GO:0047275:   glucosaminylgalactosylglucosylceramide beta-galactosyltransferase activity
Catalysis of the reaction: N-acetyl-D-glucosaminyl-(1,3)-D-galactosyl-(1,4)-D-glucosylceramide + UDP-galactose = D-galactosyl-N-acetyl-D-glucosaminyl-(1,3)-D-galactosyl-(1,4)-D-glucosylceramide + UDP.