C₁₁⋊S₄ #63164

order	264
isoclinism	isoclinic class of C₁₁⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₁₁⋊S₄
unambiguous semidirect product	A₄⋊D₁₁

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

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 44

A minimal faithful permutation representation — 2 generators on 15 points:

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

Polycyclic presentation:

2,3,11,2^2|b^a=b^2,c^a=c^10,d^a=e,e^a=d,d^b=e,e^b=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 32);