D₅×C₄²⋊C₃ #91188

order	480
isoclinism	isoclinic class of D₅×C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₄

Aliases

direct product	D₅×C₄²⋊C₃
unambiguous semidirect product	C₅⋊(C₂×C₄²⋊C₃)
unambiguous semidirect product	(C₄²×D₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄²×C₅	C₂×C₃
Frattini	C₂²	D₅×A₄
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₄²×C₅
UCS	C₁

56 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 264);