On 2014-08-15, s meagher <[email protected]> wrote:
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>
> Apologies if this is answered elsewhere in this group or in the 
> documentation, but I have not found the answer.
>
> When computing a galois group in sage using type='pari' Sage gives the 
> group a name.  I have not been able to find a guide for the nomenclature 
> used.
>
> For example, names like S_3 and D(4) are fairly clear.  But what is 2^3 S_3 
> and 2^4 S_4 - I presume they are the wreath products (\Z/2)^n . S_n.  
>
> Is there a reference?  And am I right about 2^n S_n

Not sure if D(n) is so clear. Different communities denote the dihedral group 
of order 2n
by D(n), resp. by D(2n).

I guess the notation follows the notation from "Atlas of Finite Simple Groups" 
by Conway et al.
Roughly the same is used by GAP. IIRC, PARI uses group IDs from a GAP database 
to give each group a
unique ID.

HTH,
Dima

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