Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×D289 |
| unambiguous semidirect product | (C3×D289)⋊D3 |
| Fitting, derived, Hall | C32×C289 ⋊ C22 |
| Sylow | C289 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C289 | C22 |
| Frattini | C17 | C3⋊D3×D17 |
| socle | C32×C17 | C2×D17 |
| LCS | G ▷ C32×C289 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
876 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 27);