Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C23 |
| direct product | C3×(C23⋊D23)⋊C3 |
| unambiguous semidirect product | (C23⋊D23)⋊C32 |
| unambiguous semidirect product | (C3×C23⋊D23)⋊C3 |
| Fitting, socle | C3×C232 ⋊ C2×C3 |
| derived, Sylow | C232 ⋊ C2×C32 |
| Hall | C3×C232⋊C3 ⋊ C2 |
| Hall | C23⋊D23 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C23⋊D23)⋊C3 |
| commutator, cosocle, hypocenter | C232 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C2×C3 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
282 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#15691772⋊C2, C3×#14523747⋊C3, C3×#20263661, … |
| maximal normal subgroup of | C3×#15691772⋊C2, C3×#14523747⋊C3, C3×#20263661, … |
| maximal quotient of | C3×(C23⋊Dic23)⋊C3, C2×C3×(C23⋊D23)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 22);