  We have investigated the band structure and the band symmetry of
mixed-valence insulator SmB$_{6}$ systematically within the density functional
theory (DFT). We have analyzed the symmetries and characters of Sm $4f$ and
$5d$ bands near the Fermi level ($E_F$) in terms of the non-relativistic real
cubic bases as well as the relativistic complex bases incorporating the
spin-orbit coupling and the cubic crystal field. Further, we have found that
the semi-core band located at $\sim 15$ eV below $E_F$ has the mixed parity and
thereby affects the parity eigenvalues of the special ${\bf k}$-points
considerably. We have discussed the possible surface states and topological
class of SmB$_{6}$, based on the bulk parity tables.
