A 2-Modular Matrix Group Derived from Steiner Hexads Original Research Article

The 132 Steiner hexads can be grouped in rows to form 11 12 by 12 matrices over F2. Adding the identity to each of these yields 12 involutory matrices, called Steiner matrices, which have properties similar to those of the 12 involutory permutations which are used to construct representations of L(2, 11) and the Janko group J1. The set of rows in the group, GS, generated by these matrices consists of all vectors of weights 1, 5, and 9. There is a surjection of GS onto A12 taking the Steiner matrices onto the involutory permutations, and the kernel is an elementary 2-group. L(2, 11) acts as an automorphism group on GS.