@XanderHenderson Thanks for the update. So the claim was edited from somewhat non-trivially wrong to trivially wrong. Don't worry about it too much. The review task ended as leave closed. My interest on it went down after I realized that the original version was wrong for all odd order groups anyway. Meaning that Dietrich's example wasn't too special either.
I don't think that this question is a bad question (quite the contrary---it seems borderline okay; there is some effort shown, though little context beyond that). However, I don't understand why it has 5 upvotes. It isn't that good.
I don't think that I am ever going to understand how this site works. :\