Finite Group DatabasebetaFinite Group Databasebeta| order | 9522 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C529 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C529 |
| unambiguous semidirect product | C3⋊(D3×C529) |
| Fitting, Hall | C32×C529 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C529 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C529 |
| Frattini | C23 | C3⋊D3×C23 |
| Fitting | C32×C529 | C2 |
| socle, cosocle | C32×C23 | C2×C23 |
| prime radical | C3⋊D3×C23 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C529 | |
36 conjugacy classes of subgroups.
3174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #157×C529, C529⋊#157, C3⋊D3×D529, … |
| maximal normal subgroup of | #157×C529, C529⋊#157, C3⋊D3×D529, … |
| maximal quotient of | C3⋊Dic3×C529, C2×C3⋊D3×C529 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9522, 9);