GAP has the command
ConjugacyClassesSubgroups which gives a list of the conjugacy classes of a finite group $G$. Is there a way I can specify further what types of subgroups GAP reports? For instance, can I ask GAP to only list conjugacy classes of subgroups of a certain order or isomorphism type?
My question is about subgroups in symmetric group isomorphic to others symmetric groups.
Thanks for your answers.
For instance, I have defined $S_3$ and $S_5$ and i would like to know the number of subgroups in $S_5$ isomorphic to $S_3$.
So the function
IsomorphicSubgroups(s5,s3) enable to see 2 types of classes of subgroups in $S_5$ isomorphic to $S_3$. But how see the size of these classes?
If i put:
emb := IsomorphicSubgroups(s5,s3);
And i ask:
GAP returns: "Error no method found!"
Thanks for any answer to help me!