Abstract Let G be a finite group. $H, K$ subgroups of and $H \backslash / the double coset space. If Q is probability on which constant conjugacy classes ( $Q(s^{-1} t s) = Q(t)$ ), then random walk driven by projects to Markov chain /K$ . This allows analysis lumped using representation theory Examples include coagulation-fragmentation processes natural chains contingency tables. Our main exam...