Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C36 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C32×C9 | C33 |
| commutator | C32 | C32×C27 |
| socle | C33 | C32×C9 |
| prime radical | C35 | C9 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
1961 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^7|a^3=f,f^3=g,b^a=bd,c^a=ce459 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4133);