A single crystal of ordered double perovskite oxide ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6,$ a conducting ferromagnet with $T_C\sim 420\mathrm{K},$ has been prepared by the floating zone method, and the magnetic and electronic properties have been investigated. It has been found that the ordinary and anomalous Hall coefficients are negative and positive, respectively, and that the density of the conduction electrons is estimated at $1.1\times {10}^{22}{\mathrm{cm}}^{\mathrm{-}3},$ corresponding to nearly one electron-type carrier per a pair of Fe and Mo. The electronic specific heat is about 8 mJ/(mol ${\mathrm{K}}^2$) in accord with the result of the band-structure calculation by the local density functional (LDA) method. In the optical conductivity spectrum, interband transitions from Fe $e_g$ to Mo $t_{2g}$ band with up spin across the Fermi level and from the O $2_p$ to the Mo/Fe $t_{2g}$ band with down spin are observed at 0.5 eV and 3.9 eV, respectively, which confirms the half-metallic electronic structure predicted by the LDA calculation.