KnowraSymmetric groupLinked fromLinked fromThe 20 pages that link to Symmetric group, each with the reason it gives.All 20Broader topic 7Related 8Narrower topic 2Compared with 3PermutationBroader topic: It organizes every permutation of an n-element set as one algebraic structure.Finite groupBroader topic: It provides a concrete model of finite groups through permutations.Permutation groupBroader topic: It is the largest permutation group on a given finite set.Conjugacy classBroader topic: In this group, conjugacy classes are classified by cycle type.Composition seriesBroader topic: Its composition factors illustrate how a nonabelian simple group can occur.Solvable groupBroader topic: The symmetric group on five or more symbols is a standard nonsolvable example.Inverse Galois problemBroader topic: Symmetric groups arise as Galois groups of generic polynomials and many specific polynomials.