  We provide isomorphism results for Hopf algebras that are obtained as graded
twistings of function algebras on finite groups by cocentral actions of cyclic
groups. More generally , we also consider the isomorphism problem for
finite-dimensional Hopf algebras fitting into abelian cocentral extensions. We
apply our classification results to a number of concrete examples involving
special linear groups over finite fields, alternating groups and dihedral
groups.
