C₅×#120⋊C₃ #91580

order	480
isoclinism	isoclinic class of #120⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×#120⋊C₃
unambiguous semidirect product	#120⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#120)⋊C₃

	subgroup	G/H
center, hypercenter	C₅	#120⋊C₃
commutator, cosocle, hypocenter	C₂⁴	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×A₄
Fitting	C₅×#120	C₃
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₅

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 656);