Presentation of $A_5 \times \Bbb Z_2$.

Question

I want presentation of the group $A_5\times \Bbb Z_2$ which is a group of order $120.$

I know the presentation of $A_5$ but not of product.

I tried it in GAP . In GAP its Atlas name is $2\times A_5$ but I can't type $\times $ in computer. Please given me its presentation and how I write it in GAP. Thank you very much.

Answer 1

Hint: If $\langle X\mid R\rangle$ is a presentation of $A_5$, then $$\langle X\cup\{z\}\mid \{z^2\}\cup R\cup\{xz=zx\mid x\in X\}\rangle$$ for some symbol $z\notin X$, is a presentation of $A_5\times\Bbb Z_2$, since $\Bbb Z_2$ has $\langle z\mid z^2\rangle$ as a presentation; see this.

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This chapter of the GAP Reference Manual explains how to implement direct products in GAP.