the reason for my question is the following: the two-dimensional canonical singularities are the ADE-singularities, which all are quotients of either affine space or another ADE-singularity by finite abelian Groups and even more, quotients of affine 2-space by finite solvable Groups but one - namely $E_8$, which is factorial and a quotient of $A_1$ by the perfect Group $A_5$.
Now a generalization of the ADE-singularities in Dimension 3 are the compound du Val singularities, which are canonical and are formally equivalent to $f(x,y,z)+tg(x,y,z,t)$, where f is the polynomial of an ADE-singularity.
Now some of these are again quotients of affine 3-space, while a lot more than the one before ($E_8$) are factorial. For example the one in the heading. Which means in particular, that they cannot be a Quotient of affine space by a solvable Group.
As you may see now, it would be very nice, if these singularities were also some quotients by any Groups. Any idea? I am quite sure that it can't be a finite Group and affine 3-space.
Thank you and looking forward to your suggestions, Lukas