C₂×C₉⋊S₄ #88889

order	432
isoclinism	isoclinic class of C₉⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	C₂×C₉⋊S₄
unambiguous semidirect product	(C₂×C₉)⋊S₄
unambiguous semidirect product	(C₂×A₄)⋊D₉

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

	subgroup	G/H
center, hypercenter	C₂	C₉⋊S₄
commutator, cosocle, hypocenter	C₉×A₄	C₂²
Frattini	C₃	C₂×C₃⋊S₄
Fitting	C₂³×C₉	D₃
socle	C₂³×C₃	C₃⋊D₃
LCS	G ▷ C₉×A₄
UCS	C₁ ◁ C₂

139 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 536);