1. The problem statement, all variables and given/known data Prove that no group of order 96 is simple. 2. Relevant equations The sylow theorems 3. The attempt at a solution 96 = 2^5*3. Using the third Sylow theorem, I know that n_2 = 1 or 3 and n_3 = 1 or 16. I need to show that either n_2 = 1 or n_3 = 1, but I am unsure how to do this.