  This paper uses tools in group theory and symbolic computing to give a
classification of the representations of finite groups with order lower than 9
that can be derived from the study of local reversible-equivariant vector
fields in $\rn{4}$. The results are obtained by solving algebraically matricial
equations. In particular, we exhibit the involutions used in a local study of
reversible-equivariant vector fields. Based on such approach we present, for
each element in this class, a simplified Belitiskii normal form.
