Invariants
Find invariant polynomials of components of an order parameter associated with an irreducible representation of a space group.
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Step 1
Choose a space group:
1 P1 C1-1
2 P-1 Ci-1
3 P2 C2-1
4 P2_1 C2-2
5 C2 C2-3
6 Pm Cs-1
7 Pc Cs-2
8 Cm Cs-3
9 Cc Cs-4
10 P2/m C2h-1
11 P2_1/m C2h-2
12 C2/m C2h-3
13 P2/c C2h-4
14 P2_1/c C2h-5
15 C2/c C2h-6
16 P222 D2-1
17 P222_1 D2-2
18 P2_12_12 D2-3
19 P2_12_12_1 D2-4
20 C222_1 D2-5
21 C222 D2-6
22 F222 D2-7
23 I222 D2-8
24 I2_12_12_1 D2-9
25 Pmm2 C2v-1
26 Pmc2_1 C2v-2
27 Pcc2 C2v-3
28 Pma2 C2v-4
29 Pca2_1 C2v-5
30 Pnc2 C2v-6
31 Pmn2_1 C2v-7
32 Pba2 C2v-8
33 Pna2_1 C2v-9
34 Pnn2 C2v-10
35 Cmm2 C2v-11
36 Cmc2_1 C2v-12
37 Ccc2 C2v-13
38 Amm2 C2v-14
39 Abm2 C2v-15
40 Ama2 C2v-16
41 Aba2 C2v-17
42 Fmm2 C2v-18
43 Fdd2 C2v-19
44 Imm2 C2v-20
45 Iba2 C2v-21
46 Ima2 C2v-22
47 Pmmm D2h-1
48 Pnnn D2h-2
49 Pccm D2h-3
50 Pban D2h-4
51 Pmma D2h-5
52 Pnna D2h-6
53 Pmna D2h-7
54 Pcca D2h-8
55 Pbam D2h-9
56 Pccn D2h-10
57 Pbcm D2h-11
58 Pnnm D2h-12
59 Pmmn D2h-13
60 Pbcn D2h-14
61 Pbca D2h-15
62 Pnma D2h-16
63 Cmcm D2h-17
64 Cmca D2h-18
65 Cmmm D2h-19
66 Cccm D2h-20
67 Cmma D2h-21
68 Ccca D2h-22
69 Fmmm D2h-23
70 Fddd D2h-24
71 Immm D2h-25
72 Ibam D2h-26
73 Ibca D2h-27
74 Imma D2h-28
75 P4 C4-1
76 P4_1 C4-2
77 P4_2 C4-3
78 P4_3 C4-4
79 I4 C4-5
80 I4_1 C4-6
81 P-4 S4-1
82 I-4 S4-2
83 P4/m C4h-1
84 P4_2/m C4h-2
85 P4/n C4h-3
86 P4_2/n C4h-4
87 I4/m C4h-5
88 I4_1/a C4h-6
89 P422 D4-1
90 P42_12 D4-2
91 P4_122 D4-3
92 P4_12_12 D4-4
93 P4_222 D4-5
94 P4_22_12 D4-6
95 P4_322 D4-7
96 P4_32_12 D4-8
97 I422 D4-9
98 I4_122 D4-10
99 P4mm C4v-1
100 P4bm C4v-2
101 P4_2cm C4v-3
102 P4_2nm C4v-4
103 P4cc C4v-5
104 P4nc C4v-6
105 P4_2mc C4v-7
106 P4_2bc C4v-8
107 I4mm C4v-9
108 I4cm C4v-10
109 I4_1md C4v-11
110 I4_1cd C4v-12
111 P-42m D2d-1
112 P-42c D2d-2
113 P-42_1m D2d-3
114 P-42_1c D2d-4
115 P-4m2 D2d-5
116 P-4c2 D2d-6
117 P-4b2 D2d-7
118 P-4n2 D2d-8
119 I-4m2 D2d-9
120 I-4c2 D2d-10
121 I-42m D2d-11
122 I-42d D2d-12
123 P4/mmm D4h-1
124 P4/mcc D4h-2
125 P4/nbm D4h-3
126 P4/nnc D4h-4
127 P4/mbm D4h-5
128 P4/mnc D4h-6
129 P4/nmm D4h-7
130 P4/ncc D4h-8
131 P4_2/mmc D4h-9
132 P4_2/mcm D4h-10
133 P4_2/nbc D4h-11
134 P4_2/nnm D4h-12
135 P4_2/mbc D4h-13
136 P4_2/mnm D4h-14
137 P4_2/nmc D4h-15
138 P4_2/ncm D4h-16
139 I4/mmm D4h-17
140 I4/mcm D4h-18
141 I4_1/amd D4h-19
142 I4_1/acd D4h-20
143 P3 C3-1
144 P3_1 C3-2
145 P3_2 C3-3
146 R3 C3-4
147 P-3 C3i-1
148 R-3 C3i-2
149 P312 D3-1
150 P321 D3-2
151 P3_112 D3-3
152 P3_121 D3-4
153 P3_212 D3-5
154 P3_221 D3-6
155 R32 D3-7
156 P3m1 C3v-1
157 P31m C3v-2
158 P3c1 C3v-3
159 P31c C3v-4
160 R3m C3v-5
161 R3c C3v-6
162 P-31m D3d-1
163 P-31c D3d-2
164 P-3m1 D3d-3
165 P-3c1 D3d-4
166 R-3m D3d-5
167 R-3c D3d-6
168 P6 C6-1
169 P6_1 C6-2
170 P6_5 C6-3
171 P6_2 C6-4
172 P6_4 C6-5
173 P6_3 C6-6
174 P-6 C3h-1
175 P6/m C6h-1
176 P6_3/m C6h-2
177 P622 D6-1
178 P6_122 D6-2
179 P6_522 D6-3
180 P6_222 D6-4
181 P6_422 D6-5
182 P6_322 D6-6
183 P6mm C6v-1
184 P6cc C6v-2
185 P6_3cm C6v-3
186 P6_3mc C6v-4
187 P-6m2 D3h-1
188 P-6c2 D3h-2
189 P-62m D3h-3
190 P-62c D3h-4
191 P6/mmm D6h-1
192 P6/mcc D6h-2
193 P6_3/mcm D6h-3
194 P6_3/mmc D6h-4
195 P23 T-1
196 F23 T-2
197 I23 T-3
198 P2_13 T-4
199 I2_13 T-5
200 Pm-3 Th-1
201 Pn-3 Th-2
202 Fm-3 Th-3
203 Fd-3 Th-4
204 Im-3 Th-5
205 Pa-3 Th-6
206 Ia-3 Th-7
207 P432 O-1
208 P4_232 O-2
209 F432 O-3
210 F4_132 O-4
211 I432 O-5
212 P4_332 O-6
213 P4_132 O-7
214 I4_132 O-8
215 P-43m Td-1
216 F-43m Td-2
217 I-43m Td-3
218 P-43n Td-4
219 F-43c Td-5
220 I-43d Td-6
221 Pm-3m Oh-1
222 Pn-3n Oh-2
223 Pm-3n Oh-3
224 Pn-3m Oh-4
225 Fm-3m Oh-5
226 Fm-3c Oh-6
227 Fd-3m Oh-7
228 Fd-3c Oh-8
229 Im-3m Oh-9
230 Ia-3d Oh-10