code: def M20():
      """
      Return a representation of the metacyclic group M20, a transitive subgroup
      of S5 that is one of the possible Galois groups for polys of degree 5.
  
      Notes
      =====
  
      See [1], Page 323.
  
      """
      G = PermutationGroup(
          Permutation(0, 1, 2, 3, 4), Permutation(1, 2, 4, 3)
      )
      G._degree = 5
      G._order = 20
      G._is_transitive = True
      G._is_sym = False
      G._is_alt = False
      G._is_cyclic = False
      G._is_dihedral = False
      return G
  
imports: from collections import defaultdict
  from enum import Enum
  import itertools
  from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, CyclicGroup, DihedralGroup, set_symmetric_group_properties, set_alternating_group_properties
  from sympy.combinatorics.perm_groups import PermutationGroup
  from sympy.combinatorics.permutations import Permutation
label_desc: Use image node_id 2 for calling a global function with example usage: M20() and returns: G