In a joint work with Manuel Delgado (FCUP), I have developed a GAP Packages to calculate Core-free subgroups of a given group and to provide faithful transitive permutation representations of groups.
This package also has tools to build permutation representation graphs, which are useful in understanding the action of groups.
You can find the GAP package "CoreFreeSub" available in
https://github.com/CAPiedade/CoreFreeSub
Recently, I have developed a Atlas of Hypertopes, for Rank 4.
This Atlas is still in its early stages, having very few examples.
You can find the Atlas of Regular Hypertopes of Rank 4 in
here