code: def PGL2F5():
      r"""
      Return a representation of the group $PGL_2(\mathbb{F}_5)$, as a transitive
      subgroup of S6, isomorphic to $S_5$.
  
      Notes
      =====
  
      See [1], Page 325.
  
      """
      G = PermutationGroup(
          Permutation(0, 1, 2, 3, 4), Permutation(0, 5)(1, 2)(3, 4)
      )
      set_symmetric_group_properties(G, 5, 6)
      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 14 for calling a global function with example usage: PGL2F5() and returns: G