In each table, we denote by gTi the ith transitive group of degree g called by TransitiveGroup(g, i) in the Magma program. For each transitive group G of degree g and each group N of order g, we give the total number Total of Hopf Galois structures of type N for a separable field extension L/K of degree g such that the Galois group of the normal closure E over K is isomorphic to G. Moreover, we give the number a-c of those which are almost classically Galois, the number BC of those for which the Galois correspondence is bijective and the number Gi of Hopf algebra isomorphism classes in which the Hopf Galois structures are partitioned. The transitive groups G such that the corresponding field extension L/K has no Hopf Galois structures are not included in the table.

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Compendium