In the unit square, \(n\) random points are chosen that are independently and uniformly distributed. At each point a sector is drawn with radius depending on \(n\) and with a fixed angle different from 180 degrees. The directions of the sectors are given by independent uniformly distributed orientation angles. The random sector graph \(G\) is defined as a digraph on the \(n\) points with an arc from point \(i\) to point \(j\) if and only if point \(j\) belongs to the sector from point \(i\). The chromatic number and the sizes of the maximum directed and undirected cliques of \(G\) are investigated. Asymptotic results are given as \(n\) tends to infinity.