1. The problem statement, all variables and given/known data What is the normalizer of the Sylow p-subgroup in the symmetric group Sym(p) generated by the element (1,2,...,p) where p is a prime number? Thanks 2. Relevant equations na 3. The attempt at a solution I know that the normalizer has order p(p-1). And I know that it has to include the group generated by (1,2,...,p). I know there must be elements outside <(1,2,...,p)> that conjugates (1,2,...,p) to (1,2,...,p)^n but what are their forms? Your help will be greatly appreciated.