Catalysis of the reaction: L-lysyl(20)- + 3 S-adenosyl-L-methionine = 3 H+ + N(6),N(6),N(6)-trimethyl-L-lysyl(20)- + 3 S-adenosyl-L-homocysteine. This reaction is the addition of three methyl groups to the lysine residue at position 20 of the histone H4 protein, producing histone H4K20me3.
histone lysine N-trimethyltransferase activity (H4-K20 specific)