Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C9⋊(C23⋊D23) |
| unambiguous semidirect product | C23⋊D207 |
| Fitting, derived, Hall | C9×C232 ⋊ C2 |
| Sylow | C232 ⋊ D9 |
| Sylow | C9 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C232 | C2 |
| Frattini | C3 | C3⋊(C23⋊D23) |
| socle | C3×C232 | D3 |
| LCS | G ▷ C9×C232 | |
| UCS | C1 | |
156 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23^2,3|b^3=e^2,b^a=b^2e,c^a=c^22,d^a=d^22,e^a=e^22382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C23⋊D23, D23×D207, C2×C9⋊(C23⋊D23) |
| maximal normal subgroup of | D9×C23⋊D23, D23×D207, C2×C9⋊(C23⋊D23) |
| maximal quotient of | C9⋊(C23⋊Dic23), C2×C9⋊(C23⋊D23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 19);