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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Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
36T34087 $C_3^7.C_3\wr C_2^2$ $708588$ $1$ ✓ $3$ $C_2$ x 3, $C_2^2$, $C_3\wr C_2^2$ 36T34087 x 80
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