The purpose of this app is principally pedagogical: to allow illustration of properties of the symmetric group. Users begin by specifying a symmetric group, S(n), by choosing a value for n greater than or equal to three and less than or equal to twelve. They then can either compose elements of S(n) or select a single element and create the subgroup generated by that element. If the task chosen is composition, then the elements selected are applied in the order selected. If, for example, a user specifies p1, p2, and p3 in S(n) in that order, the composition computed is p3(p2(p1())).
Permutations are selected using the graphical interface by first clicking on an element of the set {1,2,3,..n} from amongst the red points at top and then on its image under the permutation amongst the green points below. After an unique image has been selected for each red domain point, clicking 'Save Permutation' will store that permutation. If you have made a mistake in selecting the assignment for any domain element, 'Clear Arrows' allows you to start selecting the current permutatation anew without affecting previously selected permutations. After all permutations have been selected, clicking 'Compute' will either construct the cyclic subgroup of S(n) generated by that permutation if only one has been selected or find the composition of all the selected permutations if more than one has been selected. In the latter case, the graphical interface displays the composition. In the former, it merely displays the generator which the user has specified.
Permutations are displayed tabularly under the tab 'Composition/Subgroup as Table' as they are stored. After the computation is performed (click 'Compute'), the composition or generated subgroup are also displayed tabularly.