C₃×Dic₂₂ #63145

order	264
isoclinism	isoclinic class of Dic₂₂
automorphism	Aut(G) = C₂×D₄×AGL(1,𝔽₁₁) (order 1760) · Inn(G) = C₂×D₁₁ · Out(G) = C₂³×C₅
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₂₂
unambiguous semidirect product	C₁₁⋊(C₃×Q₈)

Hall	C₃×C₁₁ ⋊ Q₈
Sylow	C₁₁ ⋊ C₃×Q₈

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 13);