The symmetry groups associated with a system of balance equations of arbitrary order involving n independent and N dependent variables are discussed by employing exterior calculus. The infinitesimal generators of symmetry groups are components of isovectors fields of the closed ideal of certain exterior differential forms corresponding to an equivalent first order system of equations. Rather compact expressions which lead to the set of equations whose solutions determine isovector fields are derived. These expressions may be evaluated automatically by a computer for large systems. Similarity solutions are then obtainable as usual as group invariant solutions. An example is treated briefly to expose short cuts provided by the approach.