Robert Wilson University of Birmingham Effective computation in the monster Friday 20th September, 12-1pm, Carslaw 373. The smallest representation of the Fischer-Griess Monster (the largest of the 26 sporadic simple groups) has dimension 196882 (over the field of two elements), which poses serious problems if you want to perform explicit computations in the group. I shall describe in outline a method of overcoming these difficulties, and some applications, for example finding previously unknown subgroups such as PSL2(59) and PSL2(71).