Exploring the Group Representation Theory of the Full Symmetry of Regular Tetrahedron

In this paper we study the rotation and spatial inversion symmetry of regular tetrahedron. We obtain the representation matrix, multiplication table,the order of all group elements, all possible combinations of generator elements, the proper subgroups,conjugate classes, invariation subgroups and the corresponding cosets, quotients and homomorphic correspondence. In the end we discuss Sudoku magic group.