C₁₁×S₅ #13050431

order	1320
isoclinism	isoclinic class of S₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₁×S₅
unambiguous semidirect product	A₅⋊(C₂×C₁₁)

socle	C₁₁×A₅ ⋊ C₂
derived	A₅ ⋊ C₂×C₁₁

	subgroup	G/H
center, Fitting, hypercenter	C₁₁	S₅
commutator, cosocle, hypocenter	A₅	C₂×C₁₁
Frattini	C₁	G
socle	C₁₁×A₅	C₂
LCS	G ▷ A₅
UCS	C₁ ◁ C₁₁

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 55

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 135);