A recognition algorithm for non-generic classical groups over finite fields

In a previous paper the authors described an algorithm to determine whether a group of matrices over a finite field, generated by a given set of matri ces, contains one of the classical groups or the special linear group. The algorithm was designed to work for all sufficiently large field sizes and d imensions of the matrix group. However, it did not apply to certain small c ases. Here we present an algorithm to handle the remaining cases. The theor etical background of the algorithm presented in this paper is a substantial extension of that needed for the original algorithm.