C₅×C₂²⋊Dic₁₁ #11724905

order	880
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×C₂²⋊Dic₁₁
unambiguous semidirect product	C₂²⋊(C₅×Dic₁₁)

Hall	C₅×C₁₁ ⋊ C₂²⋊C₄
Sylow	C₁₁ ⋊ C₅×C₂²⋊C₄

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 440

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5)(6,7,9,11,13,15,16,14,12,10,8)(22,24);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(21,22)(23,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 73);