On Sun, November 20, 2016 3:05 pm, Walter Becker wrote:
> If you run the Group Extension program for getting
> cyclic group extension as follows
>
> gap> g:=SmallGroup(11^4,11);
> <pc group of size 14641 with 4 generators>
> gap> CyclicSplitExtensions(g,5);
> rec( both := [ 8192199993 ], down := [ ],
> up := [ rec( code := 298568409859696239999, order := 73205 ), rec( code :=
> 5856355022849648239999, order := 73205 ),
> rec( code := 5891490574296688239999, order := 73205 ), rec( code :=
> 11282584185874032239999, order := 73205 ),
> rec( code := 94119189388603040990846639999, order := 73205 ),
> rec( code := 94538261508559871198846639999, order := 73205 ),
> rec( code := 94106975037650140219006639999, order := 73205 ),
> rec( code := 94464989257903016937086639999, order := 73205 ),
> rec( code := 94128831738093798622846639999, order := 73205 ),
> rec( code := 94535689507097728059006639999, order := 73205 ),
> rec( code := 94162902789490357798526639999, order := 73205 ),
> rec( code := 94479775706899598272126639999, order := 73205 ),
> rec( code := 94282447553251495872126639999, order := 73205 ),
> rec( code := 94138474087584556254846639999, order := 73205 ),
> rec( code := 94760017161234627233406639999, order := 73205 ),
> rec( code := 94945130963929828861566639999, order := 73205 ),
> rec( code := 94842931761382239127166639999, order := 73205 ),
> rec( code := 94925846361529851020926639999, order := 73205 ),
> rec( code := 94794076622846695605886639999, order := 73205 ) ] )
>
> how does one get or construct the explicit groups that
> are found here.
Just do
gap> g:=SmallGroup(11^4,11);
gap> extcodes := CyclicSplitExtensions(g,5);;
gap> extgrps := List(extcodes.up,r->PcGroupCode(r.code,r.order));
[ <pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators>,
<pc group of size 73205 with 5 generators> ]
Hope this helps,
Stefan Kohl
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