Galactosyltransferase acting in the Golgi stacks. Catalyzes the transfer of galactose (Gal) from UDP-alpha-D-galactose in beta(1->4) linkage to the non-reducing terminal N-acetylglucosamine (GlcNAc) moieties of glycolipids and complex-type N-linked glycans (PubMed:16157350, PubMed:27872474, PubMed:29133956, PubMed:36280670, PubMed:37632720, PubMed:38321209). Adds one Gal residue to both GlcNAc beta(1->2)-linked to the alpha(1->3) and alpha(1->6) mannose antennae of complex-type N-glycans, enabling the formation of mono- and di- galactosylated glycoforms. Galactosylates complex-type N-glycans attached on the fragment crystallizable (Fc) of immunoglobulin-gamma isotypes (IgGs), a prerequisite for antibody glycan sialylation and related anti-inflammatory effector functions (PubMed:27872474, PubMed:29133956, PubMed:36280670, PubMed:37632720). Can also transfer a Gal residue to free GlcNAc to form N-acetyllactosamine (PubMed:16157350). With LALBA/alpha-lactalbumin forms the lactose synthase complex responsible for production of large amounts of lactose in the lactating mammary gland. Interaction with LALBA alters the sugar substrate specificity of the catalytic domain, enabling high affinity binding of glucose and its transformation to lactose (PubMed:16157350). {ECO:0000269|PubMed:16157350, ECO:0000269|PubMed:27872474, ECO:0000269|PubMed:29133956, ECO:0000269|PubMed:36280670, ECO:0000269|PubMed:37632720, ECO:0000269|PubMed:38321209}. [Isoform Long]: The cell surface form functions as a recognition molecule during a variety of cell to cell and cell to matrix interactions, like those occurring during development and egg fertilization, by binding to specific oligosaccharide ligands on opposing cells or in the extracellular matrix. Acts as a sperm receptor for ZP3 O-linked glycans on the zona pellucida leading to activation of G protein signaling and acrosome reaction. . [Processed beta-1,4-galactosyltransferase 1]: The secreted form is proficient in galactosyltransferase activity and could be involved in glycan remodeling in biological fluids. . This is the function of ENSG00000086062 (B4GALT1, beta-1,4-galactosyltransferase 1).