If $G$ is a paracompact topological group, then is $G \times G$ paracompact?

This question is raised by [Gepner and Henriques](https://arxiv.org/abs/math/0701916) (first paragraph of 2.2). Of course, this is not true for arbitrary paracompact spaces, as shown by the Sorgenfrey plane.

Actually -- what's an example of a non-paracompact group?