Involved in the degradation of galactose via the DeLey-Doudoroff pathway. Catalyzes the oxidation of galactose in the presence of NAD(+). Uses NAD(+) as a hydrogen acceptor more efficiently than NADP(+). Cells lacking this gene fail to grow on galactose as sole carbon source. Belongs to the short-chain dehydrogenases/reductases (SDR) family.