C₃×C₄⋊Dic₁₁ #10587170

order	528
isoclinism	isoclinic class of Dic₂₂
automorphism	Aut(G) = C₂×#120×AGL(1,𝔽₁₁) (order 7040) · Inn(G) = C₂×D₁₁ · Out(G) = C₂²×C₅×D₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊Dic₁₁
unambiguous semidirect product	C₄⋊(C₃×Dic₁₁)

Hall	C₃×C₁₁ ⋊ C₄⋊C₄
Sylow	C₁₁ ⋊ C₃×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 528

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 40);