Finite Group DatabasebetaFinite Group Databasebeta| order | 5634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D313⋊C3) |
| unambiguous semidirect product | (C313⋊C3)⋊D3 |
| unambiguous semidirect product | D939⋊C3 |
| Fitting, socle, derived | C3×C313 ⋊ C2×C3 |
| Hall | C3×C313⋊C3 ⋊ C2 |
| Sylow | C313 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C313 | C2×C3 |
| LCS | G ▷ C3×C313 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,313|c^a=c^2,d^a=d^312,d^b=d^214165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5634, 9);