HallSubgroup breaks current master for some groups

[hungaborhorvath]

 ┌───────┐   GAP v4.8.1-207-g606200a-dirty of 2016-01-29 09:49:09 (CET)
 │  GAP  │   http://www.gap-system.org
 └───────┘   Architecture: x86_64-pc-linux-gnu-gcc-default64
 Libs used:  gmp, readline
 Loading the library and packages ...
 Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
 Packages:   AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.6, 
             CRISP 1.4.1, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, 
             FactInt 1.5.3, FGA 1.3.0, GAPDoc 1.5.1, IO 4.4.4, 
             IRREDSOL 1.2.4, LAGUNA 3.7.0, Polenta 1.3.2, Polycyclic 2.11, 
             RadiRoot 2.7, ResClasses 3.4.0, Sophus 1.23, SpinSym 1.5, 
             TomLib 1.2.5
 Try '?help' for help. See also  '?copyright' and  '?authors'
gap> G := GL(3,4);
GL(3,4)
gap> HallSubgroup(G, [2,3]); 
Error, usage: PreImage(<map>), PreImage(<map>,<img>), PreImage(<map>,<coll>) called from
PreImage( mon, h ) at /home/ghorvath/work/gap/lib/grpnice.gi:447 called from
<compiled or corrupted statement>  called from
<function "local function">( <arguments> )
 called from read-eval loop at line 2 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> 

[markuspf]

Did this work before?

[hungaborhorvath]

I am not entirely sure if it ever worked, but @hulpke in another issue asked me to let him know about any such examples.

Anyway, I checked 4.7.9 and 4.7.5. They gave the same error message.

[markuspf]

So, what this code tries to do is trying to compute Hall subgroups of GL(3,4) via a permutation representation. Using the following:

gap> G := GL(3,4);; H := Range(IsomorphismPermGroup(G));;
gap> HallSubgroup(H);
fail

suggests that such a Hall subgroup does not exist (should it? My group theory is rusty there), and hence this would "just" a bug in the dispatch code to a nice homomorphic image, which is easily fixed.

[hungaborhorvath]

No, I doubt that such Hall subgroup exists, but I am not entirely sure, either.

[hungaborhorvath]

Taken care of in #559.