Catalysis of the reaction: UDP-N-acetyl-D-galactosamine + alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-beta-D-glucosylceramide = UDP + beta-N-acetyl-D-galactosaminyl-(1->3)-alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-beta-D-glucosylceramide.
globotriosylceramide beta-1,6-N-acetylgalactosaminyltransferase activity