[GAP Forum] asking about gap

[Malka Schaps]

Dear Roghiyeh,
      A lot of the information you want is probably on my Database of 
groups up to order 100 at
http:\\www.cs.biu.ac.il\~mschaps\math.html

In particular, the dihedral, semidihedral, and generalized quaternion 
groups are identified, some sort of description by extensions is given, 
and user friendly relations with a normal series (plus character table, block 
decomposition, ect.)

Unfortunately, this database was created a long time ago in GAP3, and so 
uses the old numbering of the solvable groups.  However, there is a 
an easy way to get the old number


>gr := SmallGroup([32,6]);
<pc group of size 32 on 5 generators>
>Gap3CatalogueIdGroup(gr);
[ 32 , 46 ]

I seem to remember that there is a function going the other way, but I 
don't find it in the online GAP4 manual.

 				Sincerely,
 				Mary Schaps




On Sat, 27 Oct 2007, Roghiyeh Adhamy wrote:

> Dear GAP Forum,
>  Thank you for your response, but I would like the structure of the following Groups:
>
>  G1=SmallGroup(32,6)
>   with the minimal generating set
>  { (1,9)(2,10)(3,12)(4,11)(5,13)(6,14)(7,16)(8,15)(17,25)(18,26)(19,28)(20, 27)(21,29)(22,30)(23,32)(24,31),
>   (1,17,3,19)(2,18,4,20)(5,22,7,24)(6,21,8,23)(9,29,11,31)(10,30,12,32)(13,26,15,28)(14,25,16,27)}
>
>  G2=SmallGroup(32,7)
>  with the minimal generating set
>  {(1,9)(2,10)(3,12)(4,11)(5,13)(6,14)(7,16)(8,15)(17,25)(18,26)(19,28)(20,27)(21,29)(22,30)(23,32)(24,31),
>   (1,17,3,19,2,18,4,20)(5,22,7,24,6,21,8,23)(9,29,11,31,10,30,12,32)(13,26,15,28,14,25,16,27) }
>
>  G3=SmallGroup(32,8)
>  with the minimal generating set
>  {(1,9,2,10)(3,12,4,11)(5,13,6,14)(7,16,8,15)(17,25,18,26)(19,28,20,27)(21,29,22,30)(23,32,24,31),
>   (1,17,3,19,2,18,4,20)(5,22,7,24,6,21,8,23)(9,29,11,31,10,30,12,32)(13,26,15,28,14,25,16,27) }
>
>  G4=SmallGroup(32,11)
> with the minimal generating set
> {(1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15)(17,25)(18,26)(19,27)(20,28)(21,30)(22,29)(23,32)(24,31),
>  (1,17,3,19,2,18,4,20)(5,22,7,24,6,21,8,23)(9,29,11,31,10,30,12,32)(13,25,15,27,14,26,16,28) }
>
>  G5=SmallGroup(32,27)
> with the minimal generating set
> {(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32),
>   (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32),
>  (1,17)(2,18)(3,19)(4,20)(5,22)(6,21)(7,24)(8,23)(9,27)(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29) }
>
>  G6=SmallGroup(32,34)
> with the minimal generating set
> {(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16)(17,21,18,22)(19,23,20,24)(25,29,26,30)(27,31,28,32),
>   (1,9,3,11)(2,10,4,12)(5,13,7,15)(6,14,8,16)(17,25,19, 27)(18,26,20,28)(21,29,23,31)(22,30,24,32),
>  (1,17)(2,18)(3,19)(4,20)(5,22)(6,21)(7,24)(8,23)(9,27)(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29) }
>
>  G7=SmallGroup(32,35)
> with the minimal generating set
> {(1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16)(17,21,18,22)(19,23,20,24)(25,29,26,30)(27,31,28,32),
>   (1,9,3,11)(2,10,4,12)(5,13,7,15)(6,14,8,16)(17,25,19,27)(18,26,20,28)(21,29,23,31)(22,30,24,32),
>  (1,17,3,19)(2,18,4,20)(5,22,7,24)(6,21,8,23)(9,27,11,25)(10,28,12,26)(13,32,15,30)(14,31,16,29) }
>
>  G8=SmallGroup(32,43)
> with the minimal generating set
> {(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32),
>   (1,9)(2,10)(3,12)(4,11)(5,13)(6,14)(7,16)(8,15)(17,25)(18,26)(19,28)(20,27)(21,29)(22,30)(23,32)(24,31),
>  (1,17)(2,18)(3,20)(4,19)(5,22)(6,21)(7,23)(8,24)(9,27)(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29) }
>
>  G9=SmallGroup(32,44)
> with the minimal generating set
> {(1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32),
>   (1,9,2,10)(3,12,4,11)(5,13,6,14)(7,16,8,15)(17,25,18,26)(19,28,20,27)(21,29,22,30)(23,32,24,31),
>  (1,17)(2,18)(3,20)(4,19)(5,22)(6,21)(7,23)(8,24)(9,27)(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29)}
>
>  G10=SmallGroup(32,49)
> with the minimal generating set
> { (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32),
>  (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32),
>  (1,9)(2,10)(3,11)(4,12)(5,14)(6,13)(7,16)(8,15)(17,25)(18,26)(19,27)(20, 28)(21,30)(22,29)(23,32)(24,31),
>   (1,17)(2,18)(3,20)(4,19)(5,21)(6,22)(7, 24)(8,23)(9,26)(10,25)(11,27)(12,28)(13,30)(14,29)(15,31)(16,32) }
>
>  G11=SmallGroup(32,50)
> with the minimal generating set
> {(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22, 24)(25,27)(26,28)(29,31)(30,32),
>   (1,5,2,6)(3,7,4,8)(9,13,10,14)(11,15,12,16)(17,21,18,22)(19,23,20,24)(25,29,26,30)(27,31,28,32),
>  (1,9,2,10)(3,11,4,12)(5,14,6,13)(7,16,8,15)(17,25,18,26)(19,27,20,28)(21,30,22,29)(23,32,24,31),
>   (1,17)(2,18)(3,20)(4,19)(5,21)(6,22)(7,24)(8,23)(9,26)(10,25)(11,27)(12,28)(13,30)(14,29)(15,31)(16,32) }
>
>  In fact I would like to know what is the isomorphism of Gi with the well-known groups (for example symmetric groups,dihedral groups,...)
>
>  I am looking forward to hearing from you.
>  With Best Regards,
>  S. R. Adhamy
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam?  Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>