The primary purpose of this paper is to report on the successful enumeration in Magma of representatives of the $195826352$ conjugacy classes of transitive subgroups of the symmetric group $S_{48}$ of degree 48. In addition, we have determined that 25707 of these groups are minimal transitive and that 713 of them are elusive. The minimal transitive examples have been used to enumerate the vertex-transitive groups of degree 48, of which there are $1538868366$, all but 0.1625% of which arise as Cayley graphs. We have also found that the largest number of elements required to generate any of these groups is 10, and we have used this fact to improve previous general bounds of the third author on the number of elements required to generate an arbitrary transitive permutation group of a given degree. The details of the proof of this improved bound will be published as a separate paper.

本文的主要目的是报告在岩浆中成功枚举$195826352$ 对称群的传递子群的共轭类 ${秒}_{48}$度数为 48。此外，我们已经确定这些群中有 25707 个是最小传递的，其中 713 个是难以捉摸的。最小传递例子已经被用来枚举度数为 48 的顶点传递群，其中有$1538868366$，除了 0.1625% 之外的所有数据都作为 Cayley 图出现。我们还发现生成这些群中任何一个所需的最大元素数是 10，我们已经利用这个事实来改进第三作者之前关于生成任意传递置换群所需元素数的一般界限给定的学位。这个改进边界的证明细节将作为单独的论文发表。