Table of Space Group Symbols
Click over the group name to see the group generators
1
P 1
2
P -1
3
P 2:
unique axis b
P 2:
unique axis c
4
P 2
1
:
unique axis b
P 2
1
:
unique axis c
5
C 2:
unique axis b
C 2:
unique axis c
6
P m:
unique axis b
P m:
unique axis c
7
P c:
unique axis b
P c:
unique axis c
8
C m:
unique axis b
C m:
unique axis c
9
C c:
unique axis b
C c:
unique axis c
10
P 2/m:
unique axis b
P 2/m:
unique axis c
11
P 2
1
/m:
unique axis b
P 2
1
/m:
unique axis c
12
C 2/m:
unique axis b
C 2/m:
unique axis c
13
P 2/c:
unique axis b
P 2/c:
unique axis c
14
P 2
1
/c:
unique axis b
P 2
1
/c:
unique axis c
15
C 2/c:
unique axis b
C 2/c:
unique axis c
16
P 2 2 2
17
P 2 2 2
1
18
P 2
1
2
1
2
19
P 2
1
2
1
2
1
20
C 2 2 2
1
21
C 2 2 2
22
F 2 2 2
23
I 2 2 2
24
I 2
1
2
1
2
1
25
P m m 2
26
P m c 2
1
27
P c c 2
28
P m a 2
29
P c a 2
1
30
P n c 2
31
P m n 2
1
32
P b a 2
33
P n a 2
1
34
P n n 2
35
C m m 2
36
C m c 2
1
37
C c c 2
38
A m m 2
39
A b m 2
40
A m a 2
41
A b a 2
42
F m m 2
43
F d d 2
44
I m m 2
45
I b a 2
46
I m a 2
47
P m m m
48
P n n n:
origin choice 1
P n n n:
origin choice 2
49
P c c m
50
P b a n:
origin choice 1
P b a n:
origin choice 2
51
P m m a
52
P n n a
53
P m n a
54
P c c a
55
P b a m
56
P c c n
57
P b c m
58
P n n m
59
P m m n:
origin choice 1
P m m n:
origin choice 2
60
P b c n
61
P b c a
62
P n m a
63
C m c m
64
C m c a
65
C m m m
66
C c c m
67
C m m a
68
C c c a:
origin choice 1
C c c a:
origin choice 2
69
F m m m
70
F d d d:
origin choice 1
F d d d:
origin choice 2
71
I m m m
72
I b a m
73
I b c a
74
I m m a
75
P 4
76
P 4
1
77
P 4
2
78
P 4
3
79
I 4
80
I 4
1
81
P -4
82
I -4
83
P 4/m
84
P 4
2
/m
85
P 4/n:
origin choice 1
P 4/n:
origin choice 2
86
P 4
2
/n:
origin choice 1
P 4
2
/n:
origin choice 2
87
I 4/m
88
I 4
1
/a:
origin choice 1
I 4
1
/a:
origin choice 2
89
P 4 2 2
90
P 4 2
1
2
91
P 4
1
2 2
92
P 4
1
2
1
2
93
P 4
2
2 2
94
P 4
2
2
1
2
95
P 4
3
2 2
96
P 4
3
2
1
2
97
I 4 2 2
98
I 4
1
2 2
99
P 4 m m
100
P 4 b m
101
P 4
2
c m
102
P 4
2
n m
103
P 4 c c
104
P 4 n c
105
P 4
2
m c
106
P 4
2
b c
107
I 4 m m
108
I 4 c m
109
I 4
1
m d
110
I 4
1
c d
111
P -4 2 m
112
P -4 2 c
113
P -4 2
1
m
114
P -4 2
1
c
115
P -4 m 2
116
P -4 c 2
117
P -4 b 2
118
P -4 n 2
119
I -4 m 2
120
I -4 c 2
121
I -4 2 m
122
I -4 2 d
123
P 4/m m m
124
P 4/m c c
125
P 4/n b m:
origin choice 1
P 4/n b m:
origin choice 2
126
P 4/n n c:
origin choice 1
P 4/n n c:
origin choice 2
127
P 4/m b m
128
P 4/m n c
129
P 4/n m m:
origin choice 1
P 4/n m m:
origin choice 2
130
P 4/n c c:
origin choice 1
P 4/n c c:
origin choice 2
131
P 4
2
/m m c
132
P 4
2
/m c m
133
P 4
2
/n b c:
origin choice 1
P 4
2
/n b c:
origin choice 2
134
P 4
2
/n n m:
origin choice 1
P 4
2
/n n m:
origin choice 2
135
P 4
2
/m b c
136
P 4
2
/m n m
137
P 4
2
/n m c:
origin choice 1
P 4
2
/n m c:
origin choice 2
138
P 4
2
/n c m:
origin choice 1
P 4
2
/n c m:
origin choice 2
139
I 4/m m m
140
I 4/m c m
141
I 4
1
/a m d:
origin choice 1
I 4
1
/a m d:
origin choice 2
142
I 4
1
/a c d:
origin choice 1
I 4
1
/a c d:
origin choice 2
143
P 3
144
P 3
1
145
P 3
2
146
R 3:
rhombohedral axes
R 3:
hexagonal axes
147
P -3
148
R -3:
rhombohedral axes
R -3:
hexagonal axes
149
P 3 1 2
150
P 3 2 1
151
P 3
1
1 2
152
P 3
1
2 1
153
P 3
2
1 2
154
P 3
2
2 1
155
R 3 2:
rhombohedral axes
R 3 2:
hexagonal axes
156
P 3 m 1
157
P 3 1 m
158
P 3 c 1
159
P 3 1 c
160
R 3 m:
rhombohedral axes
R 3 m:
hexagonal axes
161
R 3 c:
rhombohedral axes
R 3 c:
hexagonal axes
162
P -3 1 m
163
P -3 1 c
164
P -3 m 1
165
P -3 c 1
166
R -3 m:
rhombohedral axes
R -3 m:
hexagonal axes
167
R -3 c:
rhombohedral axes
R -3 c:
hexagonal axes
168
P 6
169
P 6
1
170
P 6
5
171
P 6
2
172
P 6
4
173
P 6
3
174
P -6
175
P 6/m
176
P 6
3
/m
177
P 6 2 2
178
P 6
1
2 2
179
P 6
5
2 2
180
P 6
2
2 2
181
P 6
4
2 2
182
P 6
3
2 2
183
P 6 m m
184
P 6 c c
185
P 6
3
c m
186
P 6
3
m c
187
P -6 m 2
188
P -6 c 2
189
P -6 2 m
190
P -6 2 c
191
P 6/m m m
192
P 6/m c c
193
P 6
3
/m c m
194
P 6
3
/m m c
195
P 2 3
196
F 2 3
197
I 2 3
198
P 2
1
3
199
I 2
1
3
200
P m -3
201
P n -3:
origin choice 1
P n -3:
origin choice 2
202
F m -3
203
F d -3:
origin choice 1
F d -3:
origin choice 2
204
I m -3
205
P a -3
206
I a -3
207
P 4 3 2
208
P 4
2
3 2
209
F 4 3 2
210
F 4
1
3 2
211
I 4 3 2
212
P 4
3
3 2
213
P 4
1
3 2
214
I 4
1
3 2
215
P -4 3 m
216
F -4 3 m
217
I -4 3 m
218
P -4 3 n
219
F -4 3 c
220
I -4 3 d
221
P m -3 m
222
P n -3 n:
origin choice 1
P n -3 n:
origin choice 2
223
P m -3 n
224
P n -3 m:
origin choice 1
P n -3 m:
origin choice 2
225
F m -3 m
226
F m -3 c
227
F d -3 m:
origin choice 1
F d -3 m:
origin choice 2
228
F d -3 c:
origin choice 1
F d -3 c:
origin choice 2
229
I m -3 m
230
I a -3 d
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