Alexander, Thanks. This works, except that I get a different value for the first octad (orbit of 2-Sylow group), it lists a 16-chord first, and then, Set(octad)[1] ends up being a 16-chord, and so do all the others. Do you know why it is listing a 16-chord first, and why my octad is different? I get
[ 3, 14, 22, 15, 11, 23, 17, 19 ] Paul Hjelmstad ITS Security Administration 763-582-6547 (x46547) [EMAIL PROTECTED] ----- Forwarded by Paul Hjelmstad/allianzlife on 03/27/2007 11:40 AM ----- "PAUL HJELMSTAD" <[EMAIL PROTECTED]> 03/01/2007 03:08 PM To [EMAIL PROTECTED] cc Subject FW: Re: [GAP Forum] Listing Octads >From: Alexander Hulpke <[EMAIL PROTECTED]> >To: "PAUL HJELMSTAD" <[EMAIL PROTECTED]> >CC: [EMAIL PROTECTED] >Subject: Re: [GAP Forum] Listing Octads >Date: Thu, 1 Mar 2007 11:00:39 -0700 > >Dear GAP forum, > >Paul Hjelmstad wrote: > >>Does anyone know how I would list: >Yes. > >>2) Representatives of Conjugacy Classes (26) in M24 >gap> g:=MathieuGroup(24); >gap> List(ConjugacyClasses(g),Representative); >(Careful: Order is not necessarily ATLAS order but its easy to get a >correspondence) > >>1) Octads in M24 (Are they Unique?) >The 759 octads are one orbit under M24 and are determined uniquely by 5 >points of this 5-transitive group, thus there are unique. > >As the index of an octad stabilizer is 759 and thus odd, we can get one >octad from orbits of a 2-Sylow subgroup: > >gap> s:=SylowSubgroup(g,2); ><permutation group of size 1024 with 10 generators> >gap> Orbits(s,[1..24]); >[ [ 1, 5, 24, 8, 10, 11, 14, 20 ], > [ 2, 13, 22, 19, 7, 3, 9, 23, 18, 4, 15, 12, 6, 16, 17, 21 ] ] >gap> o:=Set(last[1]); > >The set of octads then is obtained as orbit: > >gap> octads:=Orbit(g,o,OnSets);; >gap> Length(octads); >759 > >from which we see that in this labelling of M24 the lexicographically >smallest octad is > >gap> Set(octads)[1]; >[ 1, 2, 3, 4, 5, 8, 11, 13 ] > > >Best, > > Alexander Hulpke > > >-- Colorado State University, Department of Mathematics, >Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA >email: [EMAIL PROTECTED], Phone: ++1-970-4914288 >http://www.math.colostate.edu/~hulpke > > ----------------------------------------- CONFIDENTIALITY NOTICE: The information in this message, and any files transmitted with it, is confidential, may be legally privileged, and intended only for the use of the individual(s) named above. Be aware that the use of any confidential or personal information may be restricted by state and federal privacy laws. If you are not the intended recipient, do not further disseminate this message. If this message was received in error, please notify the sender and delete it. _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
