Abstract: Based on the first principle calculation of the density functional theory, we have accurately calculated the energy band structure of fluorographene. Then for a given point group of crystal structure, the valence bands and two lowest conduction bands are classified by symmetry according to compatibillity relation between the irreducible representations at the special points and those along the various lines of symmetry meeting at that point. Studying on the degeneracy of high symmetry point can provide a theoretical basis for the future study of energy structured split- ting deduced by the external field.

Key words: fluorographene, first principle, compatibility, wave vector group, crystal point group