Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C92 |
| commutator | C9 | C9×C27 |
| Frattini, cosocle | C9×C27 | C32 |
| socle, prime radical | C32 | #6864 |
| LCS | G ▷ C9 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ G | |
| LECS | G ▷ C9×C27 ▷ C3×C9 ▷ C3 ▷ C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2187 |
Polycyclic presentation:
3^7|a^3=c,b^3=d,c^3=e,d^3=f,e^3=g,b^a=be,d^a=dg,c^b=cg^2315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 82);