A₄×#168 #91189

order	480
isoclinism	isoclinic class of D₅×A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×#168
unambiguous semidirect product	(C₂²×#168)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅×A₄
commutator, hypocenter	C₂²×C₅	C₃×C₈
Fitting, cosocle	C₂²×C₄×C₅	C₂×C₃
socle	C₂³×C₅	C₃×C₄
prime radical	C₂×C₅×A₄	C₄
LCS	G ▷ C₂²×C₅
UCS	C₁ ◁ C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 17 points:

(2,3)(4,5)(7,8,9)(10,14,16,11,13,17,12,15);(1,2,4,5,3)(6,9)(7,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 265);