The group-theoretical analysis of the hexagonal perovskite structure ($3L$, space group $\frac{P{6}_3}{\mathrm{mmc}}$), considered as a common prototype phase of most hexagonal or pseudohexagonal $\mathrm{AB}{X}_3$ compounds, which was initiated recently [Pérez-Mato et al., J. Phys. C 14, 1121 (1981)], is continued in this paper. After discussing, in a general case, the distortion created by a structural phase transition in terms of symmetry modes of the prototype structure, the selection rules restricting their presence in the distortion are formulated stressing the role played by the invariance groups of the prototype-space-group irreducible representations. Then, restricting the study to the hexagonal perovskite structure, we have worked out its symmetry modes and their compatibility relations. Finally, as an example, the room-temperature phase in KNi${\mathrm{Cl}}_3$ is analyzed as a distortion from the ideal hexagonal perovskite. The possible nine symmetry modes intervening in it are described, and their relative weight in the actual distortion is calculated. Although the crystal is separated by about 260 K from the nearest reported phase transition, the distortion is surprisingly dominated by the two modes corresponding to the necessary order-parameter symmetry describing the symmetry change between the compared phases, while the amplitudes of the remaining "free" modes are at least 1 order of magnitude smaller.

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