Histone methyltransferase that specifically di- and trimethylates 'Lys-20' of histone H4 (H4K20me2/me3) (PubMed:22393255, PubMed:23028348). H4 'Lys-20' trimethylation represents a specific tag for epigenetic transcriptional repression (By similarity). Contributes to dosage compensation of X chromosome-relative to autosome-linked gene expression, possibly by converting H4K20me1 to H4K20m2/me3 on autosomes (PubMed:26641248, PubMed:23028348, PubMed:22393255). Involved in the regulation of growth and body fat metabolism downstream of the TOR complex 2 pathway (PubMed:23884442). N(6)-methyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-methionine = H(+) + N(6),N(6)-dimethyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-homocysteine N(6),N(6)-dimethyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-methionine = H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-homocysteine Mutant animals exhibit a lack of di- and trimethylation (H4K20me2/me3) and an increase of monomethylation of 'Lys-20' (H4K20me1) of histone H4 on autosomes, leading to equal H4K20me1 levels on autosomes relative to X chromosomes (PubMed:22393255, PubMed:23028348, PubMed:26641248). Decreased expression of autosomal genes (PubMed:26641248). Increase in 'Lys-16' acetylation of histone H4 (H4K16ac) on hermaphrodite X chromosomes (PubMed:22393255). Increase in binding of the RNA Pol II large subunit ama-1 on X chromosome gene promoters relative to autosomes (PubMed:26641248). In a dpy-21 mutant background, RNAi-mediated knockdown leads to embryonic lethality (PubMed:23028348). In the TOR complex 2 mutant background rict-1, suppresses the growth delay and elevated body fat index (PubMed:23884442). Belongs to the class V-like SAM-binding methyltransferase superfamily. Histone-lysine methyltransferase family. Suvar4-20 subfamily.