Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C9⋊#595 |
| unambiguous semidirect product | C9⋊(C17×#595) |
| Fitting, Hall | C9×C172 ⋊ C4 |
| derived | C9×C17 ⋊ C4×C17 |
| Sylow | C172 ⋊ Dic9 |
| Sylow | C9 ⋊ C17×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C9⋊#595 |
| commutator, hypocenter | C9×C17 | C4×C17 |
| Frattini | C3 | C17×C3⋊#595 |
| Fitting | C9×C172 | C4 |
| socle | C3×C172 | Dic3 |
| prime radical | C3×C17×D17 | D3 |
| cosocle | C9×D17 | C2×C17 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
816 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 57);