Projective special linear group:PSL(3,2)

Definition
This group is defined in many equivalent ways:


 * 1) It is the member of family::projective special linear group of degree three over the field of two elements, i.e., $$PSL(3,2)$$.
 * 2) It is the member of family::special linear group of degree three over the field of two elements, i.e., $$SL(3,2)$$.
 * 3) It is the member of family::projective general linear group of degree three over the field of two elements, i.e., $$PGL(3,2)$$.
 * 4) It is the member of family::general linear group of degree three over the field of two elements, i.e., $$GL(3,2)$$.
 * 5) It is the member of family::projective special linear group of degree two over the field of seven elements, i.e., $$PSL(2,7)$$.
 * 6) It is the conformal automorphism group of the Klein quartic surface, which is a Riemann surface and in particular a Hurwitz surface. Hence, this group is a Hurwitz group, and is in fact the unique Hurwitz group of smallest order.

Equivalence of definitions
The equivalence between definitions (1)-(4) follows from isomorphism between linear groups over field:F2.