Here is the problem:

I get thatLet N < S4 consist of all permutations (sigma) such that (sigma)(4) = 4. Is N normal in S4?

N = {(1234), (2134), (3214), (1324), (2314), (3124)}

(Where

Sorry, I don't do well with cyclic notation.)

I know I can do this "brute force" by forming all the left and right cosets. I'd like to find a less time consuming method, but haven't found any yet. Any suggestions?

-Dan