Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1587 |
| unambiguous semidirect product | C529⋊(C3⋊D3) |
| Fitting, derived, Hall | C32×C529 ⋊ C2 |
| Sylow | C529 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C529 | C2 |
| Frattini | C23 | C3⋊D69 |
| socle | C32×C23 | D23 |
| LCS | G ▷ C32×C529 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,23^2|d^23=e^22,b^a=b^2,c^a=c^2,d^a=d^22e,e^a=e^222382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×D529, D3×D1587, C2×C3⋊D1587 |
| maximal normal subgroup of | C3⋊D3×D529, D3×D1587, C2×C3⋊D1587 |
| maximal quotient of | C3⋊Dic1587, C2×C3⋊D1587 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 10);