Finite Group DatabasebetaFinite Group Databasebeta| order | 9366 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D223⋊C3 |
| unambiguous semidirect product | D223⋊(C3×C7) |
| unambiguous semidirect product | (C223⋊C3)⋊(C2×C7) |
| Fitting, socle, Hall | C7×C223 ⋊ C2×C3 |
| derived, Sylow | C223 ⋊ C2×C3×C7 |
| Hall | C7×C223⋊C3 ⋊ C2 |
| Hall | C7×D223 ⋊ C3 |
| Hall | C223⋊C3 ⋊ C2×C7 |
| Hall | D223 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D223⋊C3 |
| commutator, hypocenter | C223 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C223 | C2×C3 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9366, 13);