Actions of Δ(3,n,k) on projective line

Each conjugacy class of actions of the triangle group Δ(3,n,k) over the projective line PL(Fq) can be represented by a coset diagram D(θ,q), where θ∈Fq and q is a prime number. In this paper, we have considered conjugacy classes which arise from the actions of Δ(3,n,k)=〈r,s:r3=sn=(rs)k=1〉 over PL(Fq), where Fq is finite field. The points of PL(Fq) are the elements of Fq together with the additional point ∞.