This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SymmetricGroup

 SymmetricGroup[n] represents the symmetric group of degree n.
• The degree n of SymmetricGroup[n] must be a non-negative integer. Degrees 0 and 1 correspond to the trivial or identity group.
• SymmetricGroup[n] is represented by default as a permutation group on the points .
Number of elements of a symmetric group:
Permutation generators of a symmetric group:
Elements of a permutation representation of a symmetric group:
Number of elements of a symmetric group:
 Out[1]=

Permutation generators of a symmetric group:
 Out[1]=

Elements of a permutation representation of a symmetric group:
 Out[1]=
 Scope   (1)
Symmetric groups of degree 0 or 1 are the trivial group, only containing the identity:
In all other cases the symmetric group of degree n contains n! elements:
 Applications   (1)
Test whether two random permutations generate the symmetric group of degree 100:
Permutations returns the permuted forms of an expression under the elements of a symmetric group:
New in 8