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Questions on group theory which concern finite groups.

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Group action w.r.t. non-split extension group of the form $2^8\mathbin.(2^7\mathbin:\operato...

I have a non-split extension $2^8\mathbin.(2^7\mathbin:\operatorname{Sp}(6,2))$ of $2^8$ by $2^7\mathbin:\operatorname{Sp}(6,2)$. The question is how does $2^7\mathbin:\operatorname{Sp}(6,2)$ act on $ …