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

[johnathon simons]

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.

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