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In mathematics, the projective special linear group PSL(2, 7) (isomorphic to GL(3, 2)) is a finite simple group that has important applications in algebra, geometry, and number theory. It is the automorphism group of the Klein quartic as well as the symmetry group of the Fano plane. With 168 elements PSL(2, 7) is the second-smallest nonabelian simple group after the alternating group “A” on five letters with 60 elements (the rotational icosahedral symmetry group), or the isomorphic PSL(2, 5).

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