Dic₅×C₂₅ #92521

order	500
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×C₄×C₅×AGL(1,𝔽₅) (order 800) · Inn(G) = D₅ · Out(G) = C₂²×C₄×C₅
homology	Abelianization (H₁) = C₄×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

Dic₅×C₂₅

derived	C₅ ⋊ C₄×C₂₅
Sylow	C₅×C₂₅ ⋊ C₄

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 100

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4)(6,7)(8,9)(10,11,13,16,20,12,14,17,21,25,15,18,22,26,29,19,23,27,30,32,24,28,31,33,34);(5,6,8,9,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(500, 7);