GAP Computations Concerning Probabilistic Generation of Finite Simple Groups

This is a collection of examples showing how the GAP system [GAP12] can be used to compute information about the probabilistic generation of finite almost simple groups. It includes all examples that were needed for the computational results in [BGK08]. The purpose of this writeup is twofold. On the one hand, the computations are documented this way. On the other hand, the GAP code shown for the examples can be used as test input for automatic checking of the data and the functions used. A first version of this document, which was based on GAP 4.4.10, had been accessible in the web since April 2006 and is available in the arXiv (no. 0710.3267) since October 2007. The differences to the current version are as follows. • The format of the GAP output was adjusted to the changed behaviour of GAP 4.5. This affects mainly the way how GAP records are printed. • Several computations are now easier because more character tables of almost simple groups and maximal subgroups of such groups are available in the GAP Character Table Library. (The more involved computations from the original version have been kept in the file.) • The computation of all conjugacy classes of a subgroup of PΩ(12, 3) has been replaced by the computation of the conjugacy classes of elements of prime order in this subgroup. • The irreducible element chosen in the simple group PΩ−(10, 3) has order 61 not 122.