Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #10624562 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C32×C9 | C33 |
| commutator, socle | C33 | C32×C9 |
| prime radical | C34 | C3×C9 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
314 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 729 |
Polycyclic presentation:
3^7|a^3=f,b^3=f,c^3=d,f^3=g,b^a=bd,c^a=ce,c^b=cg315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4354);