Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type

We construct the Grothendieck rings of a class of 2n2 dimensional semisimple Hopf Algebras $$H_{2n^{2}}$$ , which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H8. All irreducible $$H_{2n^{2}}$$ -modules are classified. Furthermore, we describe the Grothendieck rings r( $$H_{2n^{2}}$$ ) by generators and relations explicitly.