Finite Group DatabasebetaFinite Group Databasebeta| order | 32799 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C841 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×C841 |
| unambiguous semidirect product | C13⋊(C3×C841) |
| unambiguous semidirect product | (C13×C841)⋊C3 |
| Fitting, Hall | C13×C841 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C841 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C841 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C841 |
| Frattini | C29 | C29×C13⋊C3 |
| Fitting | C13×C841 | C3 |
| socle, cosocle | C13×C29 | C3×C29 |
| prime radical | C29×C13⋊C3 | C29 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C841 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10933 |
5887 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32799, 2);