C₂₃×C₃⋊S₄ #13110281

order	1656
isoclinism	isoclinic class of C₃⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂₃×C₃⋊S₄
unambiguous semidirect product	C₃⋊(C₂₃×S₄)
unambiguous semidirect product	A₄⋊(D₃×C₂₃)

Fitting, socle	C₂²×C₃×C₂₃ ⋊ D₃
derived	C₃×A₄ ⋊ C₂×C₂₃

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

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 276

A minimal faithful permutation representation — 3 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,26)(29,30);(28,29,30);(25,26,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1656, 119);