A digraph is associated with a finite group by utilizing the power map f: G → G defined by f(x) = xkfor all x \in G, where k is a fixed natural number. It is denoted by γG(n, k). In this paper, the generalized quaternion and 2-groups are stud- ied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2-group are determined for a 2-group to be a generalized quaternion group. Further, the classification of two generated 2-groups as abelian or non-abelian in terms of semi-regularity of the power digraphs is completed., Uzma Ahmad, Muqadas Moeen., and Obsahuje seznam literatury