C₁₁×Dic₁₀ #89176

order	440
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂×C₅×D₄×AGL(1,𝔽₅) (order 1600) · Inn(G) = C₂×D₅ · Out(G) = C₂²×C₄×C₅
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₁₀
unambiguous semidirect product	C₅⋊(Q₈×C₁₁)

Hall	C₅×C₁₁ ⋊ Q₈
Sylow	C₅ ⋊ Q₈×C₁₁

24 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 29);