(International Tables) Symmetry relations between space groups

International Tables for Crystallography
Volume A1: Symmetry relations between space groups

First online edition (2006) ISBN: 978-1-4020-2355-2 eISBN: 978-1-4020-5413-6 doi: 10.1107/97809553602060000101

Edited by H. Wondratschek and U. Müller

Foreword  (p. ix) | html | pdf |
Th. Hahn
Scope of this volume  (p. x) | html | pdf |
Mois I. Aroyo, Ulrich Müller and Hans Wondratschek
Computer production of Parts 2 and 3  (p. xi) | html | pdf |
Preslav Konstantinov, Asen Kirov, Eli B. Kroumova, Mois I. Aroyo and Ulrich Müller
List of symbols and abbreviations used in this volume  (p. xii) | html | pdf |
Mois I. Aroyo, Ulrich Müller and Hans Wondratschek

Part 1. Space groups and their subgroups
- 1.1. Historical introduction (pp. 2-5) | html | pdf | chapter contents |
  Mois I. Aroyo, Ulrich Müller and Hans Wondratschek
  - 1.1.1. The fundamental laws of crystallography (p. 2) | html | pdf |
  - 1.1.2. Symmetry and crystal-structure determination (pp. 2-3) | html | pdf |
  - 1.1.3. Development of the theory of group–subgroup relations (pp. 3-4) | html | pdf |
  - 1.1.4. Applications of group–subgroup relations (pp. 4-5) | html | pdf |
  - References | html | pdf |
- 1.2. General introduction to the subgroups of space groups (pp. 6-23) | html | pdf | chapter contents |
  Hans Wondratschek
  - 1.2.1. General remarks (p. 6) | html | pdf |
  - 1.2.2. Mappings and matrices (pp. 6-9) | html | pdf |
    - 1.2.2.1. Crystallographic symmetry operations (pp. 6-7) | html | pdf |
    - 1.2.2.2. Coordinate systems and coordinates (p. 7) | html | pdf |
    - 1.2.2.3. The description of mappings (pp. 7-8) | html | pdf |
    - 1.2.2.4. Matrix–column pairs and $[(n+1)\times(n+1)]$ matrices (p. 8) | html | pdf |
    - 1.2.2.5. Isometries (p. 8) | html | pdf |
    - 1.2.2.6. Vectors and vector coefficients (pp. 8-9) | html | pdf |
    - 1.2.2.7. Origin shift and change of the basis (p. 9) | html | pdf |
  - 1.2.3. Groups (pp. 9-10) | html | pdf |
    - 1.2.3.1. Some properties of symmetry groups (pp. 9-10) | html | pdf |
    - 1.2.3.2. Group isomorphism and homomorphism (p. 10) | html | pdf |
  - 1.2.4. Subgroups (pp. 11-12) | html | pdf |
    - 1.2.4.1. Definition (p. 11) | html | pdf |
    - 1.2.4.2. Coset decomposition and normal subgroups (p. 11) | html | pdf |
    - 1.2.4.3. Conjugate elements and conjugate subgroups (pp. 11-12) | html | pdf |
    - 1.2.4.4. Factor groups and homomorphism (p. 12) | html | pdf |
    - 1.2.4.5. Normalizers (p. 12) | html | pdf |
  - 1.2.5. Space groups (pp. 13-16) | html | pdf |
    - 1.2.5.1. Space groups and their description (p. 13) | html | pdf |
    - 1.2.5.2. Classifications of space groups (p. 14) | html | pdf |
    - 1.2.5.3. Space groups and space-group types (pp. 14-15) | html | pdf |
    - 1.2.5.4. Point groups and crystal classes (pp. 15-16) | html | pdf |
    - 1.2.5.5. Crystal systems and crystal families (p. 16) | html | pdf |
  - 1.2.6. Types of subgroups of space groups (pp. 16-18) | html | pdf |
    - 1.2.6.1. Introductory remarks (p. 16) | html | pdf |
    - 1.2.6.2. Definitions and examples (pp. 16-18) | html | pdf |
    - 1.2.6.3. The role of normalizers for group–subgroup pairs of space groups (p. 18) | html | pdf |
  - 1.2.7. Application to domain structures (pp. 18-22) | html | pdf |
    - 1.2.7.1. Introductory remarks (pp. 18-19) | html | pdf |
    - 1.2.7.2. Domains, domain states and symmetry states (pp. 19-20) | html | pdf |
    - 1.2.7.3. Translational domain structures (translation twins) (pp. 20-21) | html | pdf |
    - 1.2.7.4. Domain structures of a general phase transition (pp. 21-22) | html | pdf |
  - 1.2.8. Lemmata on subgroups of space groups (pp. 22-23) | html | pdf |
    - 1.2.8.1. General lemmata (pp. 22-23) | html | pdf |
    - 1.2.8.2. Lemmata on maximal subgroups (p. 23) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.2.3.1. Multiplication table of a group (p. 10) | html | pdf |
- 1.3. Remarks on Wyckoff positions (pp. 24-26) | html | pdf | chapter contents |
  Ulrich Müller
  - 1.3.1. Introduction (p. 24) | html | pdf |
  - 1.3.2. Crystallographic orbits and Wyckoff positions (pp. 24-25) | html | pdf |
  - 1.3.3. Derivative structures and phase transitions (p. 25) | html | pdf |
  - 1.3.4. Relations between the positions in group–subgroup relations (pp. 25-26) | html | pdf |
  - References | html | pdf |
- 1.4. Computer checking of the subgroup data (pp. 27-28) | html | pdf | chapter contents |
  Franz Gähler
  - 1.4.1. Introduction (p. 27) | html | pdf |
  - 1.4.2. Basic capabilities of the Cryst package (p. 27) | html | pdf |
  - 1.4.3. Computing maximal subgroups (p. 27) | html | pdf |
  - 1.4.4. Description of the checks (p. 28) | html | pdf |
  - References | html | pdf |
- 1.5. The mathematical background of the subgroup tables (pp. 29-40) | html | pdf | chapter contents |
  Gabriele Nebe
  - 1.5.1. Introduction (p. 29) | html | pdf |
  - 1.5.2. The affine space (pp. 29-31) | html | pdf |
    - 1.5.2.1. Motivation (p. 29) | html | pdf |
    - 1.5.2.2. Vector spaces (pp. 29-30) | html | pdf |
    - 1.5.2.3. The affine space (p. 30) | html | pdf |
    - 1.5.2.4. The affine group (pp. 30-31) | html | pdf |
  - 1.5.3. Groups (pp. 31-34) | html | pdf |
    - 1.5.3.1. Groups (p. 31) | html | pdf |
    - 1.5.3.2. Actions of groups on sets (pp. 32-33) | html | pdf |
    - 1.5.3.3. The Sylow theorems (p. 33) | html | pdf |
    - 1.5.3.4. Isomorphisms (pp. 33-34) | html | pdf |
    - 1.5.3.5. Isomorphism theorems (p. 34) | html | pdf |
    - 1.5.3.6. An example (p. 34) | html | pdf |
  - 1.5.4. Space groups (pp. 34-36) | html | pdf |
    - 1.5.4.1. Definition of space groups (pp. 34-35) | html | pdf |
    - 1.5.4.2. Maximal subgroups of space groups (pp. 35-36) | html | pdf |
  - 1.5.5. Maximal subgroups (pp. 36-38) | html | pdf |
    - 1.5.5.1. Maximal subgroups and primitive $[{\cal G}]$ -sets (pp. 36-37) | html | pdf |
    - 1.5.5.2. Soluble groups (p. 37) | html | pdf |
    - 1.5.5.3. Maximal subgroups of soluble groups (p. 38) | html | pdf |
  - 1.5.6. Quantitative results (pp. 38-39) | html | pdf |
    - 1.5.6.1. General results (p. 38) | html | pdf |
    - 1.5.6.2. Three-dimensional space groups (pp. 38-39) | html | pdf |
  - 1.5.7. Qualitative results (pp. 39-40) | html | pdf |
    - 1.5.7.1. General theory (p. 39) | html | pdf |
    - 1.5.7.2. Three-dimensional space groups (pp. 39-40) | html | pdf |
  - References | html | pdf |

Part 2. Maximal subgroups of the plane groups and space groups
- 2.1. Guide to the subgroup tables and graphs (pp. 42-58) | html | pdf | chapter contents |
  Hans Wondratschek and Mois I. Aroyo
  - 2.1.1. Contents and arrangement of the subgroup tables (p. 42) | html | pdf |
  - 2.1.2. Structure of the subgroup tables (pp. 42-45) | html | pdf |
    - 2.1.2.1. Headline (p. 42) | html | pdf |
    - 2.1.2.2. Data from IT A (pp. 42-43) | html | pdf |
      - 2.1.2.2.1. Generators selected (p. 42) | html | pdf |
      - 2.1.2.2.2. General position (pp. 42-43) | html | pdf |
    - 2.1.2.3. Specification of the setting (p. 43) | html | pdf |
    - 2.1.2.4. Sequence of the subgroup and supergroup data (p. 43) | html | pdf |
    - 2.1.2.5. Special rules for the setting of the subgroups (pp. 43-45) | html | pdf |
      - 2.1.2.5.1. Monoclinic subgroups (p. 44) | html | pdf |
      - 2.1.2.5.2. Subgroups with two origin choices (pp. 44-45) | html | pdf |
      - 2.1.2.5.3. Space groups with a rhombohedral lattice (p. 45) | html | pdf |
  - 2.1.3. I Maximal translationengleiche subgroups ( t -subgroups) (pp. 45-48) | html | pdf |
    - 2.1.3.1. Introduction (p. 45) | html | pdf |
    - 2.1.3.2. A description in close analogy with IT A (pp. 45-46) | html | pdf |
    - 2.1.3.3. Basis transformation and origin shift (pp. 46-48) | html | pdf |
  - 2.1.4. II Maximal klassengleiche subgroups ( k -subgroups) (pp. 48-51) | html | pdf |
    - 2.1.4.1. General description (p. 48) | html | pdf |
    - 2.1.4.2. Loss of centring translations (pp. 48-49) | html | pdf |
    - 2.1.4.3. Enlarged unit cell (pp. 49-51) | html | pdf |
      - 2.1.4.3.1. Enlarged unit cell, index 2 (pp. 49-50) | html | pdf |
      - 2.1.4.3.2. Enlarged unit cell, index 3 or 4 (pp. 50-51) | html | pdf |
  - 2.1.5. Series of maximal isomorphic subgroups (pp. 51-53) | html | pdf |
    Y. Billiet
    - 2.1.5.1. General description (p. 51) | html | pdf |
    - 2.1.5.2. Basis transformation (p. 51) | html | pdf |
    - 2.1.5.3. Origin shift (p. 51) | html | pdf |
    - 2.1.5.4. Generators (p. 52) | html | pdf |
    - 2.1.5.5. Special series (pp. 52-53) | html | pdf |
      - 2.1.5.5.1. Monoclinic space groups (p. 52) | html | pdf |
      - 2.1.5.5.2. Trigonal space groups with rhombohedral lattice (p. 52) | html | pdf |
      - 2.1.5.5.3. Space groups with two origin choices (pp. 52-53) | html | pdf |
  - 2.1.6. Minimal supergroups (pp. 53-54) | html | pdf |
    - 2.1.6.1. General description (p. 53) | html | pdf |
    - 2.1.6.2. I Minimal translationengleiche supergroups (p. 53) | html | pdf |
    - 2.1.6.3. II Minimal non-isomorphic klassengleiche supergroups (pp. 53-54) | html | pdf |
    - 2.1.6.4. Isomorphic supergroups (p. 54) | html | pdf |
  - 2.1.7. The subgroup graphs (pp. 54-58) | html | pdf |
    - 2.1.7.1. General remarks (p. 54) | html | pdf |
    - 2.1.7.2. Graphs for translationengleiche subgroups (pp. 54-55) | html | pdf |
    - 2.1.7.3. Graphs for klassengleiche subgroups (pp. 55-56) | html | pdf |
    - 2.1.7.4. Graphs for plane groups (pp. 56-57) | html | pdf |
    - 2.1.7.5. Application of the graphs (pp. 57-58) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.1.7.1. Contracted graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to those subgroups with index 12 which belong to the space-group type (12) (p. 57) | html | pdf |
    - Fig. 2.1.7.2. Complete graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to one representative of those six (12) subgroups with index 12 whose monoclinic axes are along the $[\langle 110 \rangle]$ directions of $[Fm\overline{3}m]$ (p. 57) | html | pdf |
    - Fig. 2.1.7.3. Complete graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to one representative of those three (12) subgroups with index 12 whose monoclinic axes are along the $[\langle 001 \rangle]$ directions of $[Fm\overline{3}m]$ (p. 57) | html | pdf |
- 2.2. Tables of maximal subgroups of the plane groups (pp. 59-76) | html | | chapter contents |
  - Maximal subgroups of plane group 1 (p. 60) | html | pdf |
  - Maximal subgroups of plane group 2 (p. 61) | html | pdf |
  - Maximal subgroups of plane group 3 (p. 62) | html | pdf |
  - Maximal subgroups of plane group 4 (p. 63) | html | pdf |
  - Maximal subgroups of plane group 5 (p. 64) | html | pdf |
  - Maximal subgroups of plane group 6 (p. 65) | html | pdf |
  - Maximal subgroups of plane group 7 (p. 66) | html | pdf |
  - Maximal subgroups of plane group 8 (p. 67) | html | pdf |
  - Maximal subgroups of plane group 9 (p. 68) | html | pdf |
  - Maximal subgroups of plane group 10 (p. 69) | html | pdf |
  - Maximal subgroups of plane group 11 (p. 70) | html | pdf |
  - Maximal subgroups of plane group 12 (p. 71) | html | pdf |
  - Maximal subgroups of plane group 13 (p. 72) | html | pdf |
  - Maximal subgroups of plane group 14 (p. 73) | html | pdf |
  - Maximal subgroups of plane group 15 (p. 74) | html | pdf |
  - Maximal subgroups of plane group 16 (p. 75) | html | pdf |
  - Maximal subgroups of plane group 17 (p. 76) | html | pdf |
- 2.3. Tables of maximal subgroups of the space groups (pp. 77-394) | html | | chapter contents |
  - Maximal subgroups of space group 1 (pp. 78-79) | html | pdf |
  - Maximal subgroups of space group 2 (pp. 80-81) | html | pdf |
  - Maximal subgroups of space group 3 (pp. 82-84) | html | pdf |
    - Maximal subgroups of space group 3, unique axis b (pp. 82-83) | html | pdf |
    - Maximal subgroups of space group 3, unique axis c (pp. 83-84) | html | pdf |
  - Maximal subgroups of space group 4 (pp. 85-86) | html | pdf |
    - Maximal subgroups of space group 4, unique axis b (p. 85) | html | pdf |
    - Maximal subgroups of space group 4, unique axis c (p. 86) | html | pdf |
  - Maximal subgroups of space group 5 (pp. 87-89) | html | pdf |
    - Maximal subgroups of space group 5, unique axis b (pp. 87-88) | html | pdf |
    - Maximal subgroups of space group 5, unique axis c (pp. 88-89) | html | pdf |
  - Maximal subgroups of space group 6 (pp. 90-92) | html | pdf |
    - Maximal subgroups of space group 6, unique axis b (pp. 90-91) | html | pdf |
    - Maximal subgroups of space group 6, unique axis c (pp. 91-92) | html | pdf |
  - Maximal subgroups of space group 7 (pp. 93-94) | html | pdf |
    - Maximal subgroups of space group 7, unique axis b (p. 93) | html | pdf |
    - Maximal subgroups of space group 7, unique axis c (p. 94) | html | pdf |
  - Maximal subgroups of space group 8 (pp. 95-96) | html | pdf |
    - Maximal subgroups of space group 8, unique axis b (p. 95) | html | pdf |
    - Maximal subgroups of space group 8, unique axis c (p. 96) | html | pdf |
  - Maximal subgroups of space group 9 (pp. 97-98) | html | pdf |
    - Maximal subgroups of space group 9, unique axis b (p. 97) | html | pdf |
    - Maximal subgroups of space group 9, unique axis c (p. 98) | html | pdf |
  - Maximal subgroups of space group 10 (pp. 99-102) | html | pdf |
    - Maximal subgroups of space group 10, unique axis b (pp. 99-100) | html | pdf |
    - Maximal subgroups of space group 10, unique axis c (pp. 101-102) | html | pdf |
  - Maximal subgroups of space group 11 (pp. 103-105) | html | pdf |
    - Maximal subgroups of space group 11, unique axis b (pp. 103-104) | html | pdf |
    - Maximal subgroups of space group 11, unique axis c (pp. 104-105) | html | pdf |
  - Maximal subgroups of space group 12 (pp. 106-108) | html | pdf |
    - Maximal subgroups of space group 12, unique axis b (pp. 106-107) | html | pdf |
    - Maximal subgroups of space group 12, unique axis c (pp. 107-108) | html | pdf |
  - Maximal subgroups of space group 13 (pp. 109-111) | html | pdf |
    - Maximal subgroups of space group 13, unique axis b (pp. 109-110) | html | pdf |
    - Maximal subgroups of space group 13, unique axis c (pp. 110-111) | html | pdf |
  - Maximal subgroups of space group 14 (pp. 112-114) | html | pdf |
    - Maximal subgroups of space group 14, unique axis b (pp. 112-113) | html | pdf |
    - Maximal subgroups of space group 14, unique axis c (pp. 113-114) | html | pdf |
  - Maximal subgroups of space group 15 (pp. 115-117) | html | pdf |
    - Maximal subgroups of space group 15, unique axis b (pp. 115-116) | html | pdf |
    - Maximal subgroups of space group 15, unique axis c (pp. 116-117) | html | pdf |
  - Maximal subgroups of space group 16 (pp. 118-119) | html | pdf |
  - Maximal subgroups of space group 17 (p. 120) | html | pdf |
  - Maximal subgroups of space group 18 (p. 121) | html | pdf |
  - Maximal subgroups of space group 19 (p. 122) | html | pdf |
  - Maximal subgroups of space group 20 (p. 123) | html | pdf |
  - Maximal subgroups of space group 21 (pp. 124-125) | html | pdf |
  - Maximal subgroups of space group 22 (pp. 125-126) | html | pdf |
  - Maximal subgroups of space group 23 (p. 127) | html | pdf |
  - Maximal subgroups of space group 24 (p. 128) | html | pdf |
  - Maximal subgroups of space group 25 (pp. 129-130) | html | pdf |
  - Maximal subgroups of space group 26 (p. 131) | html | pdf |
  - Maximal subgroups of space group 27 (p. 132) | html | pdf |
  - Maximal subgroups of space group 28 (p. 133) | html | pdf |
  - Maximal subgroups of space group 29 (p. 134) | html | pdf |
  - Maximal subgroups of space group 30 (p. 135) | html | pdf |
  - Maximal subgroups of space group 31 (p. 136) | html | pdf |
  - Maximal subgroups of space group 32 (p. 137) | html | pdf |
  - Maximal subgroups of space group 33 (p. 138) | html | pdf |
  - Maximal subgroups of space group 34 (p. 139) | html | pdf |
  - Maximal subgroups of space group 35 (p. 140) | html | pdf |
  - Maximal subgroups of space group 36 (p. 141) | html | pdf |
  - Maximal subgroups of space group 37 (p. 142) | html | pdf |
  - Maximal subgroups of space group 38 (p. 143) | html | pdf |
  - Maximal subgroups of space group 39 (p. 144) | html | pdf |
  - Maximal subgroups of space group 40 (p. 145) | html | pdf |
  - Maximal subgroups of space group 41 (p. 146) | html | pdf |
  - Maximal subgroups of space group 42 (pp. 147-148) | html | pdf |
  - Maximal subgroups of space group 43 (p. 149) | html | pdf |
  - Maximal subgroups of space group 44 (p. 150) | html | pdf |
  - Maximal subgroups of space group 45 (p. 151) | html | pdf |
  - Maximal subgroups of space group 46 (p. 152) | html | pdf |
  - Maximal subgroups of space group 47 (pp. 153-154) | html | pdf |
  - Maximal subgroups of space group 48 (pp. 155-157) | html | pdf |
    - Maximal subgroups of space group 48, origin choice 1 (pp. 155-156) | html | pdf |
    - Maximal subgroups of space group 48, origin choice 2 (pp. 156-157) | html | pdf |
  - Maximal subgroups of space group 49 (pp. 158-159) | html | pdf |
  - Maximal subgroups of space group 50 (pp. 159-162) | html | pdf |
    - Maximal subgroups of space group 50, origin choice 1 (pp. 159-160) | html | pdf |
    - Maximal subgroups of space group 50, origin choice 2 (pp. 161-162) | html | pdf |
  - Maximal subgroups of space group 51 (pp. 162-163) | html | pdf |
  - Maximal subgroups of space group 52 (p. 164) | html | pdf |
  - Maximal subgroups of space group 53 (p. 165) | html | pdf |
  - Maximal subgroups of space group 54 (p. 166) | html | pdf |
  - Maximal subgroups of space group 55 (p. 167) | html | pdf |
  - Maximal subgroups of space group 56 (p. 168) | html | pdf |
  - Maximal subgroups of space group 57 (p. 169) | html | pdf |
  - Maximal subgroups of space group 58 (p. 170) | html | pdf |
  - Maximal subgroups of space group 59 (pp. 171-173) | html | pdf |
    - Maximal subgroups of space group 59, origin choice 1 (pp. 171-172) | html | pdf |
    - Maximal subgroups of space group 59, origin choice 2 (pp. 172-173) | html | pdf |
  - Maximal subgroups of space group 60 (p. 174) | html | pdf |
  - Maximal subgroups of space group 61 (p. 175) | html | pdf |
  - Maximal subgroups of space group 62 (p. 176) | html | pdf |
  - Maximal subgroups of space group 63 (pp. 177-178) | html | pdf |
  - Maximal subgroups of space group 64 (pp. 178-179) | html | pdf |
  - Maximal subgroups of space group 65 (pp. 180-181) | html | pdf |
  - Maximal subgroups of space group 66 (pp. 181-182) | html | pdf |
  - Maximal subgroups of space group 67 (pp. 183-184) | html | pdf |
  - Maximal subgroups of space group 68 (pp. 185-187) | html | pdf |
    - Maximal subgroups of space group 68, origin choice 1 (pp. 185-186) | html | pdf |
    - Maximal subgroups of space group 68, origin choice 2 (pp. 186-187) | html | pdf |
  - Maximal subgroups of space group 69 (pp. 188-189) | html | pdf |
  - Maximal subgroups of space group 70 (pp. 190-192) | html | pdf |
    - Maximal subgroups of space group 70, origin choice 1 (pp. 190-191) | html | pdf |
    - Maximal subgroups of space group 70, origin choice 2 (pp. 191-192) | html | pdf |
  - Maximal subgroups of space group 71 (p. 193) | html | pdf |
  - Maximal subgroups of space group 72 (p. 194) | html | pdf |
  - Maximal subgroups of space group 73 (pp. 195-196) | html | pdf |
  - Maximal subgroups of space group 74 (pp. 196-197) | html | pdf |
  - Maximal subgroups of space group 75 (p. 198) | html | pdf |
  - Maximal subgroups of space group 76 (p. 199) | html | pdf |
  - Maximal subgroups of space group 77 (p. 200) | html | pdf |
  - Maximal subgroups of space group 78 (p. 201) | html | pdf |
  - Maximal subgroups of space group 79 (p. 202) | html | pdf |
  - Maximal subgroups of space group 80 (p. 203) | html | pdf |
  - Maximal subgroups of space group 81 (p. 204) | html | pdf |
  - Maximal subgroups of space group 82 (p. 205) | html | pdf |
  - Maximal subgroups of space group 83 (p. 206) | html | pdf |
  - Maximal subgroups of space group 84 (p. 207) | html | pdf |
  - Maximal subgroups of space group 85 (pp. 208-209) | html | pdf |
    - Maximal subgroups of space group 85, origin choice 1 (p. 208) | html | pdf |
    - Maximal subgroups of space group 85, origin choice 2 (p. 209) | html | pdf |
  - Maximal subgroups of space group 86 (pp. 210-211) | html | pdf |
    - Maximal subgroups of space group 86, origin choice 1 (p. 210) | html | pdf |
    - Maximal subgroups of space group 86, origin choice 2 (p. 211) | html | pdf |
  - Maximal subgroups of space group 87 (p. 212) | html | pdf |
  - Maximal subgroups of space group 88 (pp. 213-214) | html | pdf |
    - Maximal subgroups of space group 88, origin choice 1 (p. 213) | html | pdf |
    - Maximal subgroups of space group 88, origin choice 2 (p. 214) |

International Tables for CrystallographyVolume A1: Symmetry relations between space groups

Edited by H. Wondratschek and U. Müller

Contents

International Tables for Crystallography
Volume A1: Symmetry relations between space groups