A₄⋊D₂₃ #10587794

order	552
isoclinism	isoclinic class of A₄⋊D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	A₄⋊D₂₃
unambiguous semidirect product	C₂₃⋊S₄

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

22 conjugacy classes of subgroups.

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

Polycyclic presentation:

2,3,23,2^2|b^a=b^2,c^a=c^22,d^a=e,e^a=d,d^b=e,e^b=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 32);