The Character Tables for SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2)

In this paper the character table of GL(3, q) (U(3, q 2 )), the group of all nonsingular n × n (unitary) matrices over GF(q) (GF(q 2 )), is used to obtain the character tables for the related subgroups SL(3, q), PSL(3, q) (SU(3, q 2 ), PSU(3, q 2 )), the corresponding groups of matrices of determinant unity and the projective group respectively. There are very few abstract character tables which hold for entire families of groups. Such tables are of much greater value than tables for specific groups because, among other things, they enable one to discern various patterns common to the whole family.