C₂²×C₅²×C₁₆ #13103239

order	1600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 368640
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅

Aliases

C₂²×C₅²×C₁₆

392 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 1600

A minimal faithful permutation representation — 3 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5591);