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There is a software package called GAP for "Groups, Algorithms, and Programming" with emphasis on Group Theory. You can download it for free. I did. However I'm finding it so intractable to use. I would like to find the "missing group" in the Symmetric groups. That is, the group order which divides the size of ##S_n## but is not a subgroup of ##S_n##. I'm sure GAP can do it. So far I got the following code down:

(* first just get the group *)

mygroup:=SymmetricGroup(4);

subgroups:=AllSubgroups(mygroup);

and that's about as far as I can go with it for now. At this point "subgroups" contain all the subgroups of mygroup. I would like then to create a table of group size, total subgroups, then I can find the missing ones.

Anyone here familiar with using GAP can help me with this?

Thanks,

Jack

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# Anyone familiar with "GAP" for group arithemetic?

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