A collection of Isomorphic Groups 
So the answer is

Questions
1) How exactly is $<\pi>$ isomorphic to the other integer groups? I mean $\pi$ itself isn't even an integer.
2)What is exactly is the key saying for the single element sets? Are they trying to say they are isomorphic to themselves?
3) How exactly is $\{\mathbb{Z_6}, G \}$ and $\{ \mathbb{Z_2}, S_2\}$ isomorphic?

Hint: Consider the bijection $f:a^n\to n$.
To verify that $G$ and $\mathbb{Z}_6$ are indeed isomorphic let $$a=\begin{pmatrix} 1&2&3&4&5 \\ 3&5&4&1&2 \end{pmatrix}$$
Similarly for $\{S_2,\mathbb{Z}_2\}$ let 
$$a=\begin{pmatrix} 1&2 \\ 2&1 \end{pmatrix}$$
and isomorphism between the 2 groups should follow.
