<i>SUBGROUPGRAPH</i>: a computer program for analysis of group–subgroup relations between space groups

TLDR

Group–subgroup relations between space groups are essential for phase‑transition studies, yet existing International Tables data are insufficient for detailed G > H analysis. SUBGROUPGRAPH aims to supply detailed group–subgroup analyses, constructing maximal‑subgroup chains, counting distinct subgroups, and classifying them by conjugacy, using forthcoming International Tables data. SUBGROUPGRAPH is implemented as a program that processes a preliminary CIF version of the International Tables A1 database to generate G±H graphs and related subgroup statistics.

Abstract

Group±subgroup relations between two space groups, G > H, are of essential importance for phase-transition problems: for determination of the relation between the lowand high-symmetry structures, domain structure analysis, displacement-mode analysis, etc. The available subgroup data in the International Tables for Crystallography, Vol. A (1995), are not suf®cient for a detailed treatment of G > H relations. The necessary data will be available in the forthcoming Vol. A1 of the International Tables for Crystallography (2001). The program SUBGROUPGRAPH uses a preliminary CIF version of the Vol. A1 database (Wondratchek et al., 1996). The main aim of SUBGROUPGRAPH is a detailed study of a group±subgroup relation between two space groups, including the construction of chains of maximal subgroups for G > H for a speci®ed/non-speci®ed index i = |G:H| (the so-called G±H graph), the determination of the number of different Hk < G, Hk  H, and their distribution into classes of conjugate subgroups relative to G, etc.