C₅×#170 #6031

order	200
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	Aut(G) = C₂×C₄×AGL(1,𝔽₅) (order 160) · Inn(G) = AGL(1,𝔽₅) · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₁

Aliases

derived	C₅ ⋊ C₅×C₈
Sylow	C₅² ⋊ C₈

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 40

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 18);