On symmetric designs with parameters \((176, 50, 14)\)
type: Item
instance of: scholarly article
title: On symmetric designs with parameters \((176, 50, 14)\)
zbMATH Open document ID: 0838.05010
DOI: 10.1016/0097-3165(95)90068-3
author: Zvonimir Janko
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-05-30T00:00:00Z
review text: Let \(H= (Z_4\times Z_4\times Z_4)\cdot F_{21}\), where \(F_{21}\) is the Frobenius group of order 21, operate on a symmetric \((176, 50, 14)\) design resulting in two orbits of lengths 64 and 112 (with stabilizers isomorphic to \(F_{21}\) and \(Z_{12}\), respectively). \(H\) is a second-maximal subgroup of the Higman-Sims simple group \(G\) of order 44,352,000. The author establishes that there exist precisely two such designs: the Graham-Higman design whose full automorphism group is \(G\) and a new design whose full automorphism group is \(H\). Both designs are self-dual. Base blocks are provided for both designs.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 823500
zbMATH Keywords: symmetric designs
zbMATH Keywords: Higman-Sims simple group
zbMATH Keywords: Graham-Higman design
zbMATH Keywords: automorphism group
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90068-3
OpenAlex ID: W2030045385
cites work: On the simple group of D.G. Higman and C.C. Sims
cites work: Q4028438
description: scientific article; zbMATH DE number 823500