Abstract
Generation of finite simple groups by suitable subsets is of great importance and has been studied since the origin of group theory. A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group T(l, m, n) = < x, y, z vertical bar x(l) = y(m) = z(n) = xyz = 1 >. In this article, we study some routines in the computer algebra system GAP - Groups, Algorithms and Programming to determine (p, q, r)-generations of a finite simple group and apply these techniques to compute such type of generations for the Fischer's largest sporadic simple group Fi(24)', where p, q and r are prime divisors of the vertical bar Fi (24)'vertical bar.