Held, Dieter; Hrabě de Angelis, Jörg; Pavčević, Mario-Osvin \(\text{PSp}_4(3)\) as a symmetric (36, 15, 6)-design. (English) Zbl 0935.05007 Rend. Semin. Mat. Univ. Padova 101, 95-98 (1999). Let \(G\) be a group isomorphic to \(\text{PSp}_4(3) \cong U_4(2)\) and let \(\mathcal P\) be the conjugacy class of subgroups of \(G\) isomorphic to \(S_6 \cong \text{Sp}_4(2)'\). Then \(S \in {\mathcal P}\) has three orbits \(\{S\}, B\) and \(C\) on \(\mathcal P\) of length \(1,15\) and \(20\), respectively. It is shown that \(({\mathcal P}, {\mathcal B}, I)\) is a symmetric \(2\)-\((36,15,6)\) design with set of blocks \({\mathcal B} = \{B^g \mid g \in G\}\) where a point \(R\) is incident with a block \(B^g\) if \(R\) is contained in \(B^g\). The automorphism group \(\operatorname{Aut}(G)\) acts on this design flag-transitively. Reviewer: B.Baumeister (Halle) Cited in 1 Document MSC: 05B05 Combinatorial aspects of block designs 05E20 Group actions on designs, etc. (MSC2000) 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures 51E05 General block designs in finite geometry Keywords:symmetric design; symplectic group PDFBibTeX XMLCite \textit{D. Held} et al., Rend. Semin. Mat. Univ. Padova 101, 95--98 (1999; Zbl 0935.05007) Full Text: Numdam EuDML References: [1] J.H. Conway - R.T. Curtis - S.P. Norton - R.A. Parker - R.A. Wilson , Atlas of Finite Groups , Oxford ( 1985 ). MR 827219 | Zbl 0568.20001 · Zbl 0568.20001 [2] Z. Janko , A Characterization of the finite simple group PSp4 (3 ), Canadian J. Math. , 19 ( 1967 ), pp. 872 - 894 . MR 214672 | Zbl 0178.02202 · Zbl 0178.02202 · doi:10.4153/CJM-1967-082-9 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.