  A map is a 2-cell decomposition of an orientable closed surface. A dessin is
a bipartite map with a fixed colouring of vertices. A dessin is regular if its
group of colour- and orientation-preserving automorphisms acts transitively on
the edges, and a regular dessin is symmetric if it admits an additional
external symmetry transposing the vertex colours. Regular dessins with
nilpotent automorphism groups are investigated. We show that each such dessin
is a parallel product of regular dessins whose automorphism groups are the
Sylow subgroups. Regular and symmetric dessins with abelian automorphism groups
are classified and enumerated.
