Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C92 · Schur multiplier (H2) = C34×C9 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C3×C9 | C34 |
| commutator | C3 | C32×C92 |
| socle | C32 | C33×C9 |
| prime radical | C3×H(3,𝔽3) | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ G | |
| LECS | G ▷ C3×C9 ▷ C3 ▷ C1 | |
1133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
Polycyclic presentation:
3^7|a^3=e,b^3=f,e^3=g,b^a=bg,d^c=dg747 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 7963);