order	200
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₄×C₅×S₄ (order 480) · Inn(G) = C₂² · Out(G) = C₄×C₅×D₃
homology	Abelianization (H₁) = C₂²×C₂₅ · Schur multiplier (H₂) = C₁

Aliases

Q₈×C₂₅

Subgroups

	subgroup	G/H
center	C₂×C₂₅	C₂²
commutator	C₂	C₂²×C₂₅
Frattini, socle, prime radical, cosocle	C₂×C₅	C₂²×C₅
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₅ ◁ G

18 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4)(5,8,7,6)(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);(1,5,3,7)(2,6,4,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 11);