In this article we give a self-contained existence proof for Lyons' sporadic simple group G by application of the first author's algorithm [18] to the given centralizer H approx= 2A_(11) of a 2-central involution of G. It also yields four matrix generators of G inside GL111 (5) which are given in Appendix A. From the subgroup U approx= (3 * 2A_8):2 of H approx= 2A_(11), we construct a subgroup E of G which is isomorphic to the 3-fold cover 3McL:2 of the automorphism group of the McLaughlin group McL. Furthermore, the character tables of E approx= 3McL:2 and G are determined and representatives of their conjugacy classes are given as short words in their generating matrices.
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