Using graphical methods of spin algebras, we present a direct method for the determination of the representation matrices of the symmetric group in a basis adapted to electron-pair and electron-group wave functions. In particular, we consider nonstandardrepresentations adapted to S-n1 x S-n2 x ... x S-nt where n(1) + n(2) + ... + n(t) = n. The Serber coupling scheme based on S-2 x S-2 x ... x S-2 is a special case suited for electron-pair wave functions. Our approach exploiting graphical methods of spin algebras is contrasted with the use of Young diagrams and tableaux, Yamanouchi symbols and branching diagrams.