C₃²×#6855 #14552013

order	2187
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉² · Schur multiplier (H₂) = C₃⁸

Aliases

6542 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 2187

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3);(4,5,6);(7,8,10)(9,12,14)(11,15,13)(16,17,19,18,20,22,21,23,24);(8,11,12)(10,14,15)(25,26,28,27,29,31,30,32,33)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2187, 5872);