C₅×C₁₁⋊S₄ #13050451

order	1320
isoclinism	isoclinic class of C₁₁⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×C₁₁⋊S₄
unambiguous semidirect product	A₄⋊(C₅×D₁₁)

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊S₄
commutator, cosocle, hypocenter	C₁₁×A₄	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁	D₃
LCS	G ▷ C₁₁×A₄
UCS	C₁ ◁ C₅

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 220

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3,4,5)(6,7,9,8)(11,12)(13,14)(15,16)(17,18)(19,20);(7,8,9)(10,11,13,15,17,19,20,18,16,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 155);