Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D153 |
| unambiguous semidirect product | (C9×D17)⋊D17 |
| unambiguous semidirect product | (C17×D17)⋊D9 |
| Fitting, derived, Hall | C9×C172 ⋊ C22 |
| Sylow | C172 ⋊ C2×D9 |
| Sylow | C9 ⋊ D172 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C172 | C22 |
| Frattini | C3 | D17×D51 |
| socle | C3×C172 | C2×D3 |
| LCS | G ▷ C9×C172 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 63);