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	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
3T2	$S_3$	$6$	$-1$	✓	$-1$	$3$		6T2
6T2	$S_3$	$6$	$-1$	✓	$-1$	$3$	$C_2$, $S_3$	3T2

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Results are complete for degrees $\leq 23$.