We report on the measurement of the isotope shifts of the
3d74sa5F5–3d74pz5G6o Fe i line at 358 nm between all four stable isotopes
54Fe,56Fe,57Fe, and
58Fe, as well as the hyperfine structure of that line for
57Fe, the only stable isotope having a nonzero nuclear spin. This line is of primary importance for laser-cooling applications. In addition, an experimental value of the field and specific mass shift coefficients of the transition is reported as well as the hyperfine structure magnetic dipole coupling constant
A of the transition excited state in
57Fe, namely
A(3d74pz5G6o)=31.241(48) MHz. The measurements were carried out by means of laser-induced fluorescence spectroscopy performed on an isotope-enriched iron atomic beam. All measured frequency shifts are reported with relative uncertainties below one third percent.