Dic₅×C₂₃ #90743

order	460
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂²×C₁₁×AGL(1,𝔽₅) (order 880) · Inn(G) = D₅ · Out(G) = C₂³×C₁₁
homology	Abelianization (H₁) = C₄×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

Dic₅×C₂₃

derived, Sylow	C₅ ⋊ C₄×C₂₃
Hall	C₅×C₂₃ ⋊ C₄

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 460

A minimal faithful permutation representation — 2 generators on 32 points:

(1,4,3,2)(6,7)(8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(5,6,8,9,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(460, 1);