Galois group search results

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

Results (5 matches)

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Label	Name	Degree	Order	Parity	Solvable	Nil. class	$\#\Aut(F/K)$	Transitivity	Conj. classes	Subfields	Low Degree Siblings
5T1	$C_5$	$5$	$5$	$1$	✓	$1$	$5$	$1$	$5$
5T2	$D_{5}$	$5$	$10$	$1$	✓	$-1$	$1$	$1$	$4$		10T2
5T3	$F_5$	$5$	$20$	$-1$	✓	$-1$	$1$	$2$	$5$		10T4, 20T5
5T4	$A_5$	$5$	$60$	$1$		$-1$	$1$	$3$	$5$		6T12, 10T7, 12T33, 15T5, 20T15, 30T9
5T5	$S_5$	$5$	$120$	$-1$		$-1$	$1$	$5$	$7$		6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62

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