The automorphism group of the Hoffman-Singleton graph is a group of order 252,000 isomorphic to PΣU(3,52) the semidirect product of the projective special unitary group PSU(3,52) with the cyclic group of order 2 generated by the Frobenius automorphism.
The characteristic polynomial of the Hoffman-Singleton graph is equal to (x-7) (x-2)^{28} (x+3)^{21}.