In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits.
Some unusual rank-3 permutation groups (many from (Liebeck & Saxl 1986)) are listed below.
For each row in the table below, in the grid in the column marked "size", the number to the left of the equal sign is the degree of the permutation group for the permutation group mentioned in the row.
In the grid, the sum to the right of the equal sign shows the lengths of the three orbits of the stabilizer of a point of the permutation group.
For example, the expression 15 = 1+6+8 in the first row of the table under the heading means that the permutation group for the first row has degree 15, and the lengths of three orbits of the stabilizer of a point of the permutation group are 1, 6 and 8 respectively.