Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D867 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D289) |
| unambiguous semidirect product | (C2×C289)⋊(C3×D3) |
| Fitting | C2×C32×C289 ⋊ C2 |
| derived | C3×C289 ⋊ C22×C3 |
| Hall | C32×C289 ⋊ C22 |
| Sylow | C289 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D867 |
| commutator, cosocle, hypocenter | C3×C289 | C22×C3 |
| Frattini | C17 | C2×C3×D51 |
| Fitting | C2×C32×C289 | C2 |
| socle | C2×C32×C17 | D17 |
| LCS | G ▷ C3×C289 | |
| UCS | C1 ◁ C2×C3 | |
66 conjugacy classes of subgroups.
2610 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 34);