C₂³×C₈×C₂₅ #13099218

order	1600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 860160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

C₂³×C₈×C₂₅

507 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 4 generators on 39 points:

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

1600 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 1570);