Fix several regressions introduced by #6494

[hulpke]

This fixes the error notes in #6494 post-merge

(Some of it is not strictly needed but useful caution about the domain of nice morphisms)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 76.39%. Comparing base (0ff3c4f) to head (6fde561).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6510      +/-   ##
==========================================
- Coverage   78.91%   76.39%   -2.52%     
==========================================
  Files         685      684       -1     
  Lines      294163   293922     -241     
  Branches     8669     8652      -17     
==========================================
- Hits       232147   224555    -7592     
- Misses      60215    67541    +7326     
- Partials     1801     1826      +25     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[fingolfin]

So what exactly is the fix, and why does it work?

[fingolfin]

Also, this really needs a regression test.

[fingolfin]

With this branch:

gap> AutomorphismGroupSolvableGroup(SmallGroup(864,4675));
Error, Variable: 'u' must have an assigned value
Stack trace:
*[1] if u <> fail then
    B := List( GeneratorsOfGroup( A ), function ( x )
            return x[2];
        end );
    B := Group( B );
    if not IsSubset( u, B ) then
        Info( InfoCompPairs, 1, " projection wrong, go normal" );
    else
        return A;
    fi;
else
    return A;
fi;
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcext.gi:617
 [2] CompatiblePairs( F, M, D )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcaut.gi:1343
<function "AutomorphismGroupSolvableGroup">( <arguments> )
 called from read-eval loop at *stdin*:1
you can enter 'quit;' to quit to outer loop

[hulpke]

So what exactly is the fix, and why does it work?

Magic :-)

No, The "else" case (old line 552) needs to be run if not doing the new "direct" case.

[fingolfin]

It does work with AutomorphismGroup, but there are examples where that fails, too:

gap> AutomorphismGroup(SmallGroup(864,4675));
<group of size 10368 with 11 generators>
gap> AutomorphismGroup(SmallGroup(96, 76));
Error, Variable: 'u' must have an assigned value
Stack trace:
*[1] if u <> fail then
    B := List( GeneratorsOfGroup( A ), function ( x )
            return x[2];
        end );
    B := Group( B );
    if not IsSubset( u, B ) then
        Info( InfoCompPairs, 1, " projection wrong, go normal" );
    else
        return A;
    fi;
else
    return A;
fi;
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcext.gi:617
 [2] CompatiblePairs( F, M, D )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcaut.gi:1343
 [3] AutomorphismGroupSolvableGroup( G )
   @ /Users/mhorn/Projekte/GAP/gap/lib/morpheus.gi:2562
<function "AutomorphismGroup finite groups">( <arguments> )
 called from read-eval loop at *stdin*:1
you can enter 'quit;' to quit to outer loop

[fingolfin]

Run a test computing many AutomorphismGroups, found another error (and pushed a fix):

gap> AutomorphismGroupSolvableGroup(SmallGroup(147, 4));;
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>)
Stack trace:
*[1] Error( "usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>)" );
   @ /Users/mhorn/Projekte/GAP/gap/lib/grp.gi:5114
 [2] Group( GeneratorsOfGroup( K ){B} )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcext.gi:590
 [3] CompatiblePairs( F, M, D )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcaut.gi:1343
 [4] AutomorphismGroupSolvableGroup( grps[i] );
   @ *stdin*:3
<function "unknown">( <arguments> )
 called from read-eval loop at *stdin*:3
you can enter 'quit;' to quit to outer loop, or
you can enter 'return;' to continue

[fingolfin]

Also added regression tests for the three failing groups, and cleaned up the code a bit.