C₃×C₉³ #14552007

order	2187
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 322333846848
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₉³

Aliases

C₃×C₉³

4166 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 2187

A minimal faithful permutation representation — 4 generators on 30 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)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2187, 5866);