The Schur multiplier and the outer automorphism group are both trivial.
Meyer, Neutsch & Parker (1985) showed that the Lyons group has a modular representation of dimension 111 over the field of five elements, which is the smallest dimension of any faithful linear representation and is one of the easiest ways of calculating with it.
It has also been given by several complicated presentations in terms of generators and relations, for instance those given by Sims (1973) or Gebhardt (2000).
There is also a slightly larger rank 5 permutation representation on 9606125 points with stabilizer 3.McL:2.
Wilson (1985) found the 9 conjugacy classes of maximal subgroups of Ly as follows: