Histone methyltransferase that specifically trimethylates 'Lys-20' of histone H4 to form trimethylated histone H4 lysine 20 (H4K20me3) which represents a specific tag for epigenetic transcriptional repression (PubMed:22921934, PubMed:28250819). In association with the NCoR corepressor complex, is involved in the repression of toll-like receptor 4 (TLR4)-target inflammatory genes in macrophages by catalyzing the formation of H4K20me3 at the gene promoters (PubMed:22921934). Plays an important role in embryonic stem (ES) cell self-renewal and differentiation (PubMed:28951459). Promotes ES cell maintenance by silencing differentiation genes through deposition of H4K20me3 marks (PubMed:28951459). Maintains genome stability of ES cells during differentiation through regulation of heterochromatin formation and repression of endogenous repetitive DNA elements by depositing H4K20me3 marks (PubMed:28250819). L-lysyl(20)-[histone H4] + 3 S-adenosyl-L-methionine = 3 H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(20)-[histone H4] + 3 S-adenosyl-L-homocysteine Interacts with the N-CoR complex (PubMed:22921934). Interacts with EHMT2 and CBX5 (PubMed:28250819). Up-regulated by retinoic acid treatment in embryonic carcinoma cells. Present at low levels in untreated cells. Belongs to the class V-like SAM-binding methyltransferase superfamily.