Finite Group DatabasebetaFinite Group Databasebeta| order | 5733 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C49 ⋊ C9 |
| Sylow | C49 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C49⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14274254 |
| commutator, hypocenter | C13×C49 | C9 |
| Frattini | C3×C7 | #63270 |
| Fitting | C3×C13×C49 | C3 |
| socle | C3×C7×C13 | ΓL(1,𝔽8) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,13,3,7|a^3=d,b^7=e^2,b^a=b^2e,c^a=c^3,e^a=e^2645 conjugacy classes — view the full character table.
| maximal subgroup of | #26039363, #26039367, #26039369, … |
| maximal normal subgroup of | #26039363, #26039367, #26039369, … |
| maximal quotient of | C2×#19153185, C22⋊#19153185, C5×#19153185 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5733, 4);