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Group action w.r.t. non-split extension group of the form 2^8$2^8\mathbin.(2^72^7\mathbin:\operatorname{Sp}(6,2))$

I have a non-split extension $2^8.(2^7:Sp(6,2))$$2^8\mathbin.(2^7\mathbin:\operatorname{Sp}(6,2))$ of $2^8$ by $2^7:Sp(6,2)$$2^7\mathbin:\operatorname{Sp}(6,2)$. The question is how does $2^7:Sp(6,2)$$2^7\mathbin:\operatorname{Sp}(6,2)$ act on $2^8$.This This group sits maximalmaximally inside the unique nonsplit extension $2^8.Sp(8,2)$$2^8\mathbin.\operatorname{Sp}(8,2)$.

Group action w.r.t. non-split extension group of the form 2^8.(2^7:Sp(6,2))

I have a non-split extension $2^8.(2^7:Sp(6,2))$ of $2^8$ by $2^7:Sp(6,2)$. The question is how does $2^7:Sp(6,2)$ act on $2^8$.This group sits maximal inside the unique nonsplit extension $2^8.Sp(8,2)$.

Group action w.r.t. non-split extension group of the form $2^8\mathbin.(2^7\mathbin:\operatorname{Sp}(6,2))$

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 $2^8$. This group sits maximally inside the unique nonsplit extension $2^8\mathbin.\operatorname{Sp}(8,2)$.

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Dima Pasechnik
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I have a non-split extension 2^8.(2^7:Sp(6,2))$2^8.(2^7:Sp(6,2))$ of 2^8$2^8$ by 2^7:Sp(6,2)$2^7:Sp(6,2)$. The question is how does 2^7:Sp(6,2)$2^7:Sp(6,2)$ act on 2^8$2^8$.This group sits maximal inside the unique nonsplit extension 2^8.Sp(8,2).

Best regards$2^8.Sp(8,2)$. Isaac

I have a non-split extension 2^8.(2^7:Sp(6,2)) of 2^8 by 2^7:Sp(6,2). The question is how does 2^7:Sp(6,2) act on 2^8.This group sits maximal inside the unique nonsplit extension 2^8.Sp(8,2).

Best regards. Isaac

I have a non-split extension $2^8.(2^7:Sp(6,2))$ of $2^8$ by $2^7:Sp(6,2)$. The question is how does $2^7:Sp(6,2)$ act on $2^8$.This group sits maximal inside the unique nonsplit extension $2^8.Sp(8,2)$.

added 62 characters in body
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Isaac
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I have a non-split extension 2^8.(2^7:Sp(6,2)) of 2^8 by 2^7:Sp(6,2). The question is how does 2^7:Sp(6,2) act on 2^8.This group sits maximal inside the unique nonsplit extension 2^8.Sp(8,2).

Best regards. Isaac

I have a non-split extension 2^8.(2^7:Sp(6,2)) of 2^8 by 2^7:Sp(6,2). The question is how does 2^7:Sp(6,2) act on 2^8.

Best regards. Isaac

I have a non-split extension 2^8.(2^7:Sp(6,2)) of 2^8 by 2^7:Sp(6,2). The question is how does 2^7:Sp(6,2) act on 2^8.This group sits maximal inside the unique nonsplit extension 2^8.Sp(8,2).

Best regards. Isaac

edited body; edited title
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Isaac
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YCor
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Isaac
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