[GAP Forum] hall-senior number vs small group id

[Vipul Naik]

There is a slight discrepancy between the GAP 3 catalogue numbers and
those defined in Hall-Senior's book.

For order 16, there is a mix-up between nummbers 3 and 4:

According to Hall-Senior:

(16,3) corresponds to Z4 X Z4 (GAP ID (16,2)) and (16,4) corresponds
to Z8 X Z2 (GAP ID (16,5))

According to the GAP 3 catalogue:

(16,4) corresponds to Z4 X Z4 (GAP ID (16,2)) and (16,3) corresponds
to Z8 X Z2 (GAP ID (16,5))

Vipul

* Quoting Bettina Eick who at 2012-04-17 08:59:58+0000 (Tue) wrote
> 
> Dear Forum,
> 
> as far as I remember, one can get this information as follows.
> 
> The groups of order 64 as determined by Hall and Senior are part
> of the solvable groups library of GAP 3. The id of a group in this
> GAP 3 catalogue can be obtained in GAP 4 via Gap3CatalogueIdGroup.
> Thus with
> 
> gap> hs := List(AllSmallGroups(64), x -> Gap3CatalogueIdGroup(x)[2]);;
> gap> Position(hs, 187);
> 245
> 
> one finds that the Hall-Senior group 187 is SmallGroup(64,245);
> 
> Best wishes,
> 
> Bettina
> 
> 
> 
> On Mon, 16 Apr 2012, sumeyra uskudar wrote:
> 
> >dear forum,
> >is there a function in gap (or anywhere) which can give the small group id
> >of a group when we give the hall-senior number? or visaversa?
> >
> >Indeed, I need the subgroup structure of the group of order 64 which has
> >Hall Senior number 187. but I can not get the small group ID from anywhere
> >thus it is hard to define it in GAP.
> >
> >-- 
> >*Sümeyra Bedir*
> >_______________________________________________
> >Forum mailing list
> >Forum at mail.gap-system.org
> >http://mail.gap-system.org/mailman/listinfo/forum
> >

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