Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6881 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C9 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | #732 |
| commutator | C3×C9 | C3×C27 |
| Frattini, cosocle | C3×C92 | C32 |
| socle | C32 | H(3,𝔽3)⋊C9 |
| prime radical | C33 | C32⋊C9 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ C32×C9 ◁ C3×C92 ◁ G | |
| LECS | G ▷ C3×C92 ▷ C33 ▷ C3 ▷ C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
Polycyclic presentation:
3^7|a^3=d,b^3=g,c^3=g^2,d^3=f,b^a=bc,c^a=ce,e^a=eg,c^b=ceg,e^b=eg171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 116);