Phase-fixed double-group 3-Γ symbols. VI. Real 3-Γ symbols and coupling coefficients for the group hierarchy I*⊃ C5*

It is demonstrated that for the group-subgroup hierarchy I*⊃ C5*, one may choose standard irreducible matrix representations and corresponding all-real sets of 3-Γ symbols which obey a formalism just as elegant as the classical one for the 3-j symbols of the rotation double group. The 3-Γ symbols are phase-fixed by the specification of basis functions (or, equivalently, subduction coefficients) generating them and based on functions first given by McLellan.