  Let $G$ be a finite group of order $n$, and $\xi$ an $n$-th primitive root of
unity. Consider the affine scheme $C:=\mbox{Spc}({\mathbb
Z}[\xi]\otimes_{\mathbb Z} R(G))$ where $R(G)$ is the representation ring of
$G$. We study the fibers of the formal tangent sheaf of $C$ by computing their
dimension and also finding (and measuring) the singularities of $C$. We present
explicit computations for noncommutative groups of small order, and develop
practical methods to compute these invariants for an arbitrary finite group.
