In the notebook attached below a short procedure is given to construct a group from a set of so-called generating elements. The notebook has two parts. In the first part all operations are performed on permutation cycles while the second part deals with matrices. The sequence of elements in the group is arbitrary depending on the given generating elements, but it should be quite easy to order these lists using whatever criterion. An example is shown in group O, the last calculation just before the Additional Information 1.