# Semidirect product command in GAP [duplicate]

I need to type the group

in GAP. Is it correct if I type as, "SemidirectProduct(ZmodnZ(3),AbelianGroup([7,7]));"? Will it recognize that AbelianGroup([7,7]) is the normal subgroup?

## marked as duplicate by Matthew Towers, Ivan Neretin, Jeremy Rickard, hardmath, ArsenBerkOct 4 '18 at 19:03

• Here I have considered the internal Semidirect product – Buddhini Angelika Sep 27 '18 at 10:16
• The suggested duplicate can give you a good start on the GAP syntax for this. Note that an internal semidirect product involves a subgroup $H$ "acting" on a normal subgroup $N$ with trivial intersection. It doesn't appear to me that the syntax you've shown allows for this action to be determined, even in principle. – hardmath Oct 4 '18 at 15:20

You will need to also specify the action of $$Z_3$$ on $$Z_7^2$$. Generically, you would do this by specifying as second argument (i.e. arguments are subgroup, map, normal subgroup) a homomorphism from $$Z_3$$ into the automorphism group os $$Z_7^2$$.
gap> m:=[[4,0],[0,2]]*One(GF(7));