C₉²×C₂₇ #14550211

order	2187
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 459165024
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉³

Aliases

C₉²×C₂₇

764 conjugacy classes of subgroups.

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 2187

A minimal faithful permutation representation — 3 generators on 45 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)

2187 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2187, 4070);