C₂×C₅³×C₈ #14522657

order	2000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 23808000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅³

Aliases

C₂×C₅³×C₈

704 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 2000

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5,6,7,8)(11,12,13,14,15);(9,10)(16,17,18,19,20);(21,22,23,24,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 620);