Finite Group DatabasebetaFinite Group Databasebeta| order | 32769 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C331⋊C9)⋊C11 |
| unambiguous semidirect product | (C331⋊C11)⋊C9 |
| derived, Sylow | C331 ⋊ C9×C11 |
| Hall | C331⋊C11 ⋊ C9 |
| Hall | C331⋊C9 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C331⋊C3)⋊C11 |
| commutator, hypocenter | C331 | C9×C11 |
| Fitting, socle, cosocle | C3×C331 | C3×C11 |
| prime radical | C3×C331⋊C11 | C3 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2979 |
Polycyclic presentation:
3,11,331,3|a^3=d,c^a=c^299,c^b=c^270129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32769, 2);