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The transitive permutation groups of degree 32. (English) Zbl 1175.20004
The methods and the results of a computation of a data base of all transitive permutation groups of degree \(32\) are described. There are \(2,801,324\) conjugacy classes of such groups in \(\text{Sym}(32)\), most of them \(2\)-groups. The authors have written a MAGMA function (which is also described in the paper) that takes a transitive group \(G\) of degree \(32\) as input and identifies its unique conjugate in the data base.

MSC:
20B40 Computational methods (permutation groups) (MSC2010)
20B20 Multiply transitive finite groups
20B05 General theory for finite permutation groups
20B10 Characterization theorems for permutation groups
20B35 Subgroups of symmetric groups
68W30 Symbolic computation and algebraic computation
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