Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#15691772 |
| Fitting, socle | C3×C232 ⋊ D3 |
| derived | C232⋊C3 ⋊ C2×C3 |
| Hall | C3×C232⋊C3 ⋊ C2 |
| Sylow | C232 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15691772 |
| commutator, cosocle, hypocenter | C232⋊C3 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | D3 |
| LCS | G ▷ C232⋊C3 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
372 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#15691772⋊C2, #15691772⋊D3, D3×#15691772, … |
| maximal normal subgroup of | C3×#15691772⋊C2, #15691772⋊D3, D3×#15691772, … |
| maximal quotient of | C3×#20263650, C2×C3×#15691772 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 21);