C₂²×C₅⋊S₄ #92123

order	480
isoclinism	isoclinic class of C₅⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂²×C₅⋊S₄

	subgroup	G/H
center, hypercenter	C₂²	C₅⋊S₄
commutator, cosocle, hypocenter	C₅×A₄	C₂³
Frattini	C₁	G
Fitting, socle	C₂⁴×C₅	D₃
LCS	G ▷ C₅×A₄
UCS	C₁ ◁ C₂²

262 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1199);