✓ $1$ $S_3$ 26T41, 39T45
39T46 $C_{13}^2:(C_6\times S_3)$ $6084$ $-1$ ✓ $1$ $S_3$ 26T40, 39T46
39T47 $C_3:F_{27}:C_3$ $6318$ $-1$ ✓ $1$ $C_{13}:C_3$ 39T47
39T48 $C_{13}\wr C_3$ $6591$ $1$ ✓ $13$ $C_3$ 39T48 x 47
39T49 $C_3^6:C_{13}$ $9477$ $1$ ✓ $3$ $C_{13}$ 39T49 x 25
39T50 $C_3^6:C_{13}$ $9477$ $1$ ✓ $3$ $C_{13}$ 39T50 x 25
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