Finite Group DatabasebetaFinite Group Databasebeta| order | 27243 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1009 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | C1009⋊C3 |
| commutator, hypocenter | C1009 | C27 |
| Fitting, cosocle | C9×C1009 | C3 |
| socle, prime radical | C3×C1009 | C9 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C9 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27243 |
Polycyclic presentation:
3^3,1009|a^3=b,b^3=c,d^a=d^3743051 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27243, 6);