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While exploring cayley graphs of generalized dihedral groups I get a wrong result if I use GeneralDihedralGroup([n]) to create a simple dihedral group for some values on n, 6 and 10 for instance. Sage responds that it is isomorphic to DihedralGroup(n), but the cayley graphs and group generators are not the same. Is it me or the system?
For example:
sage: gd=GeneralDihedralGroup([10]) sage: CGD10=Graph(gd.cayley_graph()) sage: CGD10.diameter() 4 sage: CGD10.degree() [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4] sage: dih10=DihedralGroup(10) sage: sage: Cdih10=Graph(dih10.cayley_graph()) sage: Cdih10.diameter() 6 sage: Cdih10.degree() [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] sage: gd.is_isomorphic(DihedralGroup(10)) True sage: dih10.gens() [(1,2,3,4,5,6,7,8,9,10), (1,10)(2,9)(3,8)(4,7)(5,6)] sage: gd.gens() [(4,7)(5,6), (3,4,5,6,7), (1,2)]

While exploring cayley graphs of generalized dihedral groups I get a wrong result if I use GeneralDihedralGroup([n]) to create a simple dihedral group for some values on n, 6 and 10 for instance. Sage responds that it is isomorphic to DihedralGroup(n), but the cayley graphs and group generators are not the same. Is it me or the system?
For example:

sage:  gd=GeneralDihedralGroup([10])  
sage:  CGD10=Graph(gd.cayley_graph())  
sage: CGD10.diameter()  
4  
sage:  CGD10.degree()  
[4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]  
sage:  dih10=DihedralGroup(10)  
sage: sage: Cdih10=Graph(dih10.cayley_graph())  
sage: Cdih10.diameter()  
6  
sage: Cdih10.degree()  
[3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]  
sage: gd.is_isomorphic(DihedralGroup(10))  
True  
sage: dih10.gens()  
[(1,2,3,4,5,6,7,8,9,10), (1,10)(2,9)(3,8)(4,7)(5,6)]  
sage: gd.gens()  
[(4,7)(5,6), (3,4,5,6,7), (1,2)]
(1,2)]`