[GAP Forum] Finding a polynomial whose Galois group is M12

[Bill Allombert]

On Thu, Sep 14, 2017 at 10:02:20AM +0000, johnathon simons wrote:
> Dear Bill,
> 
> The Galois realization of M12 is given by finding that Aut(M12) is a
> Galois group (from a rationally rigid triple of conjugacy classes) and
> then from that one can deduce that M12 is a Galois group.
> 
> If the realization is by noting that the automorphism group can be
> generated by a rational rigid triple, does that make things any
> easier? For a discussion of this see (Malle and Matzat - Inverse
> Galois Theory (Springer 1999)) page 162.

Klueners and Malle give explicit polynomials here:
<http://galoisdb.math.upb.de/groups/view?deg=12&num=295>
so they should know how to do it.

Cheers,
Bill.