Representations of finite groups over number fields are well understood in theory, but leave a large number of practical questions open. In my talk I will adress a few of them. In particular, for absolutely irreducible representations I will explain how

• the number field can be chosen that affords the representation
• to change the field
• to decide if the representation is equivalent to an integral representation
• find all classes of non-equivalent integral representation, thus giving a constructive version of the Jordan–Zassenhaus theorem