C₅×C₁₆² #11929771

order	1280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 98304
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

C₅×C₁₆²

166 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 2 generators on 37 points:

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

1280 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 39);