The graphs of Hoffman-Singleton, Higman-Sims, and McLaughlin, and the   Hermitian curve of degree 6 in characteristic 5
  We construct the graphs of Hoffman-Singleton, Higman-Sims, and McLaughlin from certain relations on the set of non-singular conics totally tangent to the Hermitian curve of degree 6 in characteristic 5. We then interpret this geometric construction in terms of the subgroup structure of the automorphism group of this Hermitian curve. 
Ichiro Shimada
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