C₂×C₅×Dic₅ #6043

order	200
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₄×D₄×AGL(1,𝔽₅) (order 640) · Inn(G) = D₅ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₅×Dic₅

derived	C₅ ⋊ C₂×C₄×C₅
Sylow	C₅² ⋊ C₂×C₄

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2)(3,4,5,6)(8,9)(10,11)(12,13,14,15,16);(1,2)(7,8,10,11,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 30);