Catalyzes the sterospecific oxidation of primary alcohols to the corresponding aldehydes. The biologically relevant substrate of the enzyme is not known as the enzyme exhibits broad substrate specificity from small alcohols through sugars to oligo- and polysaccharides (By similarity). D-galactose + O2 = D-galacto-hexodialdose + H2O2 Binds 1 Cu(2+) ion per subunit. Monomer. Galactose oxidase contains a protein-derived free radical cofactor (By similarity). In the active state, Tyr-313, which is cross-linked to Cys-269 via a thioether bond, is oxidized to a radical and acts with Cu(2+) as a two-electron acceptor in the oxidation reaction. The cross-link is believed to modulate the redox potential of the tyrosyl radical, which is further stabilized by a stacking interaction with Trp-331 in the active site. The post-translational formation of the cross-link is closely linked to the propeptide cleavage event, and both are copper-dependent, autocatalytic processes. The propeptide may act as an intramolecular chaperone, facilitating thioester bond formation and copper binding by positioning of active-site residues, including copper ligands (By similarity).