code: def test_DihedralGroup():
      G = DihedralGroup(6)
      elements = list(G.generate())
      assert len(elements) == 12
      assert G.is_transitive() is True
      assert G.is_abelian is False
      assert G.is_solvable is True
      assert G.is_nilpotent is False
      H = DihedralGroup(1)
      assert H.order() == 2
      L = DihedralGroup(2)
      assert L.order() == 4
      assert L.is_abelian is True
      assert L.is_nilpotent is True
  
file_path: sympy/sympy/combinatorics/tests/test_named_groups.py
imports: from sympy.combinatorics.named_groups import SymmetricGroup, CyclicGroup, DihedralGroup, AlternatingGroup, AbelianGroup, RubikGroup
  from sympy.testing.pytest import raises
label_desc: Use image node_id 3 for calling a global function with example usage: test_DihedralGroup() without return types