def METHOD_NAME(n):
    """
    Generates the cyclic group of order ``n`` as a permutation group.
    The generator taken is the ``n``-cycle ``(0 1 2 ... n-1)``
    (in cycle notation). After the group is generated, some of its basic
    properties are set.
    Examples
    ========
    >>> G = CyclicGroup(6)
    >>> G.is_group
    True
    >>> G.order()
    6
    >>> list(G.generate_schreier_sims(af=True))
    [[0, 1, 2, 3, 4, 5], [1, 2, 3, 4, 5, 0], [2, 3, 4, 5, 0, 1],
    [3, 4, 5, 0, 1, 2], [4, 5, 0, 1, 2, 3], [5, 0, 1, 2, 3, 4]]
    See Also
    ========
    SymmetricGroup, DihedralGroup, AlternatingGroup
    """
    a = list(range(1, n))
    a.append(0)
    gen = _af_new(a)
    G = PermutationGroup([gen])
    G._is_abelian = True
    G._is_nilpotent = True
    G._is_solvable = True
    G._degree = n
    G._is_transitive = True
    G._order = n
    return G