I am currently working through all the groups with two generators, and I am up to the group with presentation $G := \langle a, b \  \ a^2, b^3, (ab)^7, [a,b]^9 \rangle$. I have found all the finite quotients of this group, but there are also the infinite quotients of the group that I need to check. Are there any infinite quotients of this group other than the whole group? I know that there is a central element of order 2, but what I need to know is, what is this element?
