Desymmetrization of achiral skeletons by mono-substitution. Its characterization by subduction of coset representations

A set of equivalent positions in an achiral skeleton is regarded as an orbi t as-signed to a coset representation G(/G(i)), where the subgroup G(i) is C-nv or C-n. Desymmetrization of the achiral skeleton by substituting a sin gle ligand is examined by virtue of the subduction of the coset representat ion G(/G(i)) down arrow G(i), which is determined to be alphaG(i)(/G(i)) betaG(i)(/G(k)((i))). The multiplicities (alpha and beta) of the resulting coset representations are calculated from the data of the participating gro ups and the normalizer of G(i).