C₂×C₅²×C₃₂ #13099650

order	1600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 30720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂×C₅²×C₃₂

136 conjugacy classes of subgroups.

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(35,36,37,38,39);(33,34)(40,41,42,43,44)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2002);