Ascomycetes typically refer to fungus whose spores develop within the cylindrical sacs named asci.
They are also called sac fungi.
They do have chitinous cell walls.
They are unicellular such as yeast but most of the members of these groups have well-developed, profusely branched septa.
Asexual reproduction occurs by the non-motile spores such as conidia, and chlamydospores, and in unicellular organisms budding, fermentation and fission are the commonest modes of asexual reproduction.
Sexual reproduction occurs by the copulation of gametangia (eg. Yeast), contact of gametangia (Aspergillus, Penicillium, Erysiphe).
Ascospores are the haploid sexual spores that are formed in the cylindrical sac-like structure called an ascus.