Catalyzes the transfer of a phosphate from ATP to alpha-D-galactose and participates in the first committed step in the catabolism of galactose. alpha-D-galactose + ATP = ADP + alpha-D-galactose 1-phosphate + H(+) Carbohydrate metabolism; galactose metabolism. Homodimer. Belongs to the GHMP kinase family. GalK subfamily.