Am currently working on the Group of rotations of a cube in space. i have identified the 24 rotational symmetries of a cube that forms a group. And i am kind off trying to show that these symmetries forms a group by computing or creating a composition table of all the 24 elements permuting themselves. These is a tedious job to compute manually or physically. so my question or challenge is if there is any existing program or application or any other method to clearly show that the 24 symmetries forms a Group.
i came across these site but can't find the program or relate his table to what i have in mind because my symmetries are labelled C1-C24.