C₂×C₅×C₈×C₂₅ #14522256

order	2000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 32000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂×C₅×C₈×C₂₅

154 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 2000

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5,6,7,8)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35);(9,10)(36,37,38,39,40)

2000 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 219);