Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | Aut(G) order 14454396 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4761 |
| unambiguous semidirect product | C9⋊D529 |
| unambiguous semidirect product | C529⋊D9 |
| Fitting, derived, Hall | C9×C529 ⋊ C2 |
| Sylow | C529 ⋊ D9 |
| Sylow | C9 ⋊ D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C529 | C2 |
| Frattini, socle | C3×C23 | D69 |
| LCS | G ▷ C9×C529 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,3,23|b^3=d^2,c^23=e^22,b^a=b^2d,c^a=c^22e,d^a=d^2,e^a=e^222382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D529, C2×D4761, D14283 |
| maximal normal subgroup of | D9×D529, C2×D4761 |
| maximal quotient of | Dic4761, C2×D4761, D14283 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 4);