Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×(C3⋊D3)⋊D17 |
| unambiguous semidirect product | (C3⋊D3)⋊(C17×D17) |
| unambiguous semidirect product | D51⋊(D3×C17) |
| Fitting, socle, Hall | C32×C172 ⋊ C22 |
| derived | C32×C17 ⋊ C22×C17 |
| Sylow | C172 ⋊ D32 |
| Sylow | C32 ⋊ C2×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | (C3⋊D3)⋊D17 |
| commutator, cosocle, hypocenter | C32×C17 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C172 | C22 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C17 | |
184 conjugacy classes of subgroups.
969 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 137);