C₃×C₉×C₃²⋊C₉ #14552011

order	2187
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₉² · Schur multiplier (H₂) = C₃⁶×C₉

Aliases

C₃×C₉×C₃²⋊C₉

3464 conjugacy classes of subgroups; only the 1412 normal subgroups are shown.

normal subgroups only

This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 1412 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 729

A minimal faithful permutation representation — 4 generators on 30 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2187, 5870);