The full automorphism groups of the five symmetric $(15,8,4)$-designs

Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel

It is clear that the full automorphism group of the $(15,8,4)$-design of points and hyperplane complements of $\mathrm{PG}(3,2)$ is $\mathrm{GL}(4,2)$. Using methods of point-line geomet…