Re: Mathieu Group M12

In article <16418929.1153146144900.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
PaulHjelmstad <phjelmstad@xxxxxxx> writes:
I need to ask some basic questions about M12.

I have read that M12 has index 2.

Index 2 in what? M12 has index 2 in its automorphism group, which is
usually denoted my M12.2.
|M12| = 95040, |M12.2| = 190080.

Why? Also, M12 as a subgroup of M24 has index 1288 NOT 2576 as I would expect. Obviously, this involves a factor of two.

You have this wrong. M24 has a maximal subgroup isomorphic to M12.2, with
index 1288. The index of M12 in M24 is 2576.

Derek Holt.



I thought I understood Mathieu groups, but I am stuck
on something. 5-transivity maps any pentad into another
pentad (say in S(5,6,12)). I have read that M12 is the
automorphism group of this system because it maps a block
into another block (in this case, hexads). How does this
work?

Thanks!


.

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