Hydrolysis of terminal, non-reducing alpha-D-galactose residues in alpha-D-galactosides, including galactose oligosaccharides, galactomannans and galactolipids. Binds 1 Mn(2+) ion per subunit. Binds 1 NAD(+) per subunit. Homodimer. Belongs to the glycosyl hydrolase 4 family.