  Recall that a triangular Hopf algebra A is said to have the Chevalley
property if the tensor product of any two simple A-modules is semisimple, or,
equivalently, if the radical of A is a Hopf ideal. There are two reasons to
study this class of triangular Hopf algebras: First, it contains all known
examples of finite-dimensional triangular Hopf algebras; second, it can be, in
a sense, "completely understood". Namely, it was shown in our previous work
with Andruskiewitsch that any finite-dimensional triangular Hopf algebra with
the Chevalley property is obtained by twisting of a finite-dimensional
triangular Hopf algebra with R-matrix of rank at most 2 which, in turn, is
obtained by "modifying" the group algebra of a finite supergroup. This provides
a classification of such Hopf algebras.
  The goal of this paper is to make this classification more effective and
explicit, i.e. to parameterize isomorphism classes of finite-dimensional
triangular Hopf algebras with the Chevalley property by group-theoretical
objects, similarly to how it was done in our previous work in the semisimple
case. This is achieved in Theorem 2.2, where these classes are put in bijection
with certain septuples of data. In the semisimple case, the septuples reduce to
the quadruples, and we recover the result of our previous paper. In the minimal
triangular pointed case, we recover a classification theorem from a previous
paper of the second author.
