problems with `IntermediateGroup` and `IntermediateSubgroups`

[ThomasBreuer]

A recent message to the GAP Forum asked about an explanation of a fail result of IntermediateGroup.

gap> g:= PSL( 2, 7^3 );;                                            
gap> s:= SylowSubgroup( g, 2 );;
gap> Index( g, s );
2522079
gap> IntermediateGroup( g, s );
fail

(Note that the Sylow 2-subgroups in PSL(2, 7^3) are not maximal.)

If one reads the documentation of IntermediateGroup carefully then this is not a bug.
However, I would vote for making the documentation more explicit, in the sense that fail is returned whenever the function does not find an intermediate group, and that the maximality of the given subgroup is only one possible reason.

In the case of IntermediateSubgroups, the documentation is explicit.
Thus the following is a bug.

gap> IntermediateSubgroups( g, s );
rec( inclusions := [  ], subgroups := [  ] )

I think that the problem in this case is that the IntermediateSubgroups method in question calls TryMaximalSubgroupClassReps (which is undocumented) and checks for a fail result, but the result is an empty list.

[hulpke]

This has been fixed as part of #4219 I thus close.
(The new code now does not return fail' but will try hard, giving a warning that it could be costly. Since IntermediateGroup` is not used in the library, this change should have no effect.

[ThomasBreuer]

Thanks, @hulpke, for the code fixes. I can confirm that the reported problems have disappeared after the changes, in the examples which I had found.
(The problem with IntermediateSubgroups had apparently been present only in the master branch but not in GAP 4.11.0.)