Cleaves beta-linked terminal galactosyl residues from gangliosides, glycoproteins, and glycosaminoglycans. Has high in vitro transglycosylation activity with p-nitrophenyl-beta-D-galactopyranoside, methyl-beta-D-galactopyranoside or lactose as a donor and galactose as an acceptor. Hydrolysis of terminal non-reducing beta-D-galactose residues in beta-D-galactosides. Monomer. Belongs to the glycosyl hydrolase 35 family.