Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #14550750 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | #6895 |
| commutator, Frattini, cosocle | C32×C9 | C33 |
| prime radical | C33 | C3×3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
155 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^7|a^3=efg^2,b^3=de,c^3=d,d^3=g^2,e^3=g,f^3=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg^2,c^b=cf,d^b=dg,e^b=eg^2,f^b=fg^2,e^c=eg^2123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4672);