C₅³×C₁₆ #14522508

order	2000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11904000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅³

Aliases

C₅³×C₁₆

320 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 2000

A minimal faithful permutation representation — 3 generators on 31 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);(27,28,29,30,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 471);