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The primary purpose of this paper is to report on the successful enumerationin Magma of representatives of the $195\,826\,352$ conjugacy classes oftransitive subgroups of the symmetric group $S_{48}$ of degree 48. In addition,we have determined that 25707 of these groups are minimal transitive and that713 of them are elusive. The minimal transitive examples have been used toenumerate the vertex-transitive graphs of degree $48$, of which there are$1\,538\,868\,366$, all but $0.1625\%$ of which arise as Cayley graphs. We havealso found that the largest number of elements required to generate any ofthese groups is 10, and we have used this fact to improve previous generalbounds of the third author on the number of elements required to generate anarbitrary transitive permutation group of a given degree. The details of theproof of this improved bound will be published by the third author as aseparate paper

The transitive groups of degree 48 and some applications