Clebsch-Gordan coefficients for space groups

It is shown that to find Clebsch-Gordan coefficients of space groups (both single and double), the representations of the groups of k alone are required. This is another example demonstrating the well-accepted fact that in applications of space groups it is sufficient to know the representations of the groups of k. Final formulas are derived that enable the calculation of the Clebsch-Gordan coefficients from the representations of the groups of k. As an example the spin-orbit coupling in solids is considered.