C₅×#127⋊C₃ #91582

order	480
isoclinism	isoclinic class of #127⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₄

Aliases

direct product	C₅×#127⋊C₃
unambiguous semidirect product	#127⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#127)⋊C₃

	subgroup	G/H
center, hypercenter	C₅	#127⋊C₃
commutator, cosocle, hypocenter	C₄²	C₂×C₃×C₅
Frattini	C₂²	C₂×C₅×A₄
Fitting	C₅×#127	C₃
socle	C₂²×C₅	C₂×A₄
LCS	G ▷ C₄²
UCS	C₁ ◁ 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 658);