[GAP Forum] Question

[Sandeep Murthy]

Hi,

I think you mean the semidirect product G = (C_2)^3 \rtimes C_7.
If so, then the following code:

N := DirectProduct( CyclicGroup( 2 ), CyclicGroup( 2 ), CyclicGroup( 2 ) );
A := AutomorphismGroup( N );
a := Filtered( Elements( A ), x -> Order( x ) = 7 )[1];
C7 := CyclicGroup( 7 ); 
c := C7.1;
hom := GroupHomomorphismByImages( C7, A, [c], [a] );
G := SemidirectProduct( C7, hom, N );

should construct the group.  To check this is the right group

StructureDescription( G ); IdSmallGroup( G );

should display 

"(C2 x C2 x C2) : C7"
[ 56, 11 ]

Sincerely, Sandeep.



On 8 May 2012, at 03:45, Ashkan Ramiz wrote:

> Dear forum,   I would like to know how we can build the group G=2^3:7 in gap.
> Best wishes,
> Ashkan
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