(n)
return G
Generates the symmetric group on ``n`` elements as a permutation group.

    The generators taken are the ``n``-cycle
    ``(0 1 2 ... n-1)`` and the transposition ``(0 1)`` (in cycle notation).
    (See [1]). After the group is generated, some of its basic properties
    are set.

    Examples
    ========

    >>> from sympy.combinatorics.named_groups import SymmetricGroup
    >>> G = SymmetricGroup(4)
    >>> G.is_group()
    False
    >>> G.order()
    24
    >>> list(G.generate_schreier_sims(af=True))
    [[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 1, 2, 0], [0, 2, 3, 1],
    [1, 3, 0, 2], [2, 0, 1, 3], [3, 2, 0, 1], [0, 3, 1, 2], [1, 0, 2, 3],
    [2, 1, 3, 0], [3, 0, 1, 2], [0, 1, 3, 2], [1, 2, 0, 3], [2, 3, 1, 0],
    [3, 1, 0, 2], [0, 2, 1, 3], [1, 3, 2, 0], [2, 0, 3, 1], [3, 2, 1, 0],
    [0, 3, 2, 1], [1, 0, 3, 2], [2, 1, 0, 3], [3, 0, 2, 1]]

    See Also
    ========

    CyclicGroup, DihedralGroup, AlternatingGroup

    References
    ==========

    [1] http://en.wikipedia.org/wiki/Symmetric_group#Generators_and_relations
Generates the symmetric group on ``n`` elements as a permutation group.
Generates the symmetric group on n elements as a permutation group .
def SymmetricGroup(n):
    """
    Generates the symmetric group on ``n`` elements as a permutation group.

    The generators taken are the ``n``-cycle
    ``(0 1 2 ... n-1)`` and the transposition ``(0 1)`` (in cycle notation).
    (See [1]). After the group is generated, some of its basic properties
    are set.

    Examples
    ========

    >>> from sympy.combinatorics.named_groups import SymmetricGroup
    >>> G = SymmetricGroup(4)
    >>> G.is_group()
    False
    >>> G.order()
    24
    >>> list(G.generate_schreier_sims(af=True))
    [[0, 1, 2, 3], [1, 2, 3, 0], [2, 3, 0, 1], [3, 1, 2, 0], [0, 2, 3, 1],
    [1, 3, 0, 2], [2, 0, 1, 3], [3, 2, 0, 1], [0, 3, 1, 2], [1, 0, 2, 3],
    [2, 1, 3, 0], [3, 0, 1, 2], [0, 1, 3, 2], [1, 2, 0, 3], [2, 3, 1, 0],
    [3, 1, 0, 2], [0, 2, 1, 3], [1, 3, 2, 0], [2, 0, 3, 1], [3, 2, 1, 0],
    [0, 3, 2, 1], [1, 0, 3, 2], [2, 1, 0, 3], [3, 0, 2, 1]]

    See Also
    ========

    CyclicGroup, DihedralGroup, AlternatingGroup

    References
    ==========

    [1] http://en.wikipedia.org/wiki/Symmetric_group#Generators_and_relations

    """
    if n == 1:
        G = PermutationGroup([Permutation([0])])
    elif n == 2:
        G = PermutationGroup([Permutation([1, 0])])
    else:
        a = list(range(1, n))
        a.append(0)
        gen1 = _af_new(a)
        a = list(range(n))
        a[0], a[1] = a[1], a[0]
        gen2 = _af_new(a)
        G = PermutationGroup([gen1, gen2])
    if n < 3:
        G._is_abelian = True
        G._is_nilpotent = True
    else:
        G._is_abelian = False
        G._is_nilpotent = False
    if n < 5:
        G._is_solvable = True
    else:
        G._is_solvable = False
    G._degree = n
    G._is_transitive = True
    G._is_sym = True
    return G
def SymmetricGroup ( n ) : if n == 1 : G = PermutationGroup ( [ Permutation ( [ 0 ] ) ] ) elif n == 2 : G = PermutationGroup ( [ Permutation ( [ 1 , 0 ] ) ] ) else : a = list ( range ( 1 , n ) ) a . append ( 0 ) gen1 = _af_new ( a ) a = list ( range ( n ) ) a [ 0 ] , a [ 1 ] = a [ 1 ] , a [ 0 ] gen2 = _af_new ( a ) G = PermutationGroup ( [ gen1 , gen2 ] ) if n < 3 : G . _is_abelian = True G . _is_nilpotent = True else : G . _is_abelian = False G . _is_nilpotent = False if n < 5 : G . _is_solvable = True else : G . _is_solvable = False G . _degree = n G . _is_transitive = True G . _is_sym = True return G