Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C289 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D3×C289 |
| unambiguous semidirect product | C3⋊(C22×C3×C289) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C3×C289) |
| Fitting | C2×C32×C289 ⋊ C2 |
| derived | C3 ⋊ C22×C3×C289 |
| Hall | C32×C289 ⋊ C22 |
| Sylow | C32 ⋊ C22×C289 |
66 conjugacy classes of subgroups.
5202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 33);