Finite Group DatabasebetaFinite Group Databasebeta| order | 5733 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C13⋊#89205 |
| derived, Hall | C72×C13 ⋊ C9 |
| Sylow | C72 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ #89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C13⋊#3862 |
| commutator, hypocenter | C72×C13 | C9 |
| Fitting, socle | C3×C72×C13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3,7^2,13,3|a^3=e,b^a=b^2,c^a=c^4,d^a=d^3645 conjugacy classes — view the full character table.
| maximal subgroup of | #26039450, #26039451, #26039460, … |
| maximal normal subgroup of | #26039450, #26039451, #26039460, … |
| maximal quotient of | C2×C13⋊#89205, C22⋊(C13⋊#89205), C5×C13⋊#89205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5733, 21);