Computing with Finite Simple Groups
Leech  and Birkhoff and Hall  are standard references to computational group theory. The lesser-known Petrick  contains many articles on symbolic manipulation and group-theoretic work including a description by Sims of techniques he has developed to compute with very large degree permutation groups. These ideas have been used by him  most impressively to prove the existence and uniqueness of Lyons’ simple group of order 51 765 179 004 000 000 = 2837522.214.171.124.67 by constructing a permutation representation of it on the coasts of a subgroup G 2(5) of index 8 835 156. It should be added that Lyons’ group has no proper subgroup larger than G 2(5).
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