Classification of the Super-conducting order parameters under the point group symmetry for a multi-band system: application to LaOFeAs

All the possible super-conducting order parameters for the LaOFeAs system are classified by their transformation under the complete crystal symmetry. The general forms of the super-conducting gap functions for each class are discussed. We find that the gap functions in such a multi-band system belong to three types, full gap, nodal type and finite {}``Fermi arc'' type. Possible physical consequences caused by different types of gap functions are also discussed.