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) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C27 | C92 |
| commutator | C9 | C9×C27 |
| Frattini, cosocle | C3×C81 | C32 |
| socle | C3 | #10624499 |
| prime radical | C32 | C81⋊C3 |
| LCS | G ▷ C9 ▷ C1 | |
| UCS | C1 ◁ C27 ◁ G | |
| LECS | G ▷ C3×C81 ▷ C27 ▷ C9 ▷ C3 ▷ C1 | |
46 conjugacy classes of subgroups.
| minimal degree | μ(G) = 243 |
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^7|a^3=c,b^3=d,c^3=e,e^3=f,f^3=g,b^a=bf,d^a=dg,c^b=cg^2315 conjugacy classes — view the full character table.
| Fitting subgroup of | #72277482 |
| maximal subgroup of | #72277450, #72277482 |
| maximal normal subgroup of | #72277450, #72277482 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 314);