TRIPLANES FOR (71,15,3) ADMITTING A SOLVABLE GROUP OF

ORDER 168 ACTING NON-SEMISTANDARDLY by Mirjana Garapić, Zagreb, Croatia

Abstract. Triplanes for (71,15,3) admitting an automorphism group G ≃ E_{8} · F_{21}, acting non-semistandardly, have been investigated. Here E_{8} · F_{21} is a faithful extension of an elementary abelian group E_{8} of order 8 by a Frobenious group F_{21} of order 21. It is shown by efficient methods, that exactly six such triplanes exist together with their duals. They are all nonself-dual. One of these pairs of triplanes has not been known so far. Mathematics subject classification: 05B25 Keywords: symmetric design, automorphism group, orbit structure, classification.