[GAP Forum] Easy problem - but I can't do it!

[Gordon Royle]

Hello all..

I have an easy problem, but for some reason I keep getting an error...

I am working with a cyclic subgroup of Sym(16):

gap> s16 := SymmetricGroup(16);
Sym( [ 1 .. 16 ] )
gap> g := Subgroup(s16,[(1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)]);
Group([ (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16) ])

I want to find orbits on edges of the complete graph K_{16}, and so I 
create the corresponding list

gap> edges := Orbit(s16,[1,2],OnSets);
[ [ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 1, 3 ], [ 4, 5 ], [ 2, 4 ], [ 5, 6 ],

<snip>

   [ 6, 15 ], [ 4, 14 ], [ 5, 16 ], [ 7, 16 ], [ 5, 15 ], [ 6, 16 ] ]


and then the appropriate orbits, which come out fine as sets of sets...

gap> gorb := Orbits(g,edges,OnSets);
[ [ [ 1, 2 ], [ 3, 4 ], [ 2, 3 ], [ 1, 4 ] ], [ [ 1, 3 ], [ 2, 4 ] ],
   [ [ 1, 5 ], [ 3, 7 ], [ 2, 6 ], [ 4, 8 ] ],

<snip>

   [ [ 13, 14 ], [ 15, 16 ], [ 14, 15 ], [ 13, 16 ] ],
   [ [ 13, 15 ], [ 14, 16 ] ] ]


NOW, I want to find the action of the normalizer of g on these 
objects...

gap> n := Normalizer(s16,g);
<permutation group with 7 generators>


but when I do what seems to me to be the obvious thing I get an error:

gap> Action(n,gorb,OnSetsSets);
Error, no method found! For debugging hints type ?Recovery from 
NoMethodFound
Error, no 1st choice method found for `GroupByGenerators' on 2 
arguments calle\
d from
GroupByGenerators( imgs, ImageElmActionHomomorphism( hom,
    One( Source( hom ) ) ) ) called from
ImagesSource( hom ) called from
<function>( <arguments> ) called from read-eval-loop


But I *can* do something like

gap> OnSetsSets(gorb[10],n.1);
[ [ 1, 12 ], [ 2, 9 ], [ 3, 10 ], [ 4, 11 ] ]

or

gap> Orbit(n,gorb[1],OnSetsSets);
[ [ [ 1, 2 ], [ 3, 4 ], [ 2, 3 ], [ 1, 4 ] ],
   [ [ 1, 2 ], [ 1, 4 ], [ 2, 3 ], [ 3, 4 ] ],

<snip>

   [ [ 9, 10 ], [ 9, 12 ], [ 10, 11 ], [ 11, 12 ] ],
   [ [ 9, 10 ], [ 9, 12 ], [ 10, 11 ], [ 11, 12 ] ] ]


so why can I not calculate the action?


Sorry if this is a dumb question, but it is annoying me and obviously 
is something I need to know....


Thanks

Gordon