Improvements to automorphisms/isomorphisms of solvable group

[hulpke]

These changes resolve memory use and sluggishness issues being brought up in #6478. This is done by reducing over cautious effort in computing a permutation representation, computation of compatible pairs using MeatAxe functionality,
and by using a new stabilizer routine that works along a composition series, mirrorign what the pc algorithm does. It also will try replacing a large orbit buildup with specific element tests to save on memory.

Also added special handling of 2-generator groups, which might refer back to the old routine if there are few images.

[codecov]

Codecov Report

❌ Patch coverage is 18.77729% with 186 lines in your changes missing coverage. Please review.
✅ Project coverage is 70.92%. Comparing base (153950b) to head (76ad4aa).
⚠️ Report is 4 commits behind head on master.

Files with missing lines	Patch %	Lines
lib/oprtperm.gi	0.57%	172 Missing ⚠️
lib/grppcaut.gi	33.33%	6 Missing ⚠️
lib/morpheus.gi	85.36%	6 Missing ⚠️
lib/grppcext.gi	66.66%	2 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (153950b) and HEAD (76ad4aa). Click for more details.

HEAD has 24 uploads less than BASE

Flag	BASE (153950b)	HEAD (76ad4aa)
	30	6

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6494      +/-   ##
==========================================
- Coverage   79.03%   70.92%   -8.12%     
==========================================
  Files         685      683       -2     
  Lines      293802   292998     -804     
  Branches     8664     8611      -53     
==========================================
- Hits       232219   207815   -24404     
- Misses      59782    83278   +23496     
- Partials     1801     1905     +104     

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[ThomasBreuer]

Concerning the examples from #6478 (and several examples similar to the first one), the changes cause that the computations finish quickly:

gap> G:= PcGroupCode( 135495704269114461030660305981889315450271424036046321125005843079133602927728608631986934108567747, 25392 );;
gap> H:= PcGroupCode( 135495704269114461030660305981889315450271424035062002213763081335657669881129534118574177870592195, 25392 );;
gap> IsomorphismGroups( G, H );
[ f2*f3*f4*f6^6*f7^21, f1*f2*f4*f6^11*f7^10 ] -> [ f2*f3*f4*f6^3*f7, f1*f3 ]
gap> time;
710

and

gap> order:= 20412;;
gap> G:= PcGroupCode( 10686578428610998262971791592184364557772754547145470755, order );;
gap> H:= PcGroupCode( 5343819977472525260046739767108264858899801257522787107, order );;
gap> IsomorphismGroups( G, H );
fail

[fingolfin]

Great, thanks

[fingolfin]

Unfortunately this causes the tests of several packages to fail. A minimal reproducer in pure GAP:

gap> SetAssertionLevel(2);
gap> AutomorphismGroup(SmallGroup(24,3));   # SL(2,3)
Error, Assertion failure
Stack trace:
*[1] ForAll( imgs, function ( x )
      return x in H;
  end )
   @ /Users/mhorn/Projekte/GAP/gap/lib/ghom.gi:299
 [2] GroupGeneralMappingByImagesNC( G, H, gens, imgs )
   @ /Users/mhorn/Projekte/GAP/gap/lib/ghom.gi:429
 [3] GroupHomomorphismByImagesNC( DP, D, gens, genimgs )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcext.gi:443
 [4] EXPermutationActionPairs( D )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcext.gi:646
 [5] CompatiblePairs( F, M, D )
   @ /Users/mhorn/Projekte/GAP/gap/lib/grppcaut.gi:1363
 [6] AutomorphismGroupSolvableGroup( G )
   @ /Users/mhorn/Projekte/GAP/gap/lib/morpheus.gi:2562
<function "AutomorphismGroup finite groups">( <arguments> )
 called from read-eval loop at *stdin*:2
you can enter 'quit;' to quit to outer loop, or
you can enter 'return;' to continue

I'll see if I can spot the issue quickly, otherwise we should revert it for now and @hulpke needs to reland it once he has a fix

[hulpke]

Unfortunately this causes the tests of several packages to fail. A minimal reproducer in pure GAP:
I'll see if I can spot the issue quickly, otherwise we should revert it for now and @hulpke needs to reland it once he has a fix

I just pushed a fix into the same branch, not realizing this was merged. I will do another PR.