C₂²×C₄×C₅³ #14522929

order	2000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 285696000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅³

Aliases

C₂²×C₄×C₅³

1728 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 2000

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 892);