Assume $X$ is a smooth projective curve of genus $g\geq 3$ over $\mathbb{C}$ and let $M$ be the (singular) moduli space of semistable rank two vector bundles with trivial determinant on $X$. Then there is a desingularization of $M$ due to a more general construction of Kirwan.

As far as I understand the idea, one uses that $M=Q//G$ is a GIT quotient of a subscheme of some Quot-scheme $Quot(\mathcal{O}_X^r)$ and blows up smooth subschemes in $Q$ with nontrivial stabilizers to make the stabilizers "smaller". Finally one ends up with a scheme $Q'$ such that $G$ only has finite stabilzers.

What finite groups remain in this proces in the case of the moduli space of semistable rank two vector bundles on $X$?

For $M$ it is known that the singular set is the Kummer variety $K$ associated to $X$. Points in $Q$ above the singular points of $K$ have stabilizers $PGL(2)$ and points above smooth points have stabilizer $\mathbb{C}^{*}$. After three blow ups the scheme $Q'''//G$ is a desingularization of $M$. So what my question is: are all the stabilizers of $G$ in $Q'''$ in known?