Discrepancy between groups produced by `AllSOTGroups` and `SOTGroup`

[fingolfin]

I would expect AllSOTGroups(n) and List([1..NumberOfSOTGroups(n)],i->SOTGroup(n,i)) to produce not just lists where corresponding groups are isomorphic; but in fact have identical presentations.

But this seems not to be the case for at least groups of of order $p^4 q$.

Consider this:

gap> CodePcGroup(SOTGroup(48,32));
61687858337
gap> CodePcGroup(AllSOTGroups(48)[32]);
65382416993

or this:

gap> CodePcGroup(SOTGroup(272,41));
5207512816961978383
gap> CodePcGroup(AllSOTGroups(272)[41]);
5229198979772710927

Is this known? Is it intentional? It is not strictly speaking wrong, of course, but very unexpected, and I would at least warn about it in the manual. Nicer would of course be to change this, if possible with reasonable effort.

[fingolfin]

Doesn't seem to be limited to $p^4*q$, here is a $pqrs$ example:

gap> n:=2*3*7*43;
1806
gap> CodePcGroup(SOTGroup(n,29));
207974057626033607
gap> CodePcGroup(AllSOTGroups(n)[29]);
207974469042025055

[fingolfin]

Some other affected orders:

147 = 3*7^2
150 = 2*3*5^2
156 = 2^2*3*13
260 = 2^2*5*13
294 = 2*3*7^2
625 = 5^4
1444 = 2^2*19^2
1815 = 3*5*11^2
1911 = 3*7^2*13

[xpan-eileen]

I am looking into this…

It was probably intentional but now I can’t remember why, so it was probably not for a very good reason. What I am trying to do at the moment is to see what I had in my thesis and try to use the one that agrees with that.

[xpan-eileen]

Weirdly, I couldn’t find any discrepancy for these orders? Did it show up for you which groups were causing the issue?

gap> n:=147;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=150;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=156;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=260;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=294;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=625;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=1444;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=1815;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]
gap> n:=1911;;all:=AllSOTGroups(n);;Filtered([1..NumberOfSOTGroups(n)],x->CodePcGroup(SOTGroup(n,x))<>CodePcGroup(all[x]));
[  ]

[fingolfin]

Nevermind, those orders were a fluke: I called CodePcGroup(G) a bit too later, and apparently it depends on the output of Pcgs(G), and apparently this can change (which I did not expect) as a side effect of some other code.

[fingolfin]

Thanks, your latest fix cured 48, but e.g. 1053 still has discrepancies

[fingolfin]

Also 6875, 13203

[fingolfin]

Better. But I still get a discrepancy for 6875. All else seem to work now

[fingolfin]

Seems to be resolved now, great!