Finite Group DatabasebetaFinite Group Databasebeta| order | 32409 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C277 · Schur multiplier (H2) = C3 |
| direct product | C3×C13⋊C3×C277 |
| unambiguous semidirect product | C13⋊(C32×C277) |
| unambiguous semidirect product | (C3×C13)⋊(C3×C277) |
| Fitting, socle | C3×C13×C277 ⋊ C3 |
| derived, Sylow | C13 ⋊ C32×C277 |
| Hall | C13×C277 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C277 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C32×C277 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C277 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C277 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10803 |
5817 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32409, 9);