Assume that $G = \langle a, b \rangle$ is a finite group which is generated by an
involution $a$ and an element $b$ of order 3 such that for every (complex) representation
$\varphi$ of $G$ the matrix $\varphi(a) + \varphi(b) + \varphi(b^{-1})$ has only rational eigenvalues.

> <b>Question:</b> Is there an upper bound on the order of $G$?