The symmetric group on a set X is denoted in various ways, including S X , S X , Σ Σ X , X ! , and Sym ⁡ ⁡ ( X ) . If X is the set { 1 , 2 , … … , n } then the name may be abbreviated to S n , S n , Σ Σ n , or Sym ⁡ ⁡ ( n ) .