I am looking to define the Weyl group of type $D_n$ as a subgroup of Weyl group of type $B_n$ in the software GAP. In general, one can define these groups separately. For example, let's say
H:=CoxeterGroup("D",4) defines the Weyl group of type $B_4$ and $D_4$ respectively. Under this definition, I assume that $H$ is not recognized as a normal subgroup of $G$.
The main thing I want to achieve is to visualize the conjugacy classes in these groups. For example:
cc:=ConjugacyClasses(H); will return the list of conjugacy classes in $H$. Now, a command as:
ConjugacyClass(G,cc); is not making sense here although theoretically it makes sense. I hope I have been able to explain the problem properly. Thank you in advance for any kind of help.