[GAP Forum] Steiner systems of Mathieu Group M12

[PAUL HJELMSTAD]

Nevermind I got it and then some it's running the sets right now

Get Outlook for Android<https://aka.ms/ghei36>


________________________________
From: PAUL HJELMSTAD <phjelmstad at msn.com>
Sent: Friday, January 13, 2017 4:16:57 PM
To: Dmitrii Pasechnik
Cc: forum at mail.gap-system.org
Subject: Re: [GAP Forum] Steiner systems of Mathieu Group M12


Thanks

Paul Hjelmstad

Get Outlook for Android<https://aka.ms/ghei36>


________________________________
From: dmitrii.pasechnik at cs.ox.ac.uk <dmitrii.pasechnik at cs.ox.ac.uk>
Sent: Friday, January 13, 2017 3:35:14 PM
To: PAUL HJELMSTAD
Cc: forum at mail.gap-system.org
Subject: Re: [GAP Forum] Steiner systems of Mathieu Group M12

Dear Forum,
On Tue, Jan 10, 2017 at 09:00:49PM +0000, PAUL HJELMSTAD wrote:
> Simply, is there a way to ask GAP to list all 5040 Steiner systems of the Mathieu Group M12?
yes, it is easy.
Get the hexads of one S(5,6,12), consider them as a "set of sets"
and compute the orbit of S_12 on them using OnSetsSets action.
In more detail:

gap> m12:=MathieuGroup(12);
gap> he:=Set(Orbit(m12,[1,2,3,4,5,7],OnSets));
gap> OrbitLength(SymmetricGroup(12),he,OnSetsSets);
5040


HTH,
Dmitrii
>
> That is S12/[M12] Systems of hexads
>
>
> Get Outlook for Android<https://aka.ms/ghei36>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum