In this paper, by using rotational matrice which is the subgroups of the manifold M corresponding to rotation, some certain results of describing the surface are given in detail obtaining Killing vector field in G3, the rotational surfaces generated by the rotational matrices are given using an isotropic curve and isotropic matrice of rotation in G3. Moreover, taking the Gaussian and mean curvatures of this special rotational surface, we express the conditions being linear Weingarten surfaces and HK−quadric surface, harmonic surface.