[GAP Forum] asking about gap

[Laurent Bartholdi]

Dear Roghiyeh Adhamy,
There have been quite a few responses to your email, but it seems to
me that you could help us in specifying a bit more what you mean by
"the structure" of a group.
One could understand this as: asking for a presentation; or a
decomposition as a direct product; or by extensions; etc.

Here's an example:
gap> G1:=SmallGroup(32,6);
<pc group of size 32 with 5 generators>
gap> StructureDescription(G1);
"((C4 x C2) : C2) : C2"

which describes G1 by extensions.
You may check that the generating set you give does generate G1:
gap> IsomorphismGroups(G1,Group((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)));
[ f1, f2, f3, f4, f5 ] -> [
(1,32,7,26)(2,31,8,25)(3,29,5,27)(4,30,6,28)(9,20,15,22)(10,19,16,21)(11,17,13,
    23)(12,18,14,24),
(1,10)(2,9)(3,11)(4,12)(5,14)(6,13)(7,15)(8,16)(17,26)(18,25)(19,27)(20,28)(21,30)(22,
    29)(23,31)(24,32),
(1,6)(2,5)(3,8)(4,7)(9,14)(10,13)(11,16)(12,15)(17,22)(18,21)(19,24)(20,23)(25,
    30)(26,29)(27,32)(28,31),
(1,7)(2,8)(3,5)(4,6)(9,15)(10,16)(11,13)(12,14)(17,23)(18,24)(19,21)(20,
    22)(25,31)(26,32)(27,29)(28,30),
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,
    22)(23,24)(25,26)(27,28)(29,30)(31,32) ]

It's also easy to ask GAP to give you relators for the given presentation.
-- 
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD         \    Téléphone: +41 21-6935458
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