Isomorphism groups in Clifford algebras

A set of anticommuting multivectors in Clifford algebras can be taken as orthonormal basis set. The Clifford algebra generated by this basis is isomorphic to the original algebra. The non linear transformations between orthonormal basis sets form a group. In the four dimensionnal case six sets of five anticommuting multivectors are found. These sets yield 30 matrices defining basis sets. These matrices are representatives of left cosets, members of these cosets are related by permutation of rows. From the equivalence of all basis sets of multivectors it can be concluded that there is no canonical set of basis vectors in Clifford algebras.