C₅×#1020 #92124

order	480
isoclinism	isoclinic class of #1020
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Fitting, socle	C₂⁴×C₅ ⋊ D₃
derived	C₂²⋊A₄ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₅	#1020
commutator, cosocle, hypocenter	C₂²⋊A₄	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂⁴×C₅	D₃
LCS	G ▷ C₂²⋊A₄
UCS	C₁ ◁ C₅

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1200);