  We proposed a group-theory method to calculate topological invariant in
bi-isotropic photonic crystals invariant under crystallographic point group
symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation
operators at high symmetry k-points after the pseudo-spin polarized fields are
retrieved. Topological characters of photonic edge states and photonic band
gaps can be well predicted by total spin Chern number. Nontrivial phase
transition is found in large magnetoelectric coupling due to the jump of total
spin Chern number. Light transport is also issued at the {\epsilon}/{\mu}
mismatching boundary between air and the bi-isotropic photonic crystal. This
finding presents the relationship between group symmetry and photonic
topological systems, which enables the design of photonic nontrivial states in
a rational manner.
