Group–subgroup relations

Bertaut, E. F.

doi:10.1107/97809553602060000508

International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

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International Tables for Crystallography (2006). Vol. A. ch. 4.2, p. 61

Section 4.2.4. Group–subgroup relations

E. F. Bertaut^a ^‡

^a Laboratoire de Cristallographie, CNRS, Grenoble, France

4.2.4. Group–subgroup relations

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The following example illustrates the usefulness of multiple cells.

Example: p3m1 (14)

The symbol of this plane group, described by the triple cell h, is h31m, where the symmetry elements of the secondary and tertiary positions are interchanged. `Decentring' the h cell gives rise to maximal non-isomorphic k subgroups p31m of index [3], with lattice parameters $[a\sqrt{3}, a\sqrt{3}]$ (cf. Section 4.3.5 ).

References

International Tables for Crystallography (2006). Vol. A. ch. 4.2, p. 61