  This paper has two aims. The first one is the construction problem of
algebraic potentials of Frobenius manifolds. We show examples of such
potentials for the cases of reflection groups of types $H_4,E_6,E_7,E_8$ and
also include those which are already known. The second one is an application of
such potentials to singularity theory. We introduce families of hypersurfaces
of ${\bf C}^3$ which are deformations of $E_n$-singularities $(n=6,7,8)$ but
are not the versal families of $E_n$-singularities. We study the properties of
the families. In particular we show the correspondence between such families
and the algebraic potentials constructed in the first aim. Moreover we discuss
the relationship between the complex reflection groups $ST33$ and $ST34$ and
the two families corresponding to the $E_6$-singularity and the
$E_7$-singularity.
