C₃×C₁₆×C₂₇ #13046333

order	1296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2592
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₁₆×C₂₇

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 2 generators on 46 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)

1296 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 51);