And here is the computation showing that H_3(M12:2, Z) = Z_2 x z_2 x Z_12.
gap> LoadPackage("atlasrep");;
gap> G:=AtlasGroup("M12:2");;
gap> GroupHomology(G,3);
[ 2, 2, 4, 3 ]
Graham
School of Mathematics, Statistics & Applied Mathematics
National University of Ireland, Galway
University Road,
Galway
Ireland
http://hamilton.nuigalway.ie
tel: 091 493011
________________________________________
From: forum-boun...@gap-system.org [forum-boun...@gap-system.org] on behalf of
Dmitrii Pasechnik [dmitrii.pasech...@cs.ox.ac.uk]
Sent: Monday, January 4, 2016 3:18 PM
To: Aniket Joshi
Cc: fo...@gap-system.org
Subject: Re: [GAP Forum] Using M12 semidirect product Z_2 in GAP
On Mon, Jan 04, 2016 at 01:07:01PM +0530, Aniket Joshi wrote:
> I wish to find the homology H_3(M_{12} : Z_2, Z), where M_{12} is a Mathieu
> group of order 95040, and M_12:Z_2 indicates the semi-direct product with
> Z_2. I plan to use the GroupHomology(,) command from the HAP package for
> GAP.
>
> How do I use the semi direct product M_12:Z_2 in GAP? Is there an inbuilt
> function, or would I need to compute it separately?
just take
assuming you have AltasRep package installed, you can just do
AtlasGroup("M12:2")
to get a permutation representation of M:12:2 on 24 points.
HTH,
Dmitrii
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