Abstract: An algorithm for constructing systems of orthogonal idempotents was expounded. By exhausting the symmetry partition and taking full advantage of simultaneous diagonalization to several matrices, we got some systems of orthogonal idempotents. The class idempotent function composing systems of orthogonal idempotents is one of the fundamental tools in constructing symmetry functions and it plays an important role in symmetry designs.

Key words: class idempotent function, systems of orthogonalidempotents, symmetry functions, symmetry designs, finite groups, class idempotent function, systems of orthogonalidempotents, symmetry functions, symmetry designs