Finite Group DatabasebetaFinite Group Databasebeta| order | 5733 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#11717942 |
| derived | C7×C13 ⋊ C7×C9 |
| Hall | C72×C13 ⋊ C9 |
| Sylow | C72 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #63271 |
| commutator, hypocenter | C7×C13 | C7×C9 |
| Frattini | C3 | C7×#63271 |
| Fitting, socle | C3×C72×C13 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C7 | |
32 conjugacy classes of subgroups.
693 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5733, 15);