Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D17×D51 |
| unambiguous semidirect product | (C3×D17)⋊(C3×D17) |
| unambiguous semidirect product | (C17×D17)⋊(C3×D3) |
| Fitting, socle, Hall | C32×C172 ⋊ C22 |
| derived | C3×C172 ⋊ C22×C3 |
| Sylow | C172 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ D172 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×D51 |
| commutator, cosocle, hypocenter | C3×C172 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C172 | C22 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 ◁ C3 | |
160 conjugacy classes of subgroups.
810 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 125);