C₃×C₉×C₉⋊C₉ #14552012

order	2187
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉² · Schur multiplier (H₂) = C₃⁵×C₉

Aliases

C₃×C₉×C₉⋊C₉

2114 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);(14,16,19)(17,21,20)(22,23,25,24,26,28,27,29,30);(13,14,17,15,16,20,18,19,21)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2187, 5871);