theory – Is Higman’s group a free product?

Higman constructed an example of a finitely presented simple group here:

Higman, Graham
A finitely generated infinite simple group.
J. London Math. Soc. 26 (1951), 61–64.

It is a quotient of what is called Higman’s group, which is an amalgamated free product.

Question: is either group isomorphic to a (non-trivial) free product? (i.e. amalgamated over the trivial group)