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
36T33061 $C_3^5.S_3^2\wr C_2$ $629856$ $-1$ ✓ $1$ $C_2$, $D_{4}$, $C_3^2:D_4$, $D_6\wr C_2$
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