  The goal of this article is to show that five explicitly given
transformations, a rotation, two screw Heisenberg rotations, a vertical
translation and an involution generate the Euclidean Picard modular groups with
coefficient in the Euclidean ring of integers of a quadratic imaginary number
field. We also obtain the relations of the isotropy subgroup by analysis of the
combinatorics of the fundamental domain in Heisenberg group.
