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
20T26	$C_5:F_5$	$20$	$100$	$-1$	✓	$-1$	$5$	$1$	$13$	$C_2$, $C_4$	25T11
25T11	$C_5:F_5$	$25$	$100$	$-1$	✓	$-1$	$1$	$1$	$13$	$D_{5}$, $F_5$	20T26

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