Abstract An attempt is made to account for the group structure of elementary particles by assuming that they are obtained by combining a limited number of basic fields. It is shown that if the basic fields are all taken to be fermions, one needs three fields to ? for the continuous group structure only, but four fields are necessary if distinct operation for C and P are to be incorporated in the scheme. On the other hand, a model with ? number of independent field components can describe the group structure corrects of the bosons and fermions are taken as basic fields, their common feature in this case ? that they are all strange fields. Difficulties inherent in such schemes are discussed.