Baum and Clausen have presented in  an algorithm, refered to as BC-Algorithm, for the construction of a complete list of pairwise inequivalent ordinary irreducible representations for a given finite supersolvable group G. This algorithm is almost optimal in the sense that the running time is proportional to the length of the output up to some logarithmic factors. In this paper we describe an implementation, which realizes this algorithm for the first time efficiently concerning the running time as well as the memory requirements. Extensive tests have shown that the actual running time behaviour of the computer program reflects very well the theoretical complexity bounds. Furthermore, all arithmetic operations of the BC-Algorithm are done symbolically over Z/Ze, where e denotes the exponent of G
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