% List of space groups
% List of space groups
%============================================================
%   column 1: space group number
%   column 2: Hermann-Mauguin (H-M) symbol
%   column 3: unique axis (for monoclinic groups)
%             cell setting (for orthorhombic groups)
%             - (for all others)
%
% Information on space groups is from
%   Th. Hahn (ed.)
%   International Tables for Crystallography, Vol.A: Space Group Symmetry
%   5th edition 2002, corrected reprint 2005, Springer
%
% Compared to this reference, this list includes the following additions and omissions:
% - For monoclinic groups, short-form H-M symbols are given for all cell choices, not just one for cell choice 1.
% - For orthorhombic groups, for each H-M symbol only one setting is listed, even if here are more.
% - For tetragonal groups , only standard cells P and I are supported, not multiple cell C or F.
% - For trigonal groups, only standard cells P and R are supported, not triple cell H.
% - For hexagonal groups, only standard cell P is supported, not tripe cell H.


%============================================================
% Triclinic system 
%============================================================
% Point group 1 (C1), Laue class -1 (Ci)
%------------------------------------------------------------
  1 P1         -
% Point group -1 (Ci), Laue class -1 (Ci)
%------------------------------------------------------------
  2 P-1        -



%============================================================
% Monoclinic system
%============================================================
% Point group 2 (C2), Laue class 2/m (C2h)
%------------------------------------------------------------
  3 P2         b
  3 P121       b
  3 P112       c
  3 P211       a
  4 P21        b
  4 P1211      b
  4 P1121      c
  4 P2111      a
  5 C2         b
  5 A2         b
  5 I2         b
  5 C121       b
  5 A121       b
  5 I121       b
  5 A112       c
  5 B112       c
  5 I112       c
  5 B211       a
  5 C211       a
  5 I211       a
% Point group m (Cs), Laue class 2/m (C2h)
%------------------------------------------------------------
  6 Pm         b
  6 P1m1       b
  6 P11m       c
  6 Pm11       a
  7 Pc         b
  7 Pn         b
  7 Pa         b
  7 P1c1       b
  7 P1n1       b
  7 P1a1       b
  7 P11a       c
  7 P11n       c
  7 P11b       c
  7 Pb11       a
  7 Pn11       a
  7 Pc11       a
  8 Cm         b
  8 Am         b
  8 Im         b
  8 C1m1       b
  8 A1m1       b
  8 I1m1       b
  8 A11m       c
  8 B11m       c
  8 I11m       c
  8 Bm11       a
  8 Cm11       a
  8 Im11       a
  9 Cc         b
  9 An         b
  9 Ia         b
  9 C1c1       b
  9 A1n1       b
  9 I1a1       b
  9 A1a1       -b
  9 C1n1       -b
  9 I1c1       -b
  9 A11a       c
  9 B11n       c
  9 I11b       c
  9 B11b       -c
  9 A11n       -c
  9 I11a       -c
  9 Bb11       a
  9 Cn11       a
  9 Ic11       a
  9 Cc11       -a
  9 Bn11       -a
  9 Ib11       -a
% Point group 2/m (C2h), Laue class 2/m (C2h)
%------------------------------------------------------------
 10 P2/m       b
 10 P12/m1     b
 10 P112/m     c
 10 P2/m11     a
 11 P21/m      b
 11 P121/m1    b
 11 P1121/m    c
 11 P21/m11    a
 12 C2/m       b
 12 A2/m       b
 12 I2/m       b
 12 C12/m1     b
 12 A12/m1     b
 12 I12/m1     b
 12 A112/m     c
 12 B112/m     c
 12 I112/m     c
 12 B2/m11     a
 12 C2/m11     a
 12 I2/m11     a
 13 P2/c       b
 13 P2/n       b
 13 P2/a       b
 13 P12/c1     b
 13 P12/n1     b
 13 P12/a1     b
 13 P112/a     c
 13 P112/n     c
 13 P112/b     c
 13 P2/b11     a
 13 P2/n11     a
 13 P2/c11     a
 14 P21/c      b
 14 P21/n      b
 14 P21/a      b
 14 P121/c1    b
 14 P121/n1    b
 14 P121/a1    b
 14 P1121/a    c
 14 P1121/n    c
 14 P1121/b    c
 14 P21/b11    a
 14 P21/n11    a
 14 P21/c11    a
 15 C2/c       b
 15 A2/n       b
 15 I2/a       b
 15 C12/c1     b
 15 A12/n1     b
 15 I12/a1     b
 15 A12/a1     -b
 15 C12/n1     -b
 15 I12/c1     -b
 15 A112/a     c
 15 B112/n     c
 15 I112/b     c
 15 B112/b     -c
 15 A112/n     -c
 15 I112/a     -c
 15 B2/b11     a
 15 C2/n11     a
 15 I2/c11     a
 15 C2/c11     -a
 15 B2/n11     -a
 15 I2/b11     -a



%============================================================
% Orthorhombic system
%============================================================
% Point group 222 (D2), Laue class mmm (D2h)
%------------------------------------------------------------
 16 P222       abc
 17 P2221      abc
 17 P2122      cab
 17 P2212      bca
 18 P21212     abc
 18 P22121     cab
 18 P21221     bca
 19 P212121    abc
 20 C2221      abc
 20 A2122      cab
 20 B2212      bca
 21 C222       abc
 21 A222       cab
 21 B222       bca
 22 F222       abc
 23 I222       abc
 24 I212121    abc
% Point group mm2 (C2v), Laue class mmm (D2h)
%------------------------------------------------------------
 25 Pmm2       abc
 25 P2mm       cab
 25 Pm2m       bca
 26 Pmc21      abc
 26 Pcm21      ba-c
 26 P21ma      cab
 26 P21am      -cba
 26 Pb21m      bca
 26 Pm21b      a-cb
 27 Pcc2       abc
 27 P2aa       cab
 27 Pb2b       bca
 28 Pma2       abc
 28 Pbm2       ba-c
 28 P2mb       cab
 28 P2cm       -cba
 28 Pc2m       bca
 28 Pm2a       a-cb
 29 Pca21      abc
 29 Pbc21      ba-c
 29 P21ab      cab
 29 P21ca      -cba
 29 Pc21b      bca
 29 Pb21a      a-cb
 30 Pnc2       abc
 30 Pcn2       ba-c
 30 P2na      cab
 30 P2an      -cba
 30 Pb2n      bca
 30 Pn2b      a-cb
 31 Pmn21     abc
 31 Pnm21     ba-c
 31 P21mn     cab
 31 P21nm     -cba
 31 Pn21m     bca
 31 Pm21n     a-cb
 32 Pba2      abc
 32 P2cb      cab
 32 Pc2a      bca
 33 Pna21     abc
 33 Pbn21     ba-c
 33 P21nb     cab
 33 P21cn     -cba
 33 Pc21n     bca
 33 Pn21a     a-cb
 34 Pnn2      abc
 34 P2nn      cab
 34 Pn2n      bca
 35 Cmm2      abc
 35 A2mm      cab
 35 Bm2m      bca
 36 Cmc21     abc
 36 Ccm21     ba-c
 36 A21ma     cab
 36 A21am     -cba
 36 Bb21m     bca
 36 Bm21b     a-cb
 37 Ccc2      abc
 37 A2aa      cab
 37 Bb2b      bca
 38 Amm2      abc
 38 Bmm2      ba-c
 38 B2mm      cab
 38 C2mm      -cba
 38 Cm2m      bca
 38 Am2m      a-cb
 39 Aem2      abc
 39 Bme2      ba-c
 39 B2em      cab
 39 C2me      -cba
 39 Cm2e      bca
 39 Ae2m      a-cb
 40 Ama2      abc
 40 Bbm2      ba-c
 40 B2mb      cab
 40 C2cm      -cba
 40 Cc2m      bca
 40 Am2a      a-cb
 41 Aea2      abc
 41 Bbe2      ba-c
 41 B2eb      cab
 41 C2ce      cba
 41 Cc2e      -cba
 41 Ae2a      a-cb
 42 Fmm2      abc
 42 F2mm      cab
 42 Fm2m      bca
 43 Fdd2      abc
 43 F2dd      cab
 43 Fd2d      bca
 44 Imm2      abc
 44 I2mm      cab
 44 Im2m      bca
 45 Iba2      abc
 45 I2cb      cab
 45 Ic2a      bca
 46 Ima2      abc
 46 Ibm2      ba-c
 46 I2mb      cab
 46 I2cm      -cba
 46 Ic2m      bca
 46 Im2a      a-cb
% Point group mmm (D2h), Laue class mmm (D2h)
%------------------------------------------------------------
 47 Pmmm      abc
 48 Pnnn      abc
 49 Pccm      abc
 49 Pmaa      cab
 49 Pbmb      bca
 50 Pban      abc
 50 Pncb      cab
 50 Pcna      bca
 51 Pmma      abc
 51 Pmmb      ba-c
 51 Pbmm      cab
 51 Pcmm      -cba
 51 Pmcm      bca
 51 Pmam      a-cb
 52 Pnna      abc
 52 Pnnb      ba-c
 52 Pbnn      cab
 52 Pcnn      -cba
 52 Pncn      bca
 52 Pnan      a-cb
 53 Pmna      abc
 53 Pnmb      ba-c
 53 Pbmn      cab
 53 Pcnm      -cba
 53 Pncm      bca
 53 Pman      a-cb
 54 Pcca      abc
 54 Pccb      ba-c
 54 Pbaa      cab
 54 Pcaa      -cba
 54 Pbcb      bca
 54 Pbab      a-cb
 55 Pbam      abc
 55 Pmcb      cab
 55 Pcma      bca
 56 Pccn      abc
 56 Pnaa      cab
 56 Pbnb      bca
 57 Pbcm      abc
 57 Pcam      ba-c
 57 Pmca      cab
 57 Pmab      -cba
 57 Pbma      bca
 57 Pcmb      a-cb
 58 Pnnm      abc
 58 Pmnn      cab
 58 Pnmn      bca
 59 Pmmn      abc
 59 Pnmm      cab
 59 Pmnm      bca
 60 Pbcn      abc
 60 Pcan      ba-c
 60 Pnca      cab
 60 Pnab      -cba
 60 Pbna      bca
 60 Pcnb      a-cb
 61 Pbca      abc
 61 Pcab      ba-c
 62 Pnma      abc
 62 Pmnb      ba-c
 62 Pbnm      cab
 62 Pcmn      -cba
 62 Pmcn      bca
 62 Pnam      a-cb
 63 Cmcm      abc
 63 Ccmm      ba-c
 63 Amma      cab
 63 Amam      -cba
 63 Bbmm      bca
 63 Bmmb      a-cb
 64 Cmce      abc
 64 Ccme      ba-c
 64 Aema      cab
 64 Aeam      -cba
 64 Bbem      bca
 64 Bmeb      a-cb
 65 Cmmm      abc
 65 Ammm      cab
 65 Bmmm      bca
 66 Cccm      abc
 66 Amaa      cab
 66 Bbmb      bca
 67 Cmme      abc
 67 Aemm      cab
 67 Bmem      bca
 68 Ccce      abc
 68 Aeaa      cab
 68 Bbeb      bca
 69 Fmmm      abc
 70 Fddd      abc
 71 Immm      abc
 72 Ibam      abc
 72 Imcb      cab
 72 Icma      bca
 73 Ibca      abc
 73 Icab      ba-c
 74 Imma      abc
 74 Immb      ba-c
 74 Ibmm      cab
 74 Icmm      -cba
 74 Imcm      bca
 74 Imam      a-cb


%============================================================
% Tetragonal groups
%============================================================
% Point group 4 (C4), Laue class 4/m (C4h)
%------------------------------------------------------------
 75 P4        -
 76 P41       -
 77 P42       -
 78 P43       -
 79 I4        -
 80 I41       -
% Point group -4 (S4), Laue class 4/m (C4h)
%------------------------------------------------------------
 81 P-4       -
 82 I-4       -
% Point group 4/m (C4h), Laue class 4/m (C4h)
%------------------------------------------------------------
 83 P4/m      -
 84 P42/m     -
 85 P4/n      -
 86 P42/n     -
 87 I4/m      -
 88 I41/a     -
% Point group 422 (D4), Laue class 4/mmm (D4h)
%------------------------------------------------------------
 89 P422      -
 90 P4212     -
 91 P4122     -
 92 P41212    -
 93 P4222     -
 94 P42212    -
 95 P4322     -
 96 P43212    -
 97 I422      -
 98 I4122     -
% Point group 4mm (C4v), Laue class 4/mmm (D4h)
%------------------------------------------------------------
 99 P4mm      -
100 P4bm      -
101 P42cm     -
102 P42nm     -
103 P4cc      -
104 P4nc      -
105 P42mc     -
106 P42bc     -
107 I4mm      -
108 I4cm      -
109 I41md     -
110 I41cd     -
% Point group -42m (D2d), Laue class 4/mmm (D4h)
%------------------------------------------------------------
111 P-42m     -
112 P-42c     -
113 P-421m    -
114 P-421c    -
115 P-4m2     -
116 P-4c2     -
117 P-4b2     -
118 P-4n2     -
119 I-4m2     -
120 I-4c2     -
121 I-42m     -
122 I-42d     -
% Point group 4/mmm (D4h), Laue class 4/mmm (D4h)
%------------------------------------------------------------
123 P4/mmm    -
124 P4/mcc    -
125 P4/nbm    -
126 P4/nnc    -
127 P4/mbm    -
128 P4/mnc    -
129 P4/nmm    -
130 P4/ncc    -
131 P42/mmc   -
132 P42/mcm   -
133 P42/nbc   -
134 P42/nnm   -
135 P42/mbc   -
136 P42/mnm   -
137 P42/nmc   -
138 P42/ncm   -
139 I4/mmm    -
140 I4/mcm    -
141 I41/amd   -
142 I41/acd   -



%============================================================
% Trigonal system
%============================================================
% Point group 3 (C3), Laue class -3 (C3i)
%------------------------------------------------------------
143 P3        -
144 P31       -
145 P32       -
146 R3        -
% Point group -3 (C3), Laue class -3 (C3i)
%------------------------------------------------------------
147 P-3       -
148 R-3       -
% Point group 32 (D3), Laue class -3m (D3d)
%------------------------------------------------------------
149 P312      -
150 P321      -
151 P3112     -
152 P3121     -
153 P3212     -
154 P3221     -
155 R32       -
% Point group 3m (C3v), Laue class -3m (D3d)
%------------------------------------------------------------
156 P3m1      -
157 P31m      -
158 P3c1      -
159 P31c      -
160 R3m       -
161 R3c       -
% Point group -3m (D3d), Laue class -3m (D3d)
%------------------------------------------------------------
162 P-31m     -
163 P-31c     -
164 P-3m1     -
165 P-3c1     -
166 R-3m      -
167 R-3c      -



%============================================================
% Hexagonal system
%============================================================
% Point group 6 (C6), Laue class 6/m (C6h)
%------------------------------------------------------------
168 P6        -
169 P61       -
170 P65       -
171 P62       -
172 P64       -
173 P63       -
% Point group -6 (C3h), Laue class 6/m (C6h)
%------------------------------------------------------------
174 P-6       -
% Point group 6/m (C6h), Laue class 6/m (C6h)
%------------------------------------------------------------
175 P6/m      -
176 P63/m     -
% Point group 622 (D6), Laue class 6/mmm (D6h)
%------------------------------------------------------------
177 P622      -
178 P6122     -
179 P6522     -
180 P6222     -
181 P6422     -
182 P6322     -
% Point group 6mm (C6v), Laue class 6/mmm (D6h)
%------------------------------------------------------------
183 P6mm      -
184 P6cc      -
185 P63cm     -
186 P63mc     -
% Point group -62m (D3h), Laue class 6/mmm (D6h)
%------------------------------------------------------------
187 P-6m2     -
188 P-6c2     -
189 P-62m     -
190 P-62c     -
% Point group 6/mmm (D6h), Laue class 6/mmm (D6h)
%------------------------------------------------------------
191 P6/mmm    -
192 P6/mcc    -
193 P63/mcm   -
194 P63/mmc   -



%============================================================
% Cubic system
%============================================================
% Point group 23 (T), Laue class m-3 (Th)
%------------------------------------------------------------
195 P23       -
196 F23       -
197 I23       -
198 P213      -
199 I213      -
% Point group m-3 (Th), Laue class m-3 (Th)
%------------------------------------------------------------
200 Pm-3      -
201 Pn-3      -
202 Fm-3      -
203 Fd-3      -
204 Im-3      -
205 Pa-3      -
206 Ia-3      -
% Point group 432 (O), Laue class m-3m (Oh)
%------------------------------------------------------------
207 P432      -
208 P4232     -
209 F432      -
210 F4132     -
211 I432      -
212 P4332     -
213 P4132     -
214 I4132     -
% Point group -43m (Td), Laue class m-3m (Oh)
%------------------------------------------------------------
215 P-43m     -
216 F-43m     -
217 I-43m     -
218 P-43n     -
219 F-43c     -
220 I-43d     -
% Point group m-3m (Oh), Laue class m-3m (Oh)
%------------------------------------------------------------
221 Pm-3m     -
222 Pn-3n     -
223 Pm-3n     -
224 Pn-3m     -
225 Fm-3m     -
226 Fm-3c     -
227 Fd-3m     -
228 Fd-3c     -
229 Im-3m     -
230 Ia-3d     -
