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)

  displayed columns for results
Label Name Order Parity Solvable $\#\Aut(F/K)$ Subfields Low Degree Siblings
27T271 $C_3^3:S_3^2$ $972$ $-1$ ✓ $1$ $S_3$ x 2, $S_3^2$ 27T271, 27T285 x 2
27T285 $C_3^3:S_3^2$ $972$ $-1$ ✓ $1$ $C_3$, $S_3$, $S_3\times C_3$ 27T271 x 2, 27T285
  displayed columns for results