Histone methyltransferase specifically trimethylating ‘Lys-36’ of histone H3 forming H3K36me3 (PubMed:21239497). Also monomethylates ‘Lys-9’ of histone H3 (H3K9me1) in vitro (By similarity). The physiological significance of the H3K9me1 activity is unclear (By similarity).