Decide whether the following staement is true of false. If true, prove it. If false, provide a counterexample
Let G1, G2 be a finite groups such as for all prime p, p-sylow subgroups of G1 isomorpic ($\cong$) to p-sylow subgroups of G2 and |G1|=|G2| then G1$\cong$G2.
I think this statement is false but I didn't find counterexample yet, I think it's false because I thought about dividing the group to p-sylow subgroups or write her has a direct product of them and then do a uoion or direct product of the isomorphisms but there is no diviton og G1 and G2 to her p-sylow so I couldn't prove it so I tried to find counterexample but I didn't find one.
If you found one please help me :)