Recognition of a subgroup of GL(11,13) isomorphic to `L2_23` gets stuck in endless loop

[fingolfin]

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

G2:=Group(Z(13)^0 * [
[
  [  3,-3, 8, 2, 4,-3, 4,-2, 4,-2, 1 ],
  [  1, 4, 4,-2, 2, 8, 8,-3, 8, 7, 5 ],
  [  1,-3,-1, 9, 8, 2, 6, 4,-2, 1, 4 ],
  [  5, 7, 5,-3,-3, 1,-1, 0,-1, 6, 9 ],
  [  3, 4, 9,-2,-3,-2, 3,-1, 7, 0, 8 ],
  [  1,-1, 2, 1,-3, 5, 2, 2, 6,-3, 0 ],
  [  4,-1,-1,-2, 2, 0, 1,-1, 9, 0, 6 ],
  [  4, 8, 4, 6, 9, 2, 6, 1, 9, 9, 3 ],
  [  8, 6, 8, 2, 3,-1, 1, 0, 0, 7, 4 ],
  [ -3, 9, 6, 8,-1, 3, 5, 3,-1, 6, 6 ],
  [  0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1 ]
],
[
  [  9, 4, 5, 9, 4, 8,-2, 7, 3, 5, 0 ],
  [  4,-1, 4, 5,-2, 7, 2, 6, 6, 0, 1 ],
  [ -1, 1,-2,-1, 3, 8,-2,-2, 7, 3, 0 ],
  [ -3, 7,-2, 4, 4, 3, 6,-2,-1, 3,-1 ],
  [  5, 9, 9, 0,-1,-2,-1, 6, 3, 1, 8 ],
  [ -1, 8, 3,-3, 5,-1, 5, 8, 4, 1, 3 ],
  [  1, 7, 6,-1, 9, 3,-3, 6, 9, 8,-2 ],
  [  6, 6, 5,-2, 1, 5, 8,-1, 0, 4,-2 ],
  [  7, 9, 9, 5, 8, 4, 8, 1, 4, 8, 0 ],
  [  0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
  [  2,-3, 7,-3,-3, 1, 4, 5,-2, 4, 4 ] ]
]);

Then:

gap> SetInfoLevel(InfoRecog, 4);
gap> SetInfoLevel(InfoMethSel, 4);
gap> RecognizeGroup(G2);
#I  Recognising: Group([...])
#I  Calling rank 3100 method "TrivialGroup"...
#I  Finished rank 3100 method "TrivialGroup": NeverApplicable.
#I  Skipping inapplicable rank 3100 method "TrivialGroup".
#I  Calling rank 1175 method "KnownStabilizerChain"...
#I  Finished rank 1175 method "KnownStabilizerChain": NeverApplicable.
#I  Skipping inapplicable rank 3100 method "TrivialGroup".
#I  Skipping inapplicable rank 1175 method "KnownStabilizerChain".
#I  Calling rank 1100 method "DiagonalMatrices"...
#I  Finished rank 1100 method "DiagonalMatrices": NeverApplicable.
#I  Skipping inapplicable rank 3100 method "TrivialGroup".
#I  Skipping inapplicable rank 1175 method "KnownStabilizerChain".
#I  Skipping inapplicable rank 1100 method "DiagonalMatrices".
#I  Calling rank 1000 method "ReducibleIso"...
#I  Finished rank 1000 method "ReducibleIso": NeverApplicable.
#I  Skipping inapplicable rank 3100 method "TrivialGroup".
#I  Skipping inapplicable rank 1175 method "KnownStabilizerChain".
#I  Skipping inapplicable rank 1100 method "DiagonalMatrices".
#I  Skipping inapplicable rank 1000 method "ReducibleIso".
#I  Calling rank 900 method "GoProjective"...
#I  Going projective...
#I  Finished rank 900 method "GoProjective": success.
#I  Going to the image (depth=0, try=1, dim=11, field=13).
#I  Recognising: Group([...])
#I  Calling rank 3000 method "TrivialGroup"...
#I  Finished rank 3000 method "TrivialGroup": NeverApplicable.
#I  Skipping inapplicable rank 3000 method "TrivialGroup".
#I  Calling rank 1300 method "ProjDeterminant"...
#I  Finished rank 1300 method "ProjDeterminant": NeverApplicable.
#I  Skipping inapplicable rank 3000 method "TrivialGroup".
#I  Skipping inapplicable rank 1300 method "ProjDeterminant".
#I  Calling rank 1200 method "ReducibleIso"...
#I  Finished rank 1200 method "ReducibleIso": NeverApplicable.
#I  Skipping inapplicable rank 3000 method "TrivialGroup".
#I  Skipping inapplicable rank 1300 method "ProjDeterminant".
#I  Skipping inapplicable rank 1200 method "ReducibleIso".
#I  Calling rank 1100 method "NotAbsolutelyIrred"...
#I  Finished rank 1100 method "NotAbsolutelyIrred": NeverApplicable.
#I  Skipping inapplicable rank 3000 method "TrivialGroup".
#I  Skipping inapplicable rank 1300 method "ProjDeterminant".
#I  Skipping inapplicable rank 1200 method "ReducibleIso".
#I  Skipping inapplicable rank 1100 method "NotAbsolutelyIrred".
#I  Calling rank 1050 method "ClassicalNatural"...
#I  ClassicalNatural: this is PSL_n!
#I  Finding an SL2...
#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11
...........B#I  Dimension: 11

Note that it believes that the group is PSL_n -- but it clearly is not!

Indeed the group is small enough that GAP can directly computes is size via BSGS, and identify it

gap> Size(G2);
6072
gap> IsSimpleGroup(G2);
true
gap> IsomorphismTypeInfoFiniteSimpleGroup(G2);
rec( name := "A(1,23) = L(2,23) ~ B(1,23) = O(3,23) ~ C(1,23) = S(2,23) ~ 2A(1,23) = U(2,23)",
  parameter := [ 2, 23 ], series := "L", shortname := "L2(23)" )

It seems RecogniseClassical is not working right for this group

gap> DisplayRecog(RecogniseClassical(G2));
Reducible : false
Forms: linear i.e. no forms
E : [ 10, 11 ]
LE : [ 11 ]
BE : [ 10 ]
Mathieu ruled out: true
An ruled out: true
PSL ruled out: true
--------> contains SL(11,13)

Which is clearly wrong by the above.

@aniemeyer maybe you can have a look?

[fingolfin]

I should add that this module is absolutely irreducible:

gap> M:=NaturalGModule(G2);;
gap> MTX.IsAbsolutelyIrreducible(M);
true