Galois group search results

The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

Results (displaying both matches)

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Label	Name	Degree	Order	Parity	Solvable	Nil. class	$\#\Aut(F/K)$	Transitivity	Conj. classes	Subfields	Low Degree Siblings
27T2093	$C_3^6.Q_8\wr S_3:S_3$	$27$	$13436928$	$-1$	✓	$-1$	$1$	$1$	$113$	$S_3$	36T62251
36T62251	$C_3^6.Q_8\wr S_3:S_3$	$36$	$13436928$	$1$	✓	$-1$	$1$	$1$	$113$	$S_3$, $C_2^6:S_3^2$	27T2093

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