order	200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₄×C₅ (order 80) · Inn(G) = C₁ · Out(G) = C₂²×C₄×C₅
holomorph	G ⋊ Aut(G) = AGL(1,ℤ/8)×AGL(1,ℤ/25)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₀₀
abelian	C₈×C₂₅

Subgroups

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 1 generator on 33 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 2);