Is any of these two groups a smooth manifold?

Question

This question came to my mind while I was going through Iian B. Smythe's talk titled A Crash Course in Topological Groups.

In the talk it is mentioned that,

Lie group G is a group, which is also a smooth manifold

My question is:

1. Is the automorphism group of a graph, $A$, a smooth manifold?
2. Is the group $\mathbb{Z}_n$ a smooth manifold?

My effort: I understand that I have to prove the following.

1. $A$ and $\mathbb{Z}_n$ are Hausdorff
2. $A$ and $\mathbb{Z}_n$ are second countable
3. $A$ and $\mathbb{Z}_n$ are locally Euclidean
4. Somehow I have to prove that they are differentiable.

Could anyone help me to at least start?