Finite Group DatabasebetaFinite Group Databasebeta| order | 9222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1537 |
| unambiguous semidirect product | C29⋊(C3×D53) |
| unambiguous semidirect product | C53⋊(C3×D29) |
| Fitting, socle, Hall | C3×C29×C53 ⋊ C2 |
| derived, Hall | C29×C53 ⋊ C2×C3 |
| Hall | C3×C53 ⋊ D29 |
| Hall | C3×C29 ⋊ D53 |
| Sylow | C53 ⋊ C3×D29 |
| Sylow | C29 ⋊ C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1537 |
| commutator, hypocenter | C29×C53 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C53 | C2 |
| LCS | G ▷ C29×C53 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
2310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20259617, C3×#20259618, C3×D29×D53, … |
| maximal normal subgroup of | C3×#20259617, C3×#20259618, C3×D29×D53, … |
| maximal quotient of | C3×Dic1537, C2×C3×D1537, C9×D1537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9222, 4);