Problem with computation of maximal subgroups in an almost simple group, possible bug in MaxesAlmostSimple?

[RamonEstebanRomero]

Dear colleagues,

Sorry if I am not using this system in a proper way for bug reports, this is the first time I do it.

The following group is an almost simple group with socle isomorphic to PSL(3,4). When I try to compute the conjugacy classes of maximal subgroups with MaximalSubgroupClassReps or ConjugacyClassesMaximalSubgroups I get an error.

gap> g:=Group(
> [ (3,5,4)(7,8,9)(10,18,14)(11,20,17)(12,21,15)(13,19,16)(22,32,41)(24,36,
>     29)(25,40,33)(26,28,37)(30,42,34)(31,35,39),
>   (1,2,7,3,11,10,6)(4,15,20,21,13,18,9)(5,19,17,16,12,14,8)(22,34,39,40,29,
>     32,28)(23,27,33,37,42,35,38)(24,26,36,30,31,25,41),
>   (7,8,9)(10,14,18)(11,16,21)(12,17,19)(13,15,20)(22,28,29)(24,32,37)(25,40,
>     33)(26,36,41)(31,39,35), (1,38)(2,23)(3,42)(4,34)(5,30)(6,27)(7,33)(8,
>     40)(9,25)(10,35)(11,37)(12,36)(13,22)(14,39)(15,29)(16,32)(17,26)(18,
>     31)(19,41)(20,28)(21,24) ]);
<permutation group with 4 generators>
gap> MaximalSubgroupClassReps(g);         
Error, <G> must be simple called from
IsomorphismTypeInfoFiniteSimpleGroup( G ) at /home/estebanr/Baixades/gap4r8/grp/simple.gi:814 called from
DataAboutSimpleGroup( G ) at /home/estebanr/Baixades/gap4r8/lib/maxsub.gi:537 called from
MaxesAlmostSimple( ImagesSource( act[2] ) ) at /home/estebanr/Baixades/gap4r8/lib/maxsub.gi:831 called from
<function "DoMaxesTF">( <arguments> )
 called from read-eval loop at line 54 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

It seems that the possible problem is in the function MaxesAlmostSimple.

brk> Print(MaxesAlmostSimple, "\n");
function ( G )
    local  id, m, epi;
    if IsNaturalSymmetricGroup( G ) or IsNaturalAlternatingGroup( G )  then
        Info( InfoLattice, 1, "MaxesAlmostSimple: Use S_n/A_n" );
        return MaximalSubgroupClassReps( G );
    fi;
    m := TomDataMaxesAlmostSimple( G );
    if m <> fail  then
        return m;
    fi;
    id := DataAboutSimpleGroup( G );
    if id.idSimple.series = "A"  then
        Info( InfoWarning, 1, "Alternating recognition needed!" );
    elif id.idSimple.series = "L"  then
        m := ClassicalMaximals( "L", id.idSimple.parameter[1], id.idSimple.parameter[2] );
        if m <> fail  then
            epi := EpimorphismFromClassical( G );
            if epi <> fail  then
                m := List( m, function ( x )
                        return SubgroupNC( Range( epi ), List( GeneratorsOfGroup( x ), function ( y )
                                  return ImageElm( epi, y );
                              end ) );
                    end );
                return m;
            fi;
        fi;
    fi;
    if ValueOption( "cheap" ) = true  then
        return [  ];
    fi;
    Info( InfoLattice, 1, "MaxesAlmostSimple: Fallback to lattice" );
    return MaxesByLattice( G );
end

It seems that the function is assuming that the group is simple instead of almost simple. I have been able to compute the maximal subgroups with MaxesByLattice.

Can you please check whether something is wrong? I am using GAP version 4.8.2.

All the best,

Ramon Esteban-Romero.

[markuspf]

This is absolutely the correct place to file bug reports.

I suspect that the line that goes

id :=   DataAboutSimpleGroup(G);

should use the minimal normal subgroup of G. I am sure @hulpke knows how to fix this, but I can also go and find how the maximal subgroup computation should continue here.

[markuspf]

By the way, using github markdown you can format your report more nicely using the "code" environment. I have edited your post accordingly to make it more easily readable.

[RamonEstebanRomero]

Thank you, @markuspf. I also think that perhaps that line should refer to the minimal normal subgroup of the almost simple group.

All the best,

Ramón.

[hulpke]

No, the is a case that currently (until we have proper `ClassicalMaximals') should only be called if the group is simple. I will submit a fix.

[olexandr-konovalov]

Fixed in PR #682.