Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C289 · Schur multiplier (H2) = C2 |
| direct product | D32×C289 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C289) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C289) |
| Fitting, Hall | C32×C289 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D32 |
| commutator, hypocenter | C32 | C22×C289 |
| Frattini | C17 | D32×C17 |
| Fitting | C32×C289 | C22 |
| socle, cosocle | C32×C17 | C22×C17 |
| prime radical | D32×C17 | C17 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C289 | |
66 conjugacy classes of subgroups.
2601 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 28);