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May 3, 2013 at 10:30 history edited Peter Michor CC BY-SA 3.0
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May 3, 2013 at 7:05 comment added Peter Michor It is not so simple, since it also involves the central extension $Z(N)\to N\to \text{Inn}(N)$. I did not work it out.
May 3, 2013 at 6:18 comment added Mark Grant This answer and the reference to your book are hugely helpful, thanks. Could you clarify how the central extension is "described by the cohomology class in $H^2(G,Z(N))$"? Are you pulling back said cohomology class using the projection map $G\times\mathrm{Inn}(N)\to G$?
May 2, 2013 at 18:35 history answered Peter Michor CC BY-SA 3.0