Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| isoclinism | isoclinic class of D207 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D207 |
| unambiguous semidirect product | C9⋊(C23×D23) |
| unambiguous semidirect product | C23⋊(D9×C23) |
| Fitting, Hall | C9×C232 ⋊ C2 |
| derived | C9×C23 ⋊ C2×C23 |
| Sylow | C232 ⋊ D9 |
| Sylow | C9 ⋊ C23×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D207 |
| commutator, cosocle, hypocenter | C9×C23 | C2×C23 |
| Frattini | C3 | C23×D69 |
| Fitting | C9×C232 | C2 |
| socle | C3×C232 | D3 |
| LCS | G ▷ C9×C23 | |
| UCS | C1 ◁ C23 | |
57 conjugacy classes of subgroups.
2415 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C23×D23, D23×D207, D207⋊D23, … |
| maximal normal subgroup of | D9×C23×D23, D23×D207, D207⋊D23, … |
| maximal quotient of | C23×Dic207, C2×C23×D207 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 18);