let h be a hopf algebra over an algebraically closed field of characteristic not 2. assume that the antipode of h has period 2, and let v be a finite-dimensional representation of h. then if v is self-dual, it must be either ``orthogonal'' or ``symplectic'' , in the sense that it admits a non-degenerate h-invariant bilinear form which is either symmetric or skew-symmetric. we consider various hopf algebras constructed from finite groups, and investigate when all of their (fin dim) representations are orthogonal in the above sense.