[GAP Forum] Primitive Group Library problems

[Stefan Kohl]

Dear Gordon,

> I work with both GAP and Magma which use a different numbering system for their
> respective PrimitiveGroup libraries.
>
> Therefore I keep having to work out which “Gap-number” corresponds to which
> “Magma-number” for particular groups.
>
> So I decided to make a “once and for all” calculation and create a master table with the
> correspondence between the two numbering systems.
>
> During routine sanity checking at the end of this process, I was surprised to discover
> that the two libraries contain different numbers of groups.
>
> In particular,
>
> gap> NrPrimitiveGroups(1575);
> 6
>> NumberOfPrimitiveGroups(1575);
> 8
>
> Closer inspection reveals that the GAP library is missing two groups - they have orders
> 14742000000 and 29484000000; the first one can be identified as PSU(4,5) and it is
> contained in the second group.

Thank you very much for reporting this bug!

Indeed the smaller of the two missing groups can be constructed as follows:

gap> G := Image(SmallerDegreePermutationRepresentation(PSU(4,5)));;
gap> S := Group(G.1^3,G.2);;
gap> P := Action(G,RightCosets(G,S),OnRight);
<permutation group with 2 generators>

Now we see that P is missing in the Library:

gap> DegreeAction(P);
1575
gap> IsPrimitive(P,[1..1575]);
true
gap> Size(P);
14742000000
gap> List(AllPrimitiveGroups(DegreeAction,1575),Size);
[ 174182400, 348364800, 522547200, 1045094400,
  <integer 251...000 (4354 digits)>, <integer 502...000 (4354 digits)> ]

Identifying P in the Library is of course not possible:

gap> PrimitiveIdentification(P);
Error, Uh-Oh, this should never happen [  ] called from
<function "unknown">( <arguments> )
 called from read-eval loop at line 11 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk>

Best wishes,

    Stefan

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