Let G be an order 957 group. I have to prove that it is cyclic.
When I calculate Sylow p-subgroups for p=3, I find that 319 is a valid number or Sylow 3-subgroups. p=11 and p=29 gives me a normal Sylow p-subgroup for each of them.
I know that, if all Sylow groups were normal, we could probe the isomorfism to cyclic 957 group. By Sylow, how could this be solved?
A quick look here tells us that $957$ is coprime to $\phi(957)$, where $\phi$ is the totient function. So we can use the strategy discussed here.