  In a previous joint paper with Wu and Yakimov, we gave an explicit
description of the lowest discriminant ideal in a Cayley-Hamilton Hopf algebra
(H,C,tr) of degree d over an algebraically closed field k, char k $\notin[1,
d]$ with basic identity fiber, i.e. all irreducible representations over the
kernel of the counit of the central Hopf subalgebra C are one-dimensional.
Using results developed in that paper, we compute relevant quantities
associated with irreducible representations to explicitly describe the zero set
of the lowest discriminant ideal in the group algebra of a central extension of
the product of two arbitrary finitely generated Abelian groups by any finite
Abelian group under some conditions. Over a fixed maximal ideal of C the
representations are tensor products of representations each corresponding to a
central extension of a subgroup isomorphic to the product of two cyclic groups
of the same order. A description of the orbit of the identity, i.e. the kernel
of the counit of C, under winding automorphisms is also given.
