Element structure of projective special linear group:PSL(3,2)

This article describes the element structure of projective special linear group:PSL(3,2), which is the same as $$SL(3,2)$$, $$GL(3,2)$$. It is also isomorphic to the projective special linear group of degree two over field:F7, i.e., the group $$PSL(2,7)$$.

Interpretation as projective special linear group of degree two
We consider the group as $$PSL(2,q)$$, $$q = 7$$. We use the letter $$q$$ to denote the generic case of $$q \equiv 3 \pmod 4$$.

Interpretation as general linear group of degree three over field:F2
Compare with element structure of general linear group of degree three. Since many cases (namely, those that rely on distinct eigenvalues) do not arise over field:F2, the cases have been omitted in the table below.