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Parity	Cyclic	Solvable	Primitive	Equivalent siblings

Degree	$T$-number	Order	Group	Nilpotency class

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Results (4 matches)

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Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
20T33	$C_5:S_4$	$120$	$-1$	✓	$-1$	$13$	$S_4$, $D_{5}$	30T19, 30T31, 40T63
30T19	$C_5:S_4$	$120$	$1$	✓	$-1$	$13$	$S_3$, $D_{5}$, $S_4$, $D_{15}$	20T33, 30T31, 40T63
30T31	$C_5:S_4$	$120$	$-1$	✓	$-1$	$13$	$S_3$, $D_{5}$, $S_4$, $D_{15}$	20T33, 30T19, 40T63
40T63	$C_5:S_4$	$120$	$1$	✓	$-1$	$13$	$C_2$, $S_4$, $D_{5}$, $S_4$, $D_5$, $C_5:S_4$	20T33, 30T19, 30T31

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Results are complete for degrees $\leq 23$.