Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C9 · Schur multiplier (H2) = C39 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9 | C34 |
| commutator | C3 | C34×C9 |
| Frattini, socle, cosocle | C32 | C35 |
| prime radical | C32×H(3,𝔽3) | C32 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9 ◁ G | |
| LECS | G ▷ C32 ▷ C1 | |
5435 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^7|a^3=g,e^3=f,b^a=bf,d^c=df747 conjugacy classes — view the full character table.
| maximal subgroup of | #72270990 |
| maximal normal subgroup of | #72270990 |
| maximal quotient of | #72270942 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 9103);