Guide to the subgroup tables and graphs

Abstract

This chapter is the users’ guide to the subgroup tables and graphs of Part 2 of this volume. Sections 2.1.1 and 2.1.2 refer to the contents, arrangement and structure of the subgroup tables of Chapters 2.2 and 2.3 . In the next three sections, the data listed for the maximal translationengleiche subgroups (Section 2.1.3), maximal klassengleiche subgroups (Section 2.1.4) and for the series of the (infinitely many) maximal isomorphic subgroups (Section 2.1.5) are described in detail with many examples. Section 2.1.6 describes the data listed for minimal supergroups. In Section 2.1.7 the procedures for the derivation of the data for minimal supergroups from the (complete) data for maximal subgroups are developed. Such procedures exist for the minimal supergroups of all space groups with the exception of minimal t-supergroups of triclinic and monoclinic space groups. The last section, Section 2.1.8, familiarizes the user with the subgroup graphs of the space groups listed in Chapters 2.4 and 2.5. The chapter is supplemented by the subgroup table of the space group R3, which is printed inside the front cover of the volume with some explanatory text. Keywords: Barnighausen trees; Hermann–Mauguin symbols; Schoenflies symbols; basis transformations; conjugate subgroups; generators; graphs of group–subgroup relations; international symbols; isomorphic subgroups; klassengleiche subgroups; minimal supergroups; maximal subgroups; space groups; subgroup graphs; isomorphic supergroups; translationengleiche supergroups; translationengleiche subgroups