My only suggestion would be to sit down anddoit! , the group of permutations on 4 "symbols", contains 4!= 24 elements. It is tedious but not impossible to write out its operation table. It has a subgroup isomorphic to the Klein group (if it didn't this problem would make no sense). Can you identify that subgroup? has 8 members. Can you work out the operation table for it from the operation table for ?