We describe how certain permutation actions of large symmetric groups can be efficiently implemented on a computer. Using a specially tailored adaptation of a general technique to enumerate huge orbits and substantial distributed computation on a cluster of workstations, we collect further evidence related to the approach to Foulkes' conjecture suggested in “A Note on Plethysm,” by S. C. Black and R. J. List.
"Some computations regarding Foulkes' conjecture." Experiment. Math. 14 (3) 277 - 283, 2005.