A question for Gene

I have been reviewing Steiner systems, in particular the system
S(5,6,12). The Mathieu group based on it has an order of 2^6*3^3*5*11.
Where does this number come from? I know there are 660 blocks in the
Steiner system, and r=330, etc. Also 660* 144 =95040. Is there any
significance to this?

Thanks

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@m...> wrote:
> I have been reviewing Steiner systems, in particular the system
> S(5,6,12). The Mathieu group based on it has an order of
2^6*3^3*5*11.
> Where does this number come from? I know there are 660 blocks in
the
> Steiner system, and r=330, etc. Also 660* 144 =95040. Is there any
> significance to this?
>
> Thanks

Sorry, should have been 132 blocks in the Steiner system. So
you get 132*720=95040

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@m...> wrote:

> Sorry, should have been 132 blocks in the Steiner system. So
> you get 132*720=95040

One thing to note about this is that you have 132 blocks, any of which
can be permuted in 6! = 720 ways. Once we have done that, the rest of
the permutation follows; so we end up with 95040 of them.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> <paul.hjelmstad@m...> wrote:
>
> > Sorry, should have been 132 blocks in the Steiner system. So
> > you get 132*720=95040
>
> One thing to note about this is that you have 132 blocks, any of
which
> can be permuted in 6! = 720 ways. Once we have done that, the rest
of
> the permutation follows; so we end up with 95040 of them.

That's right. You told me that before. I'm still trying to figure out
the other Mathieu groups, like M24 which is based on S(5,8,24) which
has 759 blocks * 322560. 322560 is 8*8!