The structural and magnetic properties of the hexagonal four-layer form of $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_{3}$ have been investigated by combining magnetization measurements, electron diffraction, and high-resolution synchrotron x-ray and neutron powder diffraction. Below $350\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, there is subtle structural phase transition from hexagonal symmetry (space group $P{6}_{3}∕mmc$) to orthorhombic symmetry (space group $C{222}_{1}$) where the hexagonal metric is preserved. The second-order phase transition involves a slight tilting of the corner-sharing ${\mathrm{Mn}}_{2}{\mathrm{O}}_{9}$ units composed of two face-sharing $\mathrm{Mn}{\mathrm{O}}_{6}$ octahedra and the associated displacement of ${\mathrm{Sr}}^{2+}$ cations. The phase transition is described in terms of symmetry-adapted displacement modes of the high symmetry phase. Upon further cooling, long range magnetic order with propagation vector $\mathbf{k}=(0,0,0)$ sets in below $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The antiferromagnetic structure, analyzed using representation theory, shows a considerably reduced magnetic moment indicating the crucial role played by direct exchange between Mn centers of the ${\mathrm{Mn}}_{2}{\mathrm{O}}_{9}$ units.