is the function that gives access to the strong generators and their base. It is hence the starting point for further programming of tools for computation with permutation groups.
Those groups for which the length of the base is much shorter than the degree of the permutations can be efficiently manipulated using strong generators.
This is a permutation representation of the sporadic simple group ConwayGroupCo3
acting on 276 points, but here a base with only 6 points is used: