 Sylow 2-subgroup of PGL2 over F4 (source code)

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= Sylow 2-subgroup of PGL2 over F4
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The translations $x\mapsto x+b$ for $b\in\mathbb F_4$ form a Sylow $2$-subgroup of $PGL_2(\mathbb F_4)$. Every nonidentity translation fixes infinity and exchanges the four finite points in two transpositions, so its action lies in $A_5$.

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