C₂×C₉×S₄ #88885

order	432
isoclinism	isoclinic class of S₄
automorphism	Aut(G) = C₂²×C₃×S₄ (order 288) · Inn(G) = S₄ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₉×S₄
unambiguous semidirect product	A₄⋊(C₂²×C₉)
unambiguous semidirect product	(C₂×A₄)⋊(C₂×C₉)

Fitting	C₂³×C₉ ⋊ D₃
derived	A₄ ⋊ C₂²×C₉

107 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 2 generators on 15 points:

(3,4,6,5)(7,11,15,9,14,10,12,8,13);(1,2)(4,5,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 532);