Maximal subgroups of the sporadic almost-simple groups


Let S be one of the sporadic groups M12, M22, HS, McL, J2, J3, Suz, He, HN, O'N, Fi22, Fi24' and let G = Aut(S). Using a permutation representation of G on a computer, we calculate explicit generators for the maximal subgroups of G. The generators of the maximal subgroups are presented as straight line programs in standard generators of G, making it easy to produce each maximal subgroup for any choice of representation and generators for G. All these straight line programs have been made available on the World Wide Web. In the proof that the generators we produce are correct, we tabulate the orbit shapes of each maximal subgroup in the smallest faithful permutation representation of G, which are useful data when attempting to identify subgroups of G.

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The full text of my MPhil thesis is available: dvi (268k), ps (587k), pdf (419k).