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 (By similarity. 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 (By similarity. Plays an important role in embryonic stem (ES cell self-renewal and differentiation (By similarity. Promotes ES cell maintenance by silencing differentiation genes through deposition of H4K20me3 marks (By similarity. Maintains genome stability of ES cells during differentiation through regulation of heterochromatin formation and repression of endogenous repetitive DNA elements by depositing H4K20me3 marks.