class_docstr: For each semisimple Lie group, we have a Weyl group.  It is a subgroup of
  the isometry group of the root system.  Specifically, it's the subgroup
  that is generated by reflections through the hyperplanes orthogonal to
  the roots.  Therefore, Weyl groups are reflection groups, and so a Weyl
  group is a finite Coxeter group.
docstr: This method returns some general information about the Weyl group for
  a given Lie algebra.  It returns the name of the group and the elements
  it acts on, if relevant.
docstr_tok: ["This","method","returns","some","general","information","about","the","Weyl","group","for","a","given","Lie","algebra",".","It","returns","the","name","of","the","group","and","the","elements","it","acts","on",",","if","relevant","."]
code: def group_name(self):
      """
      This method returns some general information about the Weyl group for
      a given Lie algebra.  It returns the name of the group and the elements
      it acts on, if relevant.
      """
      n = self.cartan_type.rank()
      if self.cartan_type.series == "A":
          return (
              "S"
              + str(n + 1)
              + ": the symmetric group acting on "
              + str(n + 1)
              + " elements."
          )
  
      if self.cartan_type.series in ("B", "C"):
          return (
              "The hyperoctahedral group acting on "
              + str(2 * n)
              + " elements."
          )
  
      if self.cartan_type.series == "D":
          return (
              "The symmetry group of the "
              + str(n)
              + "-dimensional demihypercube."
          )
  
      if self.cartan_type.series == "E":
          if n == 6:
              return "The symmetry group of the 6-polytope."
  
          if n == 7:
              return "The symmetry group of the 7-polytope."
  
          if n == 8:
              return "The symmetry group of the 8-polytope."
  
      if self.cartan_type.series == "F":
          return (
              "The symmetry group of the 24-cell, or icositetrachoron."
          )
  
      if self.cartan_type.series == "G":
          return "D6, the dihedral group of order 12, and symmetry group of the hexagon."
  
file_path: sympy/sympy/liealgebras/weyl_group.py
imports: from .cartan_type import CartanType
  from mpmath import fac
  from sympy.core.backend import Matrix, eye, Rational, igcd
  from sympy.core.basic import Atom
label_desc: Use image node_id 4 for calling the WeylGroup obj's underlying member method code with example usage: obj.group_name() and returns: unknown, unknown, unknown, str, str, str, str, str