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We assume that $G$ is a finite extension of the discrete Heisenberg group $H_3(\Bbb Z)$, that is, $$ 1 \rightarrow H_3(\Bbb Z) \rightarrow G \rightarrow F \rightarrow 1 $$ where $F$ is a finite group. Is it possible that $G$ is a perfect group?

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    $\begingroup$ It was posted under a wrong tag (abstract-algebra); possibly it would have been answered there with the correct tag. $\endgroup$
    – YCor
    Commented Mar 6, 2018 at 22:40
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    $\begingroup$ And it's now answered on MathSE (the answer is no). $\endgroup$
    – YCor
    Commented Mar 6, 2018 at 22:45
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    $\begingroup$ I'm voting to close this question as off-topic because it’s no longer relevant. $\endgroup$
    – HJRW
    Commented Mar 7, 2018 at 6:55

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