Finite Group DatabasebetaFinite Group Databasebeta| order | 32769 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C32×C331⋊C11 |
| unambiguous semidirect product | (C32×C331)⋊C11 |
| Fitting, socle, Hall | C32×C331 ⋊ C11 |
| derived, Sylow | C331 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C331⋊C11 |
| commutator, cosocle, hypocenter | C331 | C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C331 | C11 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2979 |
369 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32769, 7);