The Terwilliger algebras of the group association schemes of non-abelian finite groups admitting an abelian subgroup of index 2

In this paper, we determine the dimension of the Terwilliger algebras of non-abelian finite groups admitting an abelian subgroup of index 2 by showing that they are triply transitive. Moreover, we give a complete characterization of the Wedderburn components of the Terwilliger algebras of these groups.