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 (displaying both matches)

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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
36T16575 $\He_3^2.\SOPlus(4,2)$ $52488$ $-1$ ✓ $1$ $C_2$, $D_{4}$, $S_3^2$, $C_3:D_{12}$ 36T16575 x 5, 36T16634 x 6
36T16634 $\He_3^2.\SOPlus(4,2)$ $52488$ $-1$ ✓ $1$ $C_2$, $D_{4}$, $S_3\times C_3$, $C_6\wr C_2$ 36T16575 x 6, 36T16634 x 5
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