The group theorist Jack McLaughlin discovered that the automorphism group of this graph had a subgroup of index 2 which was a previously undiscovered finite simple group, now called the McLaughlin sporadic group.
The automorphism group has rank 3, meaning that its point stabilizer subgroup divides the remaining 274 vertices into two orbits.
The former is the colinearity graph of the generalized quadrangle GQ(3,9).
The latter is a strongly regular graph called the local McLaughlin graph.
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