Histone methyltransferase that specifically trimethylates 'Lys-20' of histone H4. H4 'Lys-20' trimethylation represents a specific tag for epigenetic transcriptional repression. Mainly functions in pericentric heterochromatin regions, thereby playing a central role in the establishment of constitutive heterochromatin in these regions. Acts as a dominant suppressor of position-effect variegation. L-lysyl(20)-[histone H4] + S-adenosyl-L-methionine = H(+) + N(6)-methyl-L-lysyl(20)-[histone H4] + S-adenosyl-L-homocysteine 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 Belongs to the class V-like SAM-binding methyltransferase superfamily. Histone-lysine methyltransferase family. Suvar4-20 subfamily. Truncated N-terminus.