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We have computed the Clebsch-Gordan coefficients for the product (1)$\otimes$ (1), where (1) is the adjoint 78-dimensional representationof $E_6$. The results are presented for the dominant weights of the irreduciblerepresentations in this product. As a simple application we express the singletoperator in $ 27 \otimes 78 \otimes \bar{27}$ in terms of multiplets of theStandard Model gauge group.Comment: 27 pages, Late

E 6 unification model building II. Clebsch–Gordan coefficients of 78⊗78