C₁₁×A₄⋊C₈ #11760679

order	1056
isoclinism	isoclinic class of S₄
automorphism	?
homology	Abelianization (H₁) = C₈×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₁×A₄⋊C₈
unambiguous semidirect product	A₄⋊(C₈×C₁₁)

A₄ ⋊ C₈×C₁₁

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17,18,20,19,21,22,23);(13,14,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 216);