Finite Group DatabasebetaFinite Group Databasebeta| order | 5733 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#14274254 |
| Fitting | C3×C13×C49 ⋊ C3 |
| derived, Hall | C13×C49 ⋊ C32 |
| Sylow | C49 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14274254 |
| commutator, hypocenter | C13×C49 | C32 |
| Frattini | C7 | C3×#63270 |
| Fitting | C3×C13×C49 | C3 |
| socle | C3×C7×C13 | ΓL(1,𝔽8) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
645 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5733, 10);