C₅³×C₁₇ #14523795

order	2125
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 23808000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅³

Aliases

C₅³×C₁₇

128 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 2125

A minimal faithful permutation representation — 3 generators on 32 points:

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

2125 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2125, 5);