C₅×#676 #87783

order	400
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂³×C₄×AGL(1,𝔽₅) (order 640) · Inn(G) = C₂×D₅ · Out(G) = C₂×C₄²
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

Fitting	C₅²×C₈ ⋊ C₂
Sylow	C₅² ⋊ M₁₆

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 18 points:

(1,2,3,4,5)(6,7,9,10,8)(11,15,13,18,14,12,17,16);(7,8)(9,10)(12,15)(16,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 77);