On the orbit graph of some 3-generator 2-groups

In this research, G is a finite 3-generator 2-group of order 16, where G can be a graph which is called the orbit graph. The orbit graph is a graph whose vertices are non-central orbits under the group action of G on a set. The two vertices are adjacent when they are conjugated to each other. Based on the definition of the orbit graph and group action, the orbit graph is determined for G in the case that G acts on itself by conjugation. Throughout this research, the graph that will be considered is a simple undirected graph.