Finite Group DatabasebetaFinite Group Databasebeta| order | 5634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D3×C313⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C313⋊C3) |
| unambiguous semidirect product | (D3×C313)⋊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.
321 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D313⋊C3, C2×D3×C313⋊C3, C5×D3×C313⋊C3, … |
| maximal normal subgroup of | D3×D313⋊C3, C2×D3×C313⋊C3, C5×D3×C313⋊C3 |
| maximal quotient of | Dic3×C313⋊C3, C2×D3×C313⋊C3, C5×D3×C313⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5634, 10);