C₅×#672 #87755

order	400
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×C₄²×AGL(1,𝔽₅) (order 640) · Inn(G) = D₅ · Out(G) = C₂²×C₄²
homology	Abelianization (H₁) = C₅×C₁₆ · Schur multiplier (H₂) = C₁

Aliases

derived	C₅ ⋊ C₅×C₁₆
Sylow	C₅² ⋊ C₁₆

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 49);