A permutation group is a mathematical concept in group theory that consists of a set of permutations of a given set combined with the operation of composition. Here's a more detailed breakdown of the concept: 1. **Permutations**: A permutation of a set is a rearrangement of its elements. For a finite set with \( n \) elements, a permutation is simply a bijective function from the set to itself.
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A subgroup of the symmetric group of a set, acting faithfully by permutations. A finite permutation group specified by generators can be enumerated by repeatedly multiplying the elements already found by those generators until no new element appears. Its orbits and conjugacy classes can then be computed directly.
