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

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