C₂×C₅×C₄²⋊C₃ #91578

order	480
isoclinism	isoclinic class of C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₄

Aliases

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

	subgroup	G/H
center, hypercenter	C₂×C₅	C₄²⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×A₄
Fitting	C₂×C₄²×C₅	C₃
socle	C₂³×C₅	A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ C₂×C₅

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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 654);