Mediates the deacetylation of lysine residues on the N-terminal part of the core histones (H2A, H2B, H3 and H4). Histone deacetylation gives a tag for epigenetic repression and plays an important role in transcriptional regulation, cell cycle progression and developmental events (By similarity). Multimer. Possibly forms a homotrimer with HDT1 and/or HDT3 (By similarity). Belongs to the histone deacetylase HD2 family.