Recognition of a subgroup of GL(8,5) isomorphic to `4_1.L3_4` gets stuck endlessly calling `SLCR.FindGoodElement`

[fingolfin]

Discovered by @chseeger while working on extending https://github.com/gap-packages/ClassicalMaximals : consider this group:

G1:= Group(Z(5)^0 * [
[ [3,3,0,3,3,2,4,0],
  [4,4,0,1,1,0,0,4],
  [1,2,4,4,0,1,0,0],
  [1,2,0,4,4,0,2,0],
  [2,2,2,3,3,3,3,4],
  [1,3,0,3,4,4,3,2],
  [1,4,1,4,1,3,3,3],
  [1,1,2,3,3,1,1,0] ],
[ [0,3,2,0,0,3,3,4],
  [2,0,0,0,0,2,0,0],
  [3,1,1,2,1,2,4,4],
  [0,3,1,1,4,3,1,0],
  [0,1,4,4,1,3,4,3],
  [2,0,1,0,0,4,0,0],
  [1,2,4,4,4,4,4,0],
  [2,2,1,4,3,0,4,4] ],
[ [2,0,0,0,0,0,0,0],
  [0,2,0,0,0,0,0,0],
  [0,0,2,0,0,0,0,0],
  [0,0,0,2,0,0,0,0],
  [0,0,0,0,2,0,0,0],
  [0,0,0,0,0,2,0,0],
  [0,0,0,0,0,0,2,0],
  [0,0,0,0,0,0,0,2] ],
]);

Then we get this:

gap> SetInfoLevel(InfoMethSel, 2);
gap> SetInfoLevel(InfoRecog, 2);
gap> RecognizeGroup(G1);
#I  Going projective...
#I  Finished rank 900 method "GoProjective": success.
#I  Going to the image (depth=0, try=1, dim=8, field=5).
#I  ClassicalNatural: Is not PSL.
#I  Finished rank 1050 method "ClassicalNatural": TemporaryFailure.
#I  G is not C5 (subfield).
#I  G is not C3 (semilinear).
#I  Finished rank 850 method "C6": TemporaryFailure.
#I  D247: Trying the involution jumper 9 times...
.........
#I  D247: Did not find normal subgroup, giving up.
#I  Finished rank 840 method "D247": TemporaryFailure.
#I  Finished rank 810 method "AltSymBBByDegree": TemporaryFailure.
#I  Finished rank 800 method "TensorDecomposable": TemporaryFailure.
#I  FindElmOfEvenNormal: Could be irreducible proper normal subgroup!
#I  FindElmOfEvenNormal: Second normal subgroup was not reducible.
#I  Finished rank 700 method "FindElmOfEvenNormal": TemporaryFailure.
#I  LowIndex: Trying 10 first elements...
...#I  Did not find nice orbit.
..#I  Did not find nice orbit.
...#I  Did not find nice orbit.
..
#I  Finished rank 600 method "LowIndex": TemporaryFailure.
#I  ThreeLargeElOrders: found [ [ 7, 5, [ "l", 3, 4 ] ] ]
#I  Trying [ 7, 5, [ "l", 3, 4 ] ]
#I  Trying constructive recognition...
SLCR.FindGoodElement with i=8  limit=56
#I  Trying constructive recognition...
SLCR.FindGoodElement with i=2  limit=56
#I  Trying constructive recognition...
SLCR.FindGoodElement with i=7  limit=56
#I  Trying constructive recognition...
SLCR.FindGoodElement with i=5  limit=56
#I  Trying constructive recognition...
SLCR.FindGoodElement with i=28  limit=56
#I  Trying constructive recognition...
SLCR.FindGoodElement with i=2  limit=56
...

and this repeats over and over (with different i values).

Backtrace:

InverseImmutable( M ) at GAPROOT/lib/matobj.gi:1476 called from
t ^ r at GAPROOT/pkg/recog/gap/matrix/slconstr.gi:1460 called from
SLCR.SL3ConstructQ( bbg, t, p, e ) at GAPROOT/pkg/recog/gap/matrix/slconstr.gi:1913 called from
SLCR.SL3DataStructure( bbg, p, e ) at GAPROOT/pkg/recog/gap/matrix/slconstr.gi:2085 called from
SLCR.SLDataStructure( GM, p, e, d ) at GAPROOT/pkg/recog/gap/matrix/slconstr.gi:2441 called from
SLCR.FindHom( ri, G, name[2], name[3] ) at GAPROOT/pkg/recog/gap/projective/almostsimple.gi:777 called from
CallFuncList( UnpackRecogMethod( m ), args ) at GAPROOT/pkg/recog/gap/base/methods.gi:89 called from
CallRecogMethod( db[i].method, methargs ) at GAPROOT/pkg/recog/gap/base/methsel.gi:89 called from
CallMethods( allmethods, 10, ri, H ) at GAPROOT/pkg/recog/gap/base/recognition.gi:489 called from
RecogniseGeneric( Group( List( GeneratorsOfGroup( H ), function ( x )
          return ImageElm( Homom( ri ), x );
      end ) ), methodsforimage( ri ), depthString, InitialDataForImageRecogNode( ri ) ) at GAPROOT/pkg/recog/gap/base/recognition.gi:563 called from
RecogniseGeneric( G, FindHomDbMatrix, "", rec(
     ) ) at GAPROOT/pkg/recog/gap/base/recognition.gi:112 called from
<function "RecogniseGroup">( <arguments> )
 called from read-eval loop at *errin*:1

So this seems to be stuck in the old / existing "natural SL_3 recognition".

Hopefully the new SL_n work will resolve this.