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Can anybody guide me towards, how I can compute semidirect product of $\mathrm{PSL}(3,4)$ and $\mathbb Z_2$ by magma? Indeed, I dont know how construct map $\phi: H \to \mathrm{Aut}(N)$, when $H=\mathbb Z_2$ and $N=\mathrm{PSL}(3,4)$, for operation SemidirectProduct$(N, H, \phi)$.

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Here's one way to do it. 

K:=PSL(3,4);
H:=CyclicGroup(2);
A:=AutomorphismGroup(K);
/* A.1 is an automorphism of order 2 */
phi:= hom< H -> A |  >;
G:=SemidirectProduct(K,H,phi);

Notice that the codomain of phi is A, which has type GrpAuto. I'm not sure if this is a requirement of the map or not.

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    I can't see your error, but try it on their online calculator: http://magma.maths.usyd.edu.au/calc/ Add another line that prints G. – 2017-01-19
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    Thanks for the answer. When I use it, the followin error occurs: Identifier 'SemidirectProduct has not been declared or assigned. – 2017-01-19
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    That means you are using a version of Magma that does not have the function SemidirectProduct. In your question, you made it sound like you were had an issue getting the function SemidirectProduct working correctly. What exactly is your original question about then? – 2017-01-19