Computation of Sha for groups of order \(256\) and \(p=2\). Part One

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The classification is currently not complete, so we cannot give global statistics. Next to each group we write "numb" for the number of groups with nontrivial Sha up to that group, "max" for the maximal order of Sha up to that group, and "nonabs" for the number of nonabelian groups up to that group. In particular, with our partial data we see that the current maximal order for Sha is \(8\).