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

[Bettina Eick]

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*
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