Tensorial covariants for the 32 crystal point groups

The recently published tables of Clebsch-Gordan products are applied to derive the tensorial covariants (bases of irreducible or physically irreducible representations) for the 32 crystal point groups. Tensors of the following intrinsic symmetries in Jahn notation are considered: ε (pseudoscalar), V (polar vector), [V²], V[V²], [[V²]²], [V²]², ε[V²], and εV[V²]. With this choice the most important tensors of optical and other properties are covered. Explicit lists of covariants in components of these tensors are given for the non- centrosymmetric groups; with the use of parity arguments the lists also apply to centrosymmetric groups. Applications, especially for phase transitions with reduction of the point symmetry, are briefly discussed.