Classification of degree-n Riordan representations of Dn over Zn for n ≥ 4

Classify all degree-n Riordan representations of the dihedral group Dn over the ring Zn for integers n ≥ 4, obtained via truncation of Riordan array representations over Zn by πn: R(Zn) → Rn(Zn).

Background

Theorem 7 constructs many faithful Riordan representations of Dn over Zn for all n ≥ 3, and Section 3 details explicit forms of such representations. However, a systematic classification by truncation degree n for n ≥ 4 is not provided.

This question seeks a full classification of degree-n Riordan representations of Dn over Zn, analogous to the classification results obtained for S3 in degree 2.