# Anyone familiar with "GAP" for group arithemetic?

1. Sep 19, 2015

### jackmell

Hi guys,

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

2. Sep 24, 2015

### Greg Bernhardt

3. Sep 24, 2015

### jackmell

Hi Greg,

I'm making progress with the code. I had started another thread pertaining to the data from GAP where I posted a brilliant piece of GAP code I painfully pieced together: