Breaking classical Lie groups to finite subgroups - an automated approach

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character formula. For some low order finite groups including $A_4$ and $\Delta(27)$ general analytical formulas are presented for the branching rules of arbitrary representations of their smallest Lie super-groups.