Three-term relations for F23(1)

For the hypergeometric function of unit argument F23(1) we prove the existence and uniqueness of three-term contiguous relations with arbitrary integer shifts. We show that not only the original F23(1) function but also other five functions related to it satisfy one and the same three-term relation. This fact together with the uniqueness mentioned above provides three-term relations with a group symmetry of order 72.