Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D172 |
| unambiguous semidirect product | (C17×D17)⋊(C2×C9) |
| Fitting, Hall | C9×C172 ⋊ C22 |
| derived, Sylow | C172 ⋊ C22×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D172 |
| commutator, hypocenter | C172 | C22×C9 |
| Frattini | C3 | C3×D172 |
| Fitting | C9×C172 | C22 |
| socle, cosocle | C3×C172 | C22×C3 |
| prime radical | C3×D172 | C3 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C9 | |
108 conjugacy classes of subgroups.
900 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 56);