Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1587 |
| unambiguous semidirect product | C3⋊(C3×D529) |
| unambiguous semidirect product | C529⋊(C3×D3) |
| Fitting, Hall | C32×C529 ⋊ C2 |
| derived | C3×C529 ⋊ C2×C3 |
| Sylow | C529 ⋊ C3×D3 |
| Sylow | C32 ⋊ D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1587 |
| commutator, cosocle, hypocenter | C3×C529 | C2×C3 |
| Frattini | C23 | C3×D69 |
| Fitting | C32×C529 | C2 |
| socle | C32×C23 | D23 |
| LCS | G ▷ C3×C529 | |
| UCS | C1 ◁ C3 | |
27 conjugacy classes of subgroups.
2385 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D529, D3×D1587, (C3⋊D3)⋊D529, … |
| maximal normal subgroup of | C3×D3×D529, D3×D1587, (C3⋊D3)⋊D529, … |
| maximal quotient of | C3×Dic1587, C2×C3×D1587 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 8);