C₅×#95⋊C₃ #90998

order	480
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×#95⋊C₃
unambiguous semidirect product	#95⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#95)⋊C₃

Fitting, Hall	C₅×#95 ⋊ C₃
derived, Sylow	#95 ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₂×C₅	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₃×C₅
Frattini	C₂³	C₅×A₄
Fitting	C₅×#95	C₃
socle	C₂³×C₅	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₅

42 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)(3,7,12)(4,8,10)(6,11,9)(13,14,15,16,17);(1,9)(3,4)(5,11,10,12)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 74);