Democrats put forward a shit candidate . On the upside , we ' ll get direct results of Tea Party ideology at the federal level and not just at the state level . So hopefully it won ' t take more than four years to see disastrous results , and then we can start to rebuild . <| sep |> Your point about the orders is not quite right in nonabelian groups the order of x and y does not tell you anything about the order of xy all dihedral groups are generated by two reflections . So the fact that 1234 has order 2 and 1234 has order 4 does not mean they can ' t generate a subgroup containing an element of order 3 . The quickest way to see that 1234 and 1234 do not generate S 4 is by noticing that each preserves the partition 1 , 3 , 2 , 4 so that the generated group is not 2 transitive .