The Terwilliger algebras of the group association schemes of three metacyclic groups

Abstract For any finite group , the Terwilliger algebra of the group association scheme satisfies the following inclusions: , where is a specific vector space and is the centralizer algebra of the permutation representation of induced by the action of conjugation. The group is said to be triply transitive if . In this paper, we determine the dimensions of and for being , and , and show that and are triply transitive. Additionally, we give a complete characterization of the Wedderburn components of the Terwilliger algebras of , and when they are triply transitive.