Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×C3⋊(C23⋊D23) |
| unambiguous semidirect product | C3⋊(C3×C23⋊D23) |
| unambiguous semidirect product | C23⋊(C3×D69) |
| Fitting, socle, Hall | C32×C232 ⋊ C2 |
| derived | C3×C232 ⋊ C2×C3 |
| Sylow | C232 ⋊ C3×D3 |
| Sylow | C32 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C23⋊D23) |
| commutator, cosocle, hypocenter | C3×C232 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C232 | C2 |
| LCS | G ▷ C3×C232 | |
| UCS | C1 ◁ C3 | |
234 conjugacy classes of subgroups.
2385 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C23⋊D23, C3×D23×D69, D3×C3⋊(C23⋊D23), … |
| maximal normal subgroup of | C3×D3×C23⋊D23, C3×D23×D69, D3×C3⋊(C23⋊D23), … |
| maximal quotient of | C3×C3⋊(C23⋊Dic23), C2×C3×C3⋊(C23⋊D23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 31);