I know that $GL(2,3)$ is one of this, but i need the characterization of all possibles of the semidirect products between $\mathbb Z_2$ and $SL(2,3)$.
Thanks, for any help.
2026-03-29 13:41:01.1774791661
How many non isomorphic semidirect products are there between $\mathbb Z_2$ and $SL(2,3)$?
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Hint: now you know there are only two possibly non-isomporphic semidirect products, namely $$\textrm{GL}(2,3)$$ and $$\mathbb{Z}_2\times \textrm{SL}(2,3).$$ Show that they are not isomorphic because their corresponding centers have different cardinality.