Phylum Basidiomycota. 1. Characteristics: basidiomycetes (club fungi); reproduce asexually by budding, fragmentation of mycelium, or forming conidia; reproduce sexually by forming a club-like basidium (pl. basidia) which bears haploid spores (usually four) on its surface; have dikaryotic stage.hylum Basidiomycota. 1. Characteristics: basidiomycetes (club fungi); reproduce asexually by budding, fragmentation of mycelium, or forming conidia; reproduce sexually by forming a club-like basidium (pl. basidia) which bears haploid spores (usually four) on its surface; have dikaryotic stage.