C₅×Dic₅ #1038

order	100
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₅) (order 160) · Inn(G) = D₅ · Out(G) = C₂²×C₄
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

derived	C₅ ⋊ C₄×C₅
Sylow	C₅² ⋊ C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 20

A minimal faithful permutation representation — 2 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(100, 6);