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I would like to use GAP to generate all the Steiner systems in M12 (There are 5040 of them), based on S12/ord(M12) = 7!. I have already asked on the GAP Forum, but it appears to be in hiatus, or possibly shut down after 2016.

Ideally, I would like to have a canonical ordering for the all the hexads, and merely number them 1 - 924. This will save on paper, of course, and then merely log the 5040 Steiner systems in 5040 rows of a spreadsheet, 132 across and 5040 down.

Then I can take it from there. Another option is to merely generate one Steiner system, and then do 12! permutations, but that seems excessive. Also, you would have to work with every element in each hexads. I might just play with an algorithm that would "know" the permutations for all 924 hexads, and then merely use GAP to generate the first Steiner, or even Excel itself I suppose. Then easily work with 12! permutations, but that is a lot of rows, I might run out of space.

(Say, (05) permutation so hexad(123)->hexad(345) for example)

PGH

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    I suppose that the question should be posed to the [GAP-community](https://www.gap-system.org), and not at MSE. Also I think, generating all Steiner systems has been already done - see for example [this article](http://www.sciencedirect.com/science/article/pii/0012365X9390222F). – 2017-01-12
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    GAP Forum should work, and there are NO plans to stop it. But it could have some temporarily problems because of recent maintenance work. Could you please write what happened to support@gap-system.org? – 2017-01-12
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    I have just posted email to the Forum and it went through. To post, you have to subscribe first. To do this, visit http://mail.gap-system.org/mailman/listinfo/forum – 2017-01-12
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    Sure...I have been on the Gap forum for many years – 2017-01-12
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    Was able to get GAP to generated the needed sets ----- Thanks – 2017-01-14

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