Catalysis of the reaction: UDP-galactose + N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galactosyl-1,4-beta-D-glucosyl-N-acylsphingosine = UDP + D-galactosyl-1,3-beta-N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galactosyl-D-glucosyl-N-acylsphingosine.
uridine diphosphogalactose-GM2 galactosyltransferase activity