code: def set_symmetric_group_properties(G, n, degree):
      """Set known properties of a symmetric group."""
      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 = degree
      G._is_transitive = True
      G._is_dihedral = n in [2, 3]
  
file_path: sympy/sympy/combinatorics/named_groups.py
imports: from sympy.combinatorics.group_constructs import DirectProduct
  from sympy.combinatorics.perm_groups import PermutationGroup
  from sympy.combinatorics.permutations import Permutation
label_desc: Use image node_id 7 for calling a global function with example usage: set_symmetric_group_properties(G, n, degree) without return types