An enzyme of the transferase class that catalyzes the transfer of galactose from UDPgalactose to glucose, forming lactose. The enzyme is a complex of the enzyme N-ACETYLLACTOSAMINE SYNTHASE and alpha-lactalbumin; the latter protein is present in lactating mammary gland cells where it alters the usual specificity of the former to make lactose synthesis the preferred reaction. (Dorland, 28th ed) EC 2.4.1.22.