Dear Dima, thanks a lot! Indeed, one should have expected it like that ... 
Anyway, maybe I'm not the only one who got stuck there, and the answer is 
useful for others too.

-- Peter Mueller 

Dima Pasechnik schrieb am Donnerstag, 30. März 2023 um 19:38:47 UTC+2:

>
>
> On Thu, 30 Mar 2023, 18:25 'Peter Mueller' via sage-support, <
> sage-s...@googlegroups.com> wrote:
>
>> When working with finite permutation groups, it seems to me that one has 
>> the choice to either use the groups as sage objects like 
>> `SymmetricGroup(4)`, or as a Gap object via `libgap.SymmetricGroup(4)`. The 
>> former has rather limited functionality (and quite a few bugs as reported 
>> earlier), so the advise was to use the latter concept.
>>
>> So after setting `g = libgap.SymmetricGroup(4)`, things like 
>> `g.Stabilizer(1)` work as expected. However, I have difficulties to figure 
>> out how for instance the equivalent of the Gap code `Stabilizer(g, [1,2], 
>> OnSets)` would look like. Something like `g. Stabilizer([1, 2], 'OnSets')` 
>> raises a GapError.
>>
>
> it is
>
> g. Stabilizer([1, 2], libgap.OnSets)
>
> (which makes sense, as in GAP you also don't pass a string to Stabilizer, 
> but you pass a GAP action)
>
>
>
>> Are these things documented somewhere? I couldn't find anything.
>>
>
> all we have is 
> https://doc.sagemath.org/html/en/reference/libs/sage/libs/gap/libgap.html
> (and source code, eg in src/sage/graphs/)
>
>  - pull requests welcome 😁
>
>  
> Dima
>
>
>
>> -- Peter Mueller
>>
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>>
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