C₅×#857 #91178

order	480
isoclinism	isoclinic class of #857
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂

Aliases

Fitting	C₄²×C₅ ⋊ D₃
derived	C₄²⋊C₃ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₅	#857
commutator, cosocle, hypocenter	C₄²⋊C₃	C₂×C₅
Frattini	C₂²	C₅×S₄
Fitting	C₄²×C₅	D₃
socle	C₂²×C₅	S₄
LCS	G ▷ C₄²⋊C₃
UCS	C₁ ◁ C₅

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 60

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 254);