Hello, I just double-checked the Hall-Senior list provided by Eamonn O'Brien against the GAP 3 catalogue. The only discrepancies are with the abelian groups, probably because abelian groups were treated as a separate layer and hence did not follow the Hall-Senior numbering procedure.
Hence, for non-abelian groups (which is most groups!), the code provided by Bettina Eick should suffice. For groups of order 16, there are two discrepancies: gap> F := Filtered([1..14], i -> not(SmallGroupToHallSenior[4][i] = Gap3CatalogueIdGroup(SmallGroup(16,i))[2])); [ 2, 5 ] gap> List(F,i -> StructureDescription(SmallGroup(16,i))); [ "C4 x C4", "C8 x C2" ] For groups of order 32, there are two discrepancies: gap> F := Filtered([1..51], i -> not(SmallGroupToHallSenior[5][i] = Gap3CatalogueIdGroup(SmallGroup(32,i))[2])); [ 3, 16, 21, 36 ] gap> List(F,i -> StructureDescription(SmallGroup(32,i))); [ "C8 x C4", "C16 x C2", "C4 x C4 x C2", "C8 x C2 x C2" ] For groups of order 64, there are two discrepancies: gap> F := Filtered([1..267], i -> not(SmallGroupToHallSenior[6][i] = Gap3CatalogueIdGroup(SmallGroup(64,i))[2])); [ 2, 50, 55, 183, 192, 246 ] gap> List(F,i -> StructureDescription(SmallGroup(64,i))); [ "C8 x C8", "C32 x C2", "C4 x C4 x C4", "C16 x C2 x C2", "C4 x C4 x C2 x C2", "C8 x C2 x C2 x C2" ] Vipul * Quoting Vipul Naik who at 2012-04-17 22:39:54+0000 (Tue) wrote > 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@mail.gap-system.org > > >http://mail.gap-system.org/mailman/listinfo/forum > > > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
