order	125
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₄×#92539 (order 2000) · Inn(G) = C₁ · Out(G) = C₄×#92539
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

C₅×C₂₅

Subgroups

14 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 125

A minimal faithful permutation representation — 2 generators on 30 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)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(125, 2);