C₂₃×S₄ #10587793

order	552
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₃×S₄
unambiguous semidirect product	A₄⋊(C₂×C₂₃)

Fitting, socle	C₂²×C₂₃ ⋊ D₃
derived	A₄ ⋊ C₂×C₂₃

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

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 92

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27);(24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 31);