[GAP Forum] Semidirect Product (second variant)

[William Giuliano]

Dear Forum,
                     I would like to construct a semidirect product of C4 x
C4 with S3 in the following way. I feel it's something easy, but I cannot
understand the error message I get.

gap> free_j:=FreeGroup("a","b");;

gap> AssignGeneratorVariables(free_j);;

#I  Assigned the global variables [ a, b ]

gap> rel_j:=[a^4,b^4,Comm(a,b)];;

gap> J:=free_j/rel_j;;

gap> StructureDescription(J);

"C4 x C4"


gap> A:=AutomorphismGroup(J);;

gap> a:=Elements(A);;

gap> x:=a[16];

[ a, b ] -> [ b, (a*b)^3 ]

gap> s:=a[9];

[ a, b ] -> [ b, a ]

gap> H:=Group([x,s]);;

gap> StructureDescription(H);

"S3"


gap> IsGroupOfAutomorphisms(H);

true

gap> AutomorphismDomain(H)=J;

true

gap> SemidirectProduct(H,J);

Error, no method found! For debugging hints type ?Recovery from
NoMethodFound

Error, no 1st choice method found for `IsomorphismFpGroup' on 2 arguments
at /Users/williamgiuliano/Downloads/gap-4.9.3/lib/methsel2.g:250 called from

IsomorphismFpGroup( G, "F" ) at
/Users/williamgiuliano/Downloads/gap-4.9.3/lib/gpfpiso.gi:21 called from

IsomorphismFpGroup( G ) at /Users/williamgiuliano/Downloads/gap-4.9.3/lib/
gprd.gi:1127 called from

SemidirectProduct( G, IdentityMapping( G ), N ) at
/Users/williamgiuliano/Downloads/gap-4.9.3/lib/gprd.gi:1077 called from

<function "unknown">( <arguments> )

 called from read-eval loop at *stdin*:16

you can 'quit;' to quit to outer loop, or

you can 'return;' to continue

brk>


Thank you ver much

William