International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 1.4, pp. 16-19

Table 1.4.2.1 

A. J. C. Wilsona

aSt John's College, Cambridge CB2 1TP, England

Table 1.4.2.1| top | pdf |
The three-dimensional space groups, arranged by arithmetic crystal class; in a few geometric crystal classes this differs somewhat from the conventional numerical order; see International Tables Volume A[link], Table 8.3.4.1[link]

Crystal systemCrystal classSpace group
GeometricArithmetic
NumberSymbolNumberSymbol
Triclinic 1 1 1P 1 P1
[\bar1] 2 [\bar1P] 2 [P\bar1]
Monoclinic 2 3 2P 3 [P2]
4 [P2_1]
4 2C 5 C2
m 5 mP 6 Pm
7 Pc
6 mC 8 Cm
9 Cc
2/m 7 2/mP 10 [P2/m]
11 [P2_1/m]
13 [P2/c]
14 [P2_1/c]
8 2/mC 12 [C2/m]
15 [C2/c]
Orthorhombic 222 9 222P 16 P222
17 [P222_1]
18 [P2_12_12]
19 [P2_12_12_1]
10 222C 20 [C222_1]
21 C222
11 222F 22 F222
12 222I 23 I222
24 [I2_12_12_1]
mm 13 mm2P 25 Pmm2
26 [Pmc2_1]
27 Pcc2
28 Pma2
29 [Pca2_1]
30 Pnc2
31 [Pmn2_1]
32 Pba2
33 [Pna2_1]
34 Pnn2
14 mm2C 35 Cmm2
36 [Cmc2_1]
37 Ccc2
15 2mmC
(Amm2)
38 C2mm
(Amm2)
39 [C2me]
(Aem2)
40 [C2cm]
[(Ama2)]
41 [C2ce]
(Aea2)
16 mm2F 42 Fmm2
43 Fdd2
17 mm2I 44 Imm2
45 Iba2
46 Ima2
mmm 18 mmmP 47 Pmmm
48 Pnnn
49 Pccm
50 Pban
51 Pmma
52 Pnna
53 Pmna
54 Pcca
55 Pbam
56 Pccn
57 Pbcm
58 Pnnm
59 Pmmn
60 Pbcn
61 Pbca
62 Pnma
19 mmmC 63 Cmcm
64 Cmce
65 Cmmm
66 Cccm
67 Cmme
68 Ccce
20 mmmF 69 Fmmm
70 Fddd
21 mmmI 71 Immm
72 Ibam
73 Ibca
74 Imma
Tetragonal 4 22 4P 75 P4
76 [P4_1]
77 [P4_2]
78 [P4_3]
23 4I 79 I4
80 [I4_1]
[\bar4] 24 [\bar4P] 81 [P\bar4]
25 [\bar4I] 82 [I\bar4]
4/m 26 4/mP 83 [P4/m]
84 [P4_2/m]
85 [P4/n]
86 [P4_2/n]
27 4/mI 87 [I4/m]
88 [I4_1/a]
422 28 422P 89 P422
90 [P42_12]
91 [P4_122]
92 [P4_12_12]
93 [P4_222]
94 [P4_22_12]
95 [P4_322]
96 [P4_32_12]
29 422I 97 [I422]
98 [I4_122]
4mm 30 4mmP 99 [P4mm]
100 [P4bm]
101 [P4_2cm]
102 [P4_2nm]
103 [P4cc]
104 [P4nc]
105 [P4_2mc]
106 [P4_2bc]
31 4mmI 107 [I4mm]
108 [I4cm]
109 [I4_1md]
110 [I4_1cd]
[\bar4m] 32 [\bar42mP] 111 [P\bar42m]
112 [P\bar42c]
113 [P\bar42_1m]
114 [P\bar42_1c]
33 [\bar4m2P] 115 [P\bar4m2]
116 [P\bar4c2]
117 [P\bar4b2]
118 [P\bar4n2]
34 [\bar4m2I] 119 [I\bar4m2]
120 [I\bar4c2]
35 [\bar42mI] 121 [I\bar42m]
122 [I\bar42d]
4/mmm 36 4/mmmP 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 [P4_2/mmc]
132 [P4_2/mcm]
133 [P4_2/nbc]
134 [P4_2/nnm]
135 [P4_2/mbc]
136 [P4_2/mnm]
137 [P4_2/nmc]
138 [P4_2/ncm]
37 4/mmmI 139 I4/mmm
140 I4/mcm
141 [I4_1/amd]
142 [I4_1/acd]
Trigonal 3 38 3P 143 P3
144 [P3_1]
145 [P3_2]
39 3R 146 R3
[\bar3] 40 [\bar3P] 147 [P\bar3]
41 [\bar3R] 148 [R\bar3]
32 42 312P 149 P312
151 [P3_112]
153 [P3_212]
43 321P 150 P321
152 [P3_121]
154 [P3_221]
44 32R 155 R32
3m 45 3m1P 156 [P3m1]
158 [P3c1]
46 31mP 157 [P31m]
159 [P31c]
47 3mR 160 [R3m]
161 [R3c]
[\bar3m] 48 [\bar31mP] 162 [P\bar31m]
163 [P\bar31c]
49 [\bar3m1P] 164 [P\bar3m1]
165 [P\bar3c1]
50 [\bar3mR] 166 [R\bar3m]
167 [R\bar3c]
Hexagonal 6 51 6P 168 P6
169 [P6_1]
170 [P6_5]
171 [P6_2]
172 [P6_4]
173 [P6_3]
[\bar6] 52 [\bar6P] 174 [P\bar6]
6/m 53 6/mP 175 [P6/m]
176 [P6_3/m]
622 54 622P 177 [P622]
178 [P6_122]
179 [P6_522]
180 [P6_222]
181 [P6_422]
182 [P6_322]
6mm 55 6mmP 183 P6mm
184 [P6cc]
185 [P6_3cm]
186 [P6_3mc]
[\bar6m] 56 [\bar6m2P] 187 [P\bar6m2]
188 [P\bar6c2]
57 [\bar62mP] 189 [P\bar62m]
190 [P\bar62c]
6/mmm 58 6/mmmP 191 [P6/mmm]
192 [P6/mmc]
193 [P6_3/mcm]
194 [P6_3/mmc]
Cubic 23 59 23P 195 P23
198 [P2_13]
60 23F 196 F23
61 23I 197 I23
199 [I2_13]
[m\bar3] 62 [m\bar3P] 200 [Pm\bar3]
201 [Pn\bar3]
205 [Pa\bar3]
63 [m\bar3F] 202 [Fm\bar3]
203 [Fd\bar3]
64 [m\bar3I] 204 [Im\bar3]
206 [Ia\bar3]
432 65 432P 207 P432
208 [P4_232]
213 [P4_132]
212 [P4_332]
66 432F 209 [F432]
210 [F4_132]
67 432I 211 I432
214 [I4_132]
[\bar43m] 68 [\bar43mP] 215 [P\bar43m]
218 [P\bar43n]
69 [\bar43mF] 216 [F\bar43m]
219 [F\bar43c]
70 [\bar43mI] 217 [I\bar43m]
220 [I\bar43d]
[m\bar3m] 71 [m\bar3mP] 221 [Pm\bar3m]
222 [Pn\bar3n]
223 [Pm\bar3n]
224 [Pn\bar3m]
72 [m\bar3mF] 225 [Fm\bar3m]
226 [Fm\bar3c]
227 [Fd\bar3m]
228 [Fd\bar3c]
73 [m\bar3mI] 229 [Im\bar3m]
230 [Ia\bar3d]