Computation of Sha for groups of order \(32\) and \(p=2\).

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There are \(44\) non-abelian groups of order \(32\). There are \(19\) combination(s) of \(G, N\) where \(G\) is not abelian with nontrivial Sha:

• \((32,4)\) : \(2\).
• \((32,5)\) : \(2\).
• \((32,7)\) : \(2\).
• \((32,8)\) : \(4\).
• \((32,10)\) : \(2\).
• \((32,12)\) : \(2\).
• \((32,14)\) : \(2\).
• \((32,15)\) : \(4\).
• \((32,17)\) : \(2\).
• \((32,19)\) : \(2\).
• \((32,20)\) : \(4\).
• \((32,23)\) : \(2\).
• \((32,35)\) : \(2\).
• \((32,37)\) : \(2\).
• \((32,38)\) : \(2\).
• \((32,40)\) : \(2\).
• \((32,41)\) : \(4\).
• \((32,44)\) : \(2\).
• \((32,47)\) : \(4\).

max order of Sha : \(4\).

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NOTE: We excluded abelian groups for which we know the result exactly.