spectrum and energies of commuting conjugacy class graph of a finite group

In this paper we compute spectrum, laplacian spectrum, signless laplacian spectrum and their corresponding energies of commuting conjugacy class graph of the group $g(p, m, n) = langle x, y : x^{p^m} = y^{p^n} = [x, y]^p = 1, [x, [x, y]] = [y, [x, y]] = 1rangle$, where $p$ is any prime, $m geq 1$ and $n geq 1$. we derive some consequences along with the fact that commuting conjugacy class graph of $g(p, m, n)$ is super integral. we also compare various energies and determine whether commuting conjugacy class graph of $g(p, m, n)$ is hyperenergetic, l-hyperenergetic or q-hyperenergetic.