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May 12, 2012 at 14:49 comment added Andreas Blass I believe that all non-cyclic groups $G$ have the property that some two non-isomorphic permutation actions have the same character. But there's no guarantee that (exactly) one of the two permutation actions contains a regular orbit.
May 12, 2012 at 9:20 history edited Jeremy Rickard CC BY-SA 3.0
added 116 characters in body
May 12, 2012 at 9:06 history answered Jeremy Rickard CC BY-SA 3.0