A digraph \(\overrightarrow {\rm{\Gamma}} \) is said to be 1-transitive if its automorphism group acts transitively on the 1-arcs but not on the 2-arcs of \(\overrightarrow {\rm{\Gamma}} \). We give a tentatively complete classification of pentavalent strongly connected 1-transitive digraphs of order 2^ap^bq, where p and q are two distinct odd primes, a ∈ {3,…, 8},b ∈ {1, …, 4}, whose automorphism groups are non-solvable. It is shown that such digraphs exist if and only if q = 3 or 13 and p ∈ {7, 11, 17, 19, 31, 41}.

中文翻译：

---

具有不可解自同构群的五价1-可传递图

如果有向图\（\ overrightarrow {\ rm {\ Gamma}} \）是自传同构群，则它的自同构群传递传递给\（\ overrightarrow {\ rm { \ Gamma}} \）。我们给出的顺序2五价强连接1-传递有向图的一个试探性地完全分类^一个p ^b q，其中p和q是两个不同的奇素数，一个∈{3，...，8}，b ∈{1，...，4 }，其自同构组是不可解的。结果表明，这样的有向图存在当且仅当q = 3或13和p ∈{7，11，17，19，31，41}。