  This paper presents an analysis of primitive permutation groups of degree
$3p$, where $p$ is a prime number, analogous to H. Wielandt's treatment of
groups of degree $2p$. It is also intended as an example of the systematic use
of combinatorial methods as surveyed in \S6 for distilling information about a
permutation group from knowledge of the decomposition of its character. The
work is organised into three parts. Part I contains the lesser half of the
calculation, the determination of the decomposition of the permutation
character. Part II contains a survey of the combinatorial methods and, based on
these methods, the major part of the calculation. Part III ties up loose ends
left earlier in the paper and gives a tabulation of detailed numerical results.
