Some extended versions of the ‘interacting boson model’ for light nuclei make use of the group O(6) as a possible candidate for a dynamical symmetry closely related to Wigner’s supermultiplet theory. It has been known for a long time that the Cartan-Weyl basis of the corresponding Lie algebra may be given in terms of bilinear expressions of bosonic operators satisfying canonical commutation relations. As is demonstrated in the present article, these operators are also convenient for constructing basis vectors within an irreducible representation. Finally, the ‘isoscalar factors’ of the chain O(6)\(\times O(6)\supset O(6)\supset O(3)\times O(3)\) are calculated which one needs in applications.