I am trying to find out how to construct a space with the following fundamental group: $ \pi_{1}(X)= \langle a,b, c \mid b^{2}ac, c^{-1}a^{2} \rangle$
What is the main strategy for solving this kind of exercises? Do i have to try to modify the relations so that i can get a space with known relations like the torus, Klein bottle and projective plane?
Thank you for your help.
Construct a CW-complex: start with a point $p$, attach 1-cells $a$ and $b$ with their boundaries identified with $p$, and then attach a 2-cell with boundary $b^2a^3$. In general this process works for constructing a space with a fundamental group given by generators and relations.
If you're curious about constructing spaces with given homotopy groups more generally, here is a note on that topic: http://www.people.fas.harvard.edu/~xiyin/Site/Notes_files/AT.pdf