EXTENSIONS OF ABELIAN 2-GROUPS BY L2(q) UNDER IRREDUCIBLE ACTION

We study groups H. which are nonsplit extensions of elementary Abelian 2-groups A by H ~ L2(q), with H acting on A irreducibly and A = Z2.Related cohornology groups are computed. Groups H are given a complete regimentation for odd q. Moreover, there is only one. up to isomorphism, group H for q=-I (mod 4) and there is none for q = 1 (mod 4). We also present an explicit construction of H treated as automorphism groups of some loops close to extraspecial groups, the so-called "code loops" brought in sight by Griess and Parker.