PGL(2,11) and PSL(2,11) (Q1067208)

The Galois field GF(11) is basis both for geometry on the 12-point line L and also for geometry in a finite plane containing a non-singular conic \(\Gamma\). The group PGL(2,11) and its subgroup PSL(2,11) occur as projectivities on the line L and as orthogonal transformations in a finite plane. By considering the geometry on either of these two projective spaces the author presents some properties of the groups and gives two permutation representations of degree 11 for each space.