CONJUGACY CLASSES IN SPORADIC SIMPLE GROUPS Ibrahim A. I. Suleiman * Department of Mathematics and Statistics, Mu’tah University, 61710 Al-Karak, Jordan Peter G. Walsh and Robert A. Wilson School of Mathematics and Statistics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Abstract We obtain efficient programs for obtaining representatives of all the conjugacy classes of all the sporadic simple groups except the Monster and the Baby Monster. 1 Introduction For many purposes, for example in calculating modular character tables (see [8], [10] etc.), or in finding particular subgroups of a group, it is useful to have representatives of the conjugacy classes of a given group readily to hand. While ‘generic’ simple groups tend to have a nicely parametrized set of conju- gacy classes, this is not true for the 26 sporadic simple groups. In this paper we try to obtain a list of class representatives, starting from the ‘standard gen- erators’ defined in [11], with (close to) as few multiplications of group elements as possible. For the groups of order less than 10 9 we are able to produce a * Currently on sabbatical at Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Sultanate of Oman 1