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# generatePermutationGroup(List) -- a method for generating a permutation group given a set of generators

## Synopsis

• Function: generatePermutationGroup
• Usage:
generatePermutationGroup(gens)
• Inputs:
• gens, a list, a list of permutations
• Outputs:
• a list, the group generated by the given set of generators

## Description

The method works by taking all multiplications of the elements in the set of generators. New elements that are found are added and the process is repeated until no new elements are found.

 i1 : generatePermutationGroup {{1,0,2,3},{1,2,3,0}} o1 = {{1, 2, 0, 3}, {1, 3, 2, 0}, {3, 1, 0, 2}, {0, 3, 1, 2}, {2, 1, 3, 0}, ------------------------------------------------------------------------ {0, 2, 3, 1}, {2, 0, 1, 3}, {3, 0, 2, 1}, {1, 0, 3, 2}, {1, 2, 3, 0}, ------------------------------------------------------------------------ {3, 0, 1, 2}, {3, 2, 1, 0}, {3, 1, 2, 0}, {0, 1, 3, 2}, {0, 2, 1, 3}, ------------------------------------------------------------------------ {2, 0, 3, 1}, {2, 3, 1, 0}, {1, 0, 2, 3}, {3, 2, 0, 1}, {1, 3, 0, 2}, ------------------------------------------------------------------------ {2, 1, 0, 3}, {0, 3, 2, 1}, {2, 3, 0, 1}, {0, 1, 2, 3}} o1 : List

This method is used to calculate the size of each conjugacy classes for the groups.