Product Replacement in the Monster

;its minimal faithful permutation and matrix representation degrees are respectively 97 239 461 142 009 186 000 and 196 882. This makes it far harder to work with than the 25 smaller sporadics. In Section 3, we describe techniques which allow limited computation in the Monster. In Section 4, we describe our experiments to assess the effectiveness of combining these techniques with a suitable version of the product replacement algorithm, and in Section 5, we present our results and conclusions.