C₁₆×C₃₂ #93663

order	512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₆

Aliases

C₁₆×C₃₂

114 conjugacy classes of subgroups.

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 2 generators on 48 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);(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 859);