Group-theoretic Construction
Alternatively, the 7 points of the plane correspond to the 7 non-identity elements of the group (Z2)3 = Z2 × Z2 × Z2. The lines of the plane correspond to the subgroups of order 4, isomorphic to Z2 × Z2. The automorphism group of the group (Z2)3 is that of the Fano plane, and has order 168.
Read more about this topic: Fano Plane
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