I wanted to ask about 3sylowsubgroup (of the group S6)
I have an example of such a group,
But I want to know
what another group is isomorphous? (otherwise known group which does not belong to S6)
Okay, well what is the order of a Sylow-3 subgroup of $\displaystyle S_6$? How many groups are there of this order? (HINT: there are only two. Why?)
You now just have to work out which of these two groups a Sylow-3 group is isomorphic to. This reduces to proving whether or not there exists an element of order 9 in your group (why?).
So, does there exist an element of order 9 in $\displaystyle S_6$?
EDIT: Alternatively, you can go back to the previous time you posted this question, here, just over two weeks ago, and do what I suggested then. That is, look at the group generated by $\displaystyle (123)$ and $\displaystyle (456)$. What is its order (from it's order you can tell if it is a Sylow-3 subgroup)? What group is it isomorphic to? (It's not cyclic, but it is abelian).