Q. Mushtaq and M. S. Saeed
Permutation representations of triangle group D(2,4,5)

Let G(2,4,Z) be a linear-fractional group generated by the transformations x=x(z) = -1/(2z) and y=y(z) = -1/(2(z+1)), satisfying the relations x²=y⁴=1. In this paper, corresponding to each t in F_p we shall determine the coset diagrams D(t,p) depicting the actions of G(2,4,Z) on PL(F_p) and find also the values of p for which there exist vertices on the vertical line of symmetry in D(t,p). Also, we find conditions for the existence of certain useful fragments of coset diagrams in D(t,p).