Find order of group given by generators and relations Let $G$ be the group defined by these relations on the generators $a$ and $b$: $\langle a, b; a^5, b^4, ab=ba^{-1}\rangle$. I need hints how to find order of $G$.

We can show by induction that any word in $a, b$ (and their inverses) is equivalent under the relators to a unique word of the form $$a^k b^l$$ where $0 \leq k <5 $ and $0 \leq l < 4$.
