Finite Group DatabasebetaFinite Group Databasebeta| order | 5634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C313⋊C9 |
| unambiguous semidirect product | (C2×C313)⋊C9 |
| derived, Sylow | C313 ⋊ C2×C9 |
| Hall | C2×C313 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C313⋊C3 |
| commutator, hypocenter | C313 | C2×C9 |
| Frattini | C3 | C2×C313⋊C3 |
| Fitting, socle | C2×C3×C313 | C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
642 conjugacy classes — view the full character table.
| maximal subgroup of | Dic313⋊C9, C4×C313⋊C9, C2×D313⋊C9, … |
| maximal normal subgroup of | Dic313⋊C9, C4×C313⋊C9, C2×D313⋊C9, … |
| maximal quotient of | C4×C313⋊C9, C22×C313⋊C9, C2×C5×C313⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5634, 3);