Finite Group DatabasebetaFinite Group Databasebeta| order | 17340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D867 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D289) |
| unambiguous semidirect product | (C2×C289)⋊(C5×D3) |
| Fitting | C2×C3×C5×C289 ⋊ C2 |
| derived, Hall | C3×C289 ⋊ C22×C5 |
| Hall | C3×C5×C289 ⋊ C22 |
| Hall | C5×C289 ⋊ C2×D3 |
| Sylow | C289 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D289 |
| Sylow | C3 ⋊ C2×C5×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D867 |
| commutator, cosocle, hypocenter | C3×C289 | C22×C5 |
| Frattini | C17 | C2×C5×D51 |
| Fitting | C2×C3×C5×C289 | C2 |
| socle | C2×C3×C5×C17 | D17 |
| LCS | G ▷ C3×C289 | |
| UCS | C1 ◁ C2×C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8670 |
4350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17340, 34);