Gapplet

Given a set of permutations of X generating the group G of S(X), and a vertex x X, determine the correspondence between cosets of H = Gx and the G-orbit of x.

Give a sequence of generators for G, e.g., (1,2,3)(4,5,6), (2,3)(5,6), (1,4)(2,5)(3,6)(7,8) 
 
Give a point x, e.g., 1 
 
 
 
The correspondence