Hurwitz groups are the nontrivial finite quotients of the (2, 3, 7) triangle group <x, y | x^2 =y^3
=(xy)7 =1>. In this paper we study the action of the smallest Hurwitz group is the simple group PS
L(2, 7) acts via linear fractional transformation on the projective line P1(7) over the field by using