The Steiner systems S(2, 4, 25) with nontrivial automorphism group

There are exactly 16 non-isomorphic Steiner systems S(2,4, 25) with nontrivial automorphism group. It is interesting to note that each of these designs has an automorphism of order 3. These 16 designs are presented along with their groups and other invariants. In particular, we determine and tabulate substructures for each of the sixteen designs inciuding Fano subplanes, ovals, complete 5-arcs, parallel classes and near-resolutions. One design has three mutually orthogonal near-resolutions and this leads to an (already known) elliptic semiplane. The sixteen designs are discriminated by means of the substructures mentioned above. Although not tabulated in this paper, we did compute the b&k-graph invariants which also discriminate the sixteen designs.