Let $G=\langle x,y|x^5=y^4=yxy^{-1}x^{-2}=1\rangle$ be a group. How would I construct the full character table of this group with no other given information?
Here is what I know regarding characters:
-If $\chi$ is an irreducible character of dimension $\chi(1)=n$, then $n$ divides the order of $G$.
-If $G$ has $r$ conjugacy classes, then the number of irreducible characters is equal to $r$.
-A character has dimension $1$ if it is irreducible. Otherwise it is the sum of irreducible characters.
-Characters are constant on conjugacy classes of $G$.