\indent we consider group-invariant cr mappings from spheres to hyperquadrics. given a finite subgroup $\gamma \subset u(n)$, a construction of d'angelo and lichtblau yields a target hyperquadric $q(\gamma)$ and a canonical map $h_{\gamma} : s^{2n-1}/\gamma \to q(\gamma)$. for every $\gamma \subset su(2)$, we determine this hyperquadric $q(\gamma)$, that is, the numbers of positive and negative eigenvalues in its defining equation. for families of cyclic and dihedral subgroups of $u(2)$, we study these numbers asymptotically as the order of group tends to infinity. finally, we explore connections with invariant theory and representation theory.