Group information

Group information#

Overview#

  • Group information

    • Point group : PDF

    • Space group : PDF

    • Magnetic point group : PDF

    • Magnetic space group : PDF

    • Compatibility relation : PDF

    • Active multipole : PDF

  • Atomic multipole

    • JML basis : PDF

    • LM basis : PDF

  • Harmonics (in terms of tesseral harmonics)

    • \(D_{\rm 6h}\)

    • \(O_{\rm h}\)

Point group#

tag

1: \(C_{\rm 1}\) (\(1\))

2: \(C_{\rm i}\) (\(\bar{1}\))

3: \(C_{\rm 2}\) (\(2\))

4: \(C_{\rm s}\) (\(m\))

5: \(C_{\rm 2h}\) (\(2/m\))

6: \(D_{\rm 2}\) (\(222\))

7: \(C_{\rm 2v}\) (\(mm2\))

8: \(D_{\rm 2h}\) (\(mmm\))

9: \(C_{\rm 4}\) (\(4\))

10: \(S_{\rm 4}\) (\(\bar{4}\))

11: \(C_{\rm 4h}\) (\(4/m\))

12: \(D_{\rm 4}\) (\(422\))

13: \(C_{\rm 4v}\) (\(4mm\))

14: \(D_{\rm 2d}\) (\(\bar{4}2m\))

15: \(D_{\rm 4h}\) (\(4/mmm\))

16: \(C_{\rm 3}\) (\(3\))

17: \(C_{\rm 3i}\) (\(\bar{3}\))

18: \(D_{\rm 3}\) (\(32\))

19: \(C_{\rm 3v}\) (\(3m\))

20: \(D_{\rm 3d}\) (\(\bar{3}m\))

21: \(C_{\rm 6}\) (\(6\))

22: \(C_{\rm 3h}\) (\(\bar{6}\))

23: \(C_{\rm 6h}\) (\(6/m\))

24: \(D_{\rm 6}\) (\(622\))

25: \(C_{\rm 6v}\) (\(6mm\))

26: \(D_{\rm 3h}\) (\(\bar{6}m2\))

27: \(D_{\rm 6h}\) (\(6/mmm\))

28: \(T_{\rm }\) (\(23\))

29: \(T_{\rm h}\) (\(m\bar{3}\))

30: \(O_{\rm }\) (\(432\))

31: \(T_{\rm d}\) (\(\bar{4}3m\))

32: \(O_{\rm h}\) (\(m\bar{3}m\))

33: \(D_{\rm 2d}(1)\) (\(\bar{4}2m\))

34: \(D_{\rm 3}(1)\) (\(32\))

35: \(C_{\rm 3v}(1)\) (\(3m\))

36: \(D_{\rm 3d}(1)\) (\(\bar{3}m\))

37: \(D_{\rm 3h}(1)\) (\(\bar{6}m2\))

38: \(C_{\rm 4}(c)\) (\(4\))

39: \(S_{\rm 4}(c)\) (\(\bar{4}\))

40: \(C_{\rm 4h}(c)\) (\(4/m\))

41: \(C_{\rm 3}(c)\) (\(3\))

42: \(C_{\rm 3i}(c)\) (\(\bar{3}\))

43: \(C_{\rm 6}(c)\) (\(6\))

44: \(C_{\rm 3h}(c)\) (\(\bar{6}\))

45: \(C_{\rm 6h}(c)\) (\(6/m\))

46: \(T_{\rm }(c)\) (\(23\))

47: \(T_{\rm h}(c)\) (\(m\bar{3}\))

Space group#

tag

1: \(C_{\rm 1}^{1}\) (\(P1\))

2: \(C_{\rm i}^{1}\) (\(P\bar{1}\))

3: \(C_{\rm 2}^{1}\) (\(P2\))

4: \(C_{\rm 2}^{2}\) (\(P2_1\))

5: \(C_{\rm 2}^{3}\) (\(C2\))

6: \(C_{\rm s}^{1}\) (\(Pm\))

7: \(C_{\rm s}^{2}\) (\(Pc\))

8: \(C_{\rm s}^{3}\) (\(Cm\))

9: \(C_{\rm s}^{4}\) (\(Cc\))

10: \(C_{\rm 2h}^{1}\) (\(P2/m\))

11: \(C_{\rm 2h}^{2}\) (\(P2_1/m\))

12: \(C_{\rm 2h}^{3}\) (\(C2/m\))

13: \(C_{\rm 2h}^{4}\) (\(P2/c\))

14: \(C_{\rm 2h}^{5}\) (\(P2_1/c\))

15: \(C_{\rm 2h}^{6}\) (\(C2/c\))

16: \(D_{\rm 2}^{1}\) (\(P222\))

17: \(D_{\rm 2}^{2}\) (\(P222_1\))

18: \(D_{\rm 2}^{3}\) (\(P2_12_12\))

19: \(D_{\rm 2}^{4}\) (\(P2_12_12_1\))

20: \(D_{\rm 2}^{5}\) (\(C222_1\))

21: \(D_{\rm 2}^{6}\) (\(C222\))

22: \(D_{\rm 2}^{7}\) (\(F222\))

23: \(D_{\rm 2}^{8}\) (\(I222\))

24: \(D_{\rm 2}^{9}\) (\(I2_12_12_1\))

25: \(C_{\rm 2v}^{1}\) (\(Pmm2\))

26: \(C_{\rm 2v}^{2}\) (\(Pmc2_1\))

27: \(C_{\rm 2v}^{3}\) (\(Pcc2\))

28: \(C_{\rm 2v}^{4}\) (\(Pma2\))

29: \(C_{\rm 2v}^{5}\) (\(Pca2_1\))

30: \(C_{\rm 2v}^{6}\) (\(Pnc2\))

31: \(C_{\rm 2v}^{7}\) (\(Pmn2_1\))

32: \(C_{\rm 2v}^{8}\) (\(Pba2\))

33: \(C_{\rm 2v}^{9}\) (\(Pna2_1\))

34: \(C_{\rm 2v}^{10}\) (\(Pnn2\))

35: \(C_{\rm 2v}^{11}\) (\(Cmm2\))

36: \(C_{\rm 2v}^{12}\) (\(Cmc2_1\))

37: \(C_{\rm 2v}^{13}\) (\(Ccc2\))

38: \(C_{\rm 2v}^{14}\) (\(Amm2\))

39: \(C_{\rm 2v}^{15}\) (\(Aem2\))

40: \(C_{\rm 2v}^{16}\) (\(Ama2\))

41: \(C_{\rm 2v}^{17}\) (\(Aea2\))

42: \(C_{\rm 2v}^{18}\) (\(Fmm2\))

43: \(C_{\rm 2v}^{19}\) (\(Fdd2\))

44: \(C_{\rm 2v}^{20}\) (\(Imm2\))

45: \(C_{\rm 2v}^{21}\) (\(Iba2\))

46: \(C_{\rm 2v}^{22}\) (\(Ima2\))

47: \(D_{\rm 2h}^{1}\) (\(Pmmm\))

48: \(D_{\rm 2h}^{2}\) (\(Pnnn\))

49: \(D_{\rm 2h}^{3}\) (\(Pccm\))

50: \(D_{\rm 2h}^{4}\) (\(Pban\))

51: \(D_{\rm 2h}^{5}\) (\(Pmma\))

52: \(D_{\rm 2h}^{6}\) (\(Pnna\))

53: \(D_{\rm 2h}^{7}\) (\(Pmna\))

54: \(D_{\rm 2h}^{8}\) (\(Pcca\))

55: \(D_{\rm 2h}^{9}\) (\(Pbam\))

56: \(D_{\rm 2h}^{10}\) (\(Pccn\))

57: \(D_{\rm 2h}^{11}\) (\(Pbcm\))

58: \(D_{\rm 2h}^{12}\) (\(Pnnm\))

59: \(D_{\rm 2h}^{13}\) (\(Pmmn\))

60: \(D_{\rm 2h}^{14}\) (\(Pbcn\))

61: \(D_{\rm 2h}^{15}\) (\(Pbca\))

62: \(D_{\rm 2h}^{16}\) (\(Pnma\))

63: \(D_{\rm 2h}^{17}\) (\(Cmcm\))

64: \(D_{\rm 2h}^{18}\) (\(Cmce\))

65: \(D_{\rm 2h}^{19}\) (\(Cmmm\))

66: \(D_{\rm 2h}^{20}\) (\(Cccm\))

67: \(D_{\rm 2h}^{21}\) (\(Cmme\))

68: \(D_{\rm 2h}^{22}\) (\(Ccce\))

69: \(D_{\rm 2h}^{23}\) (\(Fmmm\))

70: \(D_{\rm 2h}^{24}\) (\(Fddd\))

71: \(D_{\rm 2h}^{25}\) (\(Immm\))

72: \(D_{\rm 2h}^{26}\) (\(Ibam\))

73: \(D_{\rm 2h}^{27}\) (\(Ibca\))

74: \(D_{\rm 2h}^{28}\) (\(Imma\))

75: \(C_{\rm 4}^{1}\) (\(P4\))

76: \(C_{\rm 4}^{2}\) (\(P4_1\))

77: \(C_{\rm 4}^{3}\) (\(P4_2\))

78: \(C_{\rm 4}^{4}\) (\(P4_3\))

79: \(C_{\rm 4}^{5}\) (\(I4\))

80: \(C_{\rm 4}^{6}\) (\(I4_1\))

81: \(S_{\rm 4}^{1}\) (\(P\bar{4}\))

82: \(S_{\rm 4}^{2}\) (\(I\bar{4}\))

83: \(C_{\rm 4h}^{1}\) (\(P4/m\))

84: \(C_{\rm 4h}^{2}\) (\(P4_2/m\))

85: \(C_{\rm 4h}^{3}\) (\(P4/n\))

86: \(C_{\rm 4h}^{4}\) (\(P4_2/n\))

87: \(C_{\rm 4h}^{5}\) (\(I4/m\))

88: \(C_{\rm 4h}^{6}\) (\(I4_1/a\))

89: \(D_{\rm 4}^{1}\) (\(P422\))

90: \(D_{\rm 4}^{2}\) (\(P42_12\))

91: \(D_{\rm 4}^{3}\) (\(P4_122\))

92: \(D_{\rm 4}^{4}\) (\(P4_12_12\))

93: \(D_{\rm 4}^{5}\) (\(P4_222\))

94: \(D_{\rm 4}^{6}\) (\(P4_22_12\))

95: \(D_{\rm 4}^{7}\) (\(P4_322\))

96: \(D_{\rm 4}^{8}\) (\(P4_32_12\))

97: \(D_{\rm 4}^{9}\) (\(I422\))

98: \(D_{\rm 4}^{10}\) (\(I4_122\))

99: \(C_{\rm 4v}^{1}\) (\(P4mm\))

100: \(C_{\rm 4v}^{2}\) (\(P4bm\))

101: \(C_{\rm 4v}^{3}\) (\(P4_2cm\))

102: \(C_{\rm 4v}^{4}\) (\(P4_2nm\))

103: \(C_{\rm 4v}^{5}\) (\(P4cc\))

104: \(C_{\rm 4v}^{6}\) (\(P4nc\))

105: \(C_{\rm 4v}^{7}\) (\(P4_2mc\))

106: \(C_{\rm 4v}^{8}\) (\(P4_2bc\))

107: \(C_{\rm 4v}^{9}\) (\(I4mm\))

108: \(C_{\rm 4v}^{10}\) (\(I4cm\))

109: \(C_{\rm 4v}^{11}\) (\(I4_1md\))

110: \(C_{\rm 4v}^{12}\) (\(I4_1cd\))

111: \(D_{\rm 2d}^{1}\) (\(P\bar{4}2m\))

112: \(D_{\rm 2d}^{2}\) (\(P\bar{4}2c\))

113: \(D_{\rm 2d}^{3}\) (\(P\bar{4}2_1m\))

114: \(D_{\rm 2d}^{4}\) (\(P\bar{4}2_1c\))

115: \(D_{\rm 2d}^{5}\) (\(P\bar{4}m2\))

116: \(D_{\rm 2d}^{6}\) (\(P\bar{4}c2\))

117: \(D_{\rm 2d}^{7}\) (\(P\bar{4}b2\))

118: \(D_{\rm 2d}^{8}\) (\(P\bar{4}n2\))

119: \(D_{\rm 2d}^{9}\) (\(I\bar{4}m2\))

120: \(D_{\rm 2d}^{10}\) (\(I\bar{4}c2\))

121: \(D_{\rm 2d}^{11}\) (\(I\bar{4}2m\))

122: \(D_{\rm 2d}^{12}\) (\(I\bar{4}2d\))

123: \(D_{\rm 4h}^{1}\) (\(P4/mmm\))

124: \(D_{\rm 4h}^{2}\) (\(P4/mcc\))

125: \(D_{\rm 4h}^{3}\) (\(P4/nbm\))

126: \(D_{\rm 4h}^{4}\) (\(P4/nnc\))

127: \(D_{\rm 4h}^{5}\) (\(P4/mbm\))

128: \(D_{\rm 4h}^{6}\) (\(P4/mnc\))

129: \(D_{\rm 4h}^{7}\) (\(P4/nmm\))

130: \(D_{\rm 4h}^{8}\) (\(P4/ncc\))

131: \(D_{\rm 4h}^{9}\) (\(P4_2/mmc\))

132: \(D_{\rm 4h}^{10}\) (\(P4_2/mcm\))

133: \(D_{\rm 4h}^{11}\) (\(P4_2/nbc\))

134: \(D_{\rm 4h}^{12}\) (\(P4_2/nnm\))

135: \(D_{\rm 4h}^{13}\) (\(P4_2/mbc\))

136: \(D_{\rm 4h}^{14}\) (\(P4_2/mnm\))

137: \(D_{\rm 4h}^{15}\) (\(P4_2/nmc\))

138: \(D_{\rm 4h}^{16}\) (\(P4_2/ncm\))

139: \(D_{\rm 4h}^{17}\) (\(I4/mmm\))

140: \(D_{\rm 4h}^{18}\) (\(I4/mcm\))

141: \(D_{\rm 4h}^{19}\) (\(I4_1/amd\))

142: \(D_{\rm 4h}^{20}\) (\(I4_1/acd\))

143: \(C_{\rm 3}^{1}\) (\(P3\))

144: \(C_{\rm 3}^{2}\) (\(P3_1\))

145: \(C_{\rm 3}^{3}\) (\(P3_2\))

146: \(C_{\rm 3}^{4}\) (\(R3\))

147: \(C_{\rm 3i}^{1}\) (\(P\bar{3}\))

148: \(C_{\rm 3i}^{2}\) (\(R\bar{3}\))

149: \(D_{\rm 3}^{1}\) (\(P312\))

150: \(D_{\rm 3}^{2}\) (\(P321\))

151: \(D_{\rm 3}^{3}\) (\(P3_112\))

152: \(D_{\rm 3}^{4}\) (\(P3_121\))

153: \(D_{\rm 3}^{5}\) (\(P3_212\))

154: \(D_{\rm 3}^{6}\) (\(P3_221\))

155: \(D_{\rm 3}^{7}\) (\(R32\))

156: \(C_{\rm 3v}^{1}\) (\(P3m1\))

157: \(C_{\rm 3v}^{2}\) (\(P31m\))

158: \(C_{\rm 3v}^{3}\) (\(P3c1\))

159: \(C_{\rm 3v}^{4}\) (\(P31c\))

160: \(C_{\rm 3v}^{5}\) (\(R3m\))

161: \(C_{\rm 3v}^{6}\) (\(R3c\))

162: \(D_{\rm 3d}^{1}\) (\(P\bar{3}1m\))

163: \(D_{\rm 3d}^{2}\) (\(P\bar{3}1c\))

164: \(D_{\rm 3d}^{3}\) (\(P\bar{3}m1\))

165: \(D_{\rm 3d}^{4}\) (\(P\bar{3}c1\))

166: \(D_{\rm 3d}^{5}\) (\(R\bar{3}m\))

167: \(D_{\rm 3d}^{6}\) (\(R\bar{3}c\))

168: \(C_{\rm 6}^{1}\) (\(P6\))

169: \(C_{\rm 6}^{2}\) (\(P6_1\))

170: \(C_{\rm 6}^{3}\) (\(P6_5\))

171: \(C_{\rm 6}^{4}\) (\(P6_2\))

172: \(C_{\rm 6}^{5}\) (\(P6_4\))

173: \(C_{\rm 6}^{6}\) (\(P6_3\))

174: \(C_{\rm 3h}^{1}\) (\(P\bar{6}\))

175: \(C_{\rm 6h}^{1}\) (\(P6/m\))

176: \(C_{\rm 6h}^{2}\) (\(P6_3/m\))

177: \(D_{\rm 6}^{1}\) (\(P622\))

178: \(D_{\rm 6}^{2}\) (\(P6_122\))

179: \(D_{\rm 6}^{3}\) (\(P6_522\))

180: \(D_{\rm 6}^{4}\) (\(P6_222\))

181: \(D_{\rm 6}^{5}\) (\(P6_422\))

182: \(D_{\rm 6}^{6}\) (\(P6_322\))

183: \(C_{\rm 6v}^{1}\) (\(P6mm\))

184: \(C_{\rm 6v}^{2}\) (\(P6cc\))

185: \(C_{\rm 6v}^{3}\) (\(P6_3cm\))

186: \(C_{\rm 6v}^{4}\) (\(P6_3mc\))

187: \(D_{\rm 3h}^{1}\) (\(P\bar{6}m2\))

188: \(D_{\rm 3h}^{2}\) (\(P\bar{6}c2\))

189: \(D_{\rm 3h}^{3}\) (\(P\bar{6}2m\))

190: \(D_{\rm 3h}^{4}\) (\(P\bar{6}2c\))

191: \(D_{\rm 6h}^{1}\) (\(P6/mmm\))

192: \(D_{\rm 6h}^{2}\) (\(P6/mcc\))

193: \(D_{\rm 6h}^{3}\) (\(P6_3/mcm\))

194: \(D_{\rm 6h}^{4}\) (\(P6_3/mmc\))

195: \(T_{\rm }^{1}\) (\(P23\))

196: \(T_{\rm }^{2}\) (\(F23\))

197: \(T_{\rm }^{3}\) (\(I23\))

198: \(T_{\rm }^{4}\) (\(P2_13\))

199: \(T_{\rm }^{5}\) (\(I2_13\))

200: \(T_{\rm h}^{1}\) (\(Pm\bar{3}\))

201: \(T_{\rm h}^{2}\) (\(Pn\bar{3}\))

202: \(T_{\rm h}^{3}\) (\(Fm\bar{3}\))

203: \(T_{\rm h}^{4}\) (\(Fd\bar{3}\))

204: \(T_{\rm h}^{5}\) (\(Im\bar{3}\))

205: \(T_{\rm h}^{6}\) (\(Pa\bar{3}\))

206: \(T_{\rm h}^{7}\) (\(Ia\bar{3}\))

207: \(O_{\rm }^{1}\) (\(P432\))

208: \(O_{\rm }^{2}\) (\(P4_232\))

209: \(O_{\rm }^{3}\) (\(F432\))

210: \(O_{\rm }^{4}\) (\(F4_132\))

211: \(O_{\rm }^{5}\) (\(I432\))

212: \(O_{\rm }^{6}\) (\(P4_332\))

213: \(O_{\rm }^{7}\) (\(P4_132\))

214: \(O_{\rm }^{8}\) (\(I4_132\))

215: \(T_{\rm d}^{1}\) (\(P\bar{4}3m\))

216: \(T_{\rm d}^{2}\) (\(F\bar{4}3m\))

217: \(T_{\rm d}^{3}\) (\(I\bar{4}3m\))

218: \(T_{\rm d}^{4}\) (\(P\bar{4}3n\))

219: \(T_{\rm d}^{5}\) (\(F\bar{4}3c\))

220: \(T_{\rm d}^{6}\) (\(I\bar{4}3d\))

221: \(O_{\rm h}^{1}\) (\(Pm\bar{3}m\))

222: \(O_{\rm h}^{2}\) (\(Pn\bar{3}n\))

223: \(O_{\rm h}^{3}\) (\(Pm\bar{3}n\))

224: \(O_{\rm h}^{4}\) (\(Pn\bar{3}m\))

225: \(O_{\rm h}^{5}\) (\(Fm\bar{3}m\))

226: \(O_{\rm h}^{6}\) (\(Fm\bar{3}c\))

227: \(O_{\rm h}^{7}\) (\(Fd\bar{3}m\))

228: \(O_{\rm h}^{8}\) (\(Fd\bar{3}c\))

229: \(O_{\rm h}^{9}\) (\(Im\bar{3}m\))

230: \(O_{\rm h}^{10}\) (\(Ia\bar{3}d\))

Magnetic point group#

tag

1.1.1: \(1\)

1.2.2: \(11'\)

2.1.3: \(\bar{1}\)

2.2.4: \(\bar{1}1'\)

2.3.5: \(\bar{1}'\)

3.1.6: \(2\)

3.2.7: \(21'\)

3.3.8: \(2'\)

4.1.9: \(m\)

4.2.10: \(m1'\)

4.3.11: \(m'\)

5.1.12: \(2/m\)

5.2.13: \(2/m1'\)

5.3.14: \(2'/m\)

5.4.15: \(2/m'\)

5.5.16: \(2'/m'\)

6.1.17: \(222\)

6.2.18: \(2221'\)

6.3.19: \(2'2'2\)

6.4.123: \(2'2'2\)

7.1.20: \(mm2\)

7.2.21: \(mm21'\)

7.3.22: \(m'm2'\)

7.4.23: \(m'm'2\)

7.5.124: \(m'm2'\)

8.1.24: \(mmm\)

8.2.25: \(mmm1'\)

8.3.26: \(m'mm\)

8.4.27: \(m'm'm\)

8.5.28: \(m'm'm'\)

8.6.125: \(m'mm\)

8.7.126: \(m'mm\)

8.8.127: \(m'm'm\)

8.9.128: \(m'm'm\)

9.1.29: \(4\)

9.2.30: \(41'\)

9.3.31: \(4'\)

10.1.32: \(\bar{4}\)

10.2.33: \(\bar{4}1'\)

10.3.34: \(\bar{4}'\)

11.1.35: \(4/m\)

11.2.36: \(4/m1'\)

11.3.37: \(4'/m\)

11.4.38: \(4/m'\)

11.5.39: \(4'/m'\)

12.1.40: \(422\)

12.2.41: \(4221'\)

12.3.42: \(4'22'\)

12.4.43: \(42'2'\)

12.5.129: \(4'22'\)

13.1.44: \(4mm\)

13.2.45: \(4mm1'\)

13.3.46: \(4'm'm\)

13.4.47: \(4m'm'\)

13.5.130: \(4'm'm\)

14.1.48: \(\bar{4}2m\)

14.2.49: \(\bar{4}2m1'\)

14.3.50: \(\bar{4}'2'm\)

14.4.51: \(\bar{4}'2m'\)

14.5.52: \(\bar{4}2'm'\)

15.1.53: \(4/mmm\)

15.2.54: \(4/mmm1'\)

15.3.55: \(4/m'mm\)

15.4.56: \(4'/mm'm\)

15.5.57: \(4'/m'm'm\)

15.6.58: \(4/mm'm'\)

15.7.59: \(4/m'm'm'\)

15.8.136: \(4'/mm'm\)

15.9.137: \(4'/m'm'm\)

16.1.60: \(3\)

16.2.61: \(31'\)

17.1.62: \(\bar{3}\)

17.2.63: \(\bar{3}1'\)

17.3.64: \(\bar{3}'\)

18.1.65: \(32\)

18.2.66: \(321'\)

18.3.67: \(32'\)

19.1.68: \(3m\)

19.2.69: \(3m1'\)

19.3.70: \(3m'\)

20.1.71: \(\bar{3}m\)

20.2.72: \(\bar{3}m1'\)

20.3.73: \(\bar{3}'m\)

20.4.74: \(\bar{3}'m'\)

20.5.75: \(\bar{3}m'\)

21.1.76: \(6\)

21.2.77: \(61'\)

21.3.78: \(6'\)

22.1.79: \(\bar{6}\)

22.2.80: \(\bar{6}1'\)

22.3.81: \(\bar{6}'\)

23.1.82: \(6/m\)

23.2.83: \(6/m1'\)

23.3.84: \(6'/m\)

23.4.85: \(6/m'\)

23.5.86: \(6'/m'\)

24.1.87: \(622\)

24.2.88: \(6221'\)

24.3.89: \(6'22'\)

24.4.90: \(62'2'\)

24.5.149: \(6'22'\)

25.1.91: \(6mm\)

25.2.92: \(6mm1'\)

25.3.93: \(6'mm'\)

25.4.94: \(6m'm'\)

25.5.150: \(6'mm'\)

26.1.95: \(\bar{6}m2\)

26.2.96: \(\bar{6}m21'\)

26.3.97: \(\bar{6}'m'2\)

26.4.98: \(\bar{6}'m2'\)

26.5.99: \(\bar{6}m'2'\)

27.1.100: \(6/mmm\)

27.2.101: \(6/mmm1'\)

27.3.102: \(6/m'mm\)

27.4.103: \(6'/mmm'\)

27.5.104: \(6'/m'mm'\)

27.6.105: \(6/mm'm'\)

27.7.106: \(6/m'm'm'\)

27.8.156: \(6'/mmm'\)

27.9.157: \(6'/m'mm'\)

28.1.107: \(23\)

28.2.108: \(231'\)

29.1.109: \(m\bar{3}\)

29.2.110: \(m\bar{3}1'\)

29.3.111: \(m'\bar{3}'\)

30.1.112: \(432\)

30.2.113: \(4321'\)

30.3.114: \(4'32'\)

31.1.115: \(\bar{4}3m\)

31.2.116: \(\bar{4}3m1'\)

31.3.117: \(\bar{4}'3m'\)

32.1.118: \(m\bar{3}m\)

32.2.119: \(m\bar{3}m1'\)

32.3.120: \(m'\bar{3}'m\)

32.4.121: \(m\bar{3}m'\)

32.5.122: \(m'\bar{3}'m'\)

33.1.131: \(\bar{4}2m\)

33.2.132: \(\bar{4}2m1'\)

33.3.133: \(\bar{4}'2'm\)

33.4.134: \(\bar{4}'2m'\)

33.5.135: \(\bar{4}2'm'\)

34.1.138: \(32\)

34.2.139: \(321'\)

34.3.140: \(32'\)

35.1.141: \(3m\)

35.2.142: \(3m1'\)

35.3.143: \(3m'\)

36.1.144: \(\bar{3}m\)

36.2.145: \(\bar{3}m1'\)

36.3.146: \(\bar{3}'m\)

36.4.147: \(\bar{3}'m'\)

36.5.148: \(\bar{3}m'\)

37.1.151: \(\bar{6}m2\)

37.2.152: \(\bar{6}m21'\)

37.3.153: \(\bar{6}'m'2\)

37.4.154: \(\bar{6}'m2'\)

37.5.155: \(\bar{6}m'2'\)

Magnetic space group (by SG)#

tag (SG)

1: \(C_{\rm 1}^{1}\) (\(P1\))

2: \(C_{\rm i}^{1}\) (\(P\bar{1}\))

3: \(C_{\rm 2}^{1}\) (\(P2\))

4: \(C_{\rm 2}^{2}\) (\(P2_1\))

5: \(C_{\rm 2}^{3}\) (\(C2\))

6: \(C_{\rm s}^{1}\) (\(Pm\))

7: \(C_{\rm s}^{2}\) (\(Pc\))

8: \(C_{\rm s}^{3}\) (\(Cm\))

9: \(C_{\rm s}^{4}\) (\(Cc\))

10: \(C_{\rm 2h}^{1}\) (\(P2/m\))

11: \(C_{\rm 2h}^{2}\) (\(P2_1/m\))

12: \(C_{\rm 2h}^{3}\) (\(C2/m\))

13: \(C_{\rm 2h}^{4}\) (\(P2/c\))

14: \(C_{\rm 2h}^{5}\) (\(P2_1/c\))

15: \(C_{\rm 2h}^{6}\) (\(C2/c\))

16: \(D_{\rm 2}^{1}\) (\(P222\))

17: \(D_{\rm 2}^{2}\) (\(P222_1\))

18: \(D_{\rm 2}^{3}\) (\(P2_12_12\))

19: \(D_{\rm 2}^{4}\) (\(P2_12_12_1\))

20: \(D_{\rm 2}^{5}\) (\(C222_1\))

21: \(D_{\rm 2}^{6}\) (\(C222\))

22: \(D_{\rm 2}^{7}\) (\(F222\))

23: \(D_{\rm 2}^{8}\) (\(I222\))

24: \(D_{\rm 2}^{9}\) (\(I2_12_12_1\))

25: \(C_{\rm 2v}^{1}\) (\(Pmm2\))

26: \(C_{\rm 2v}^{2}\) (\(Pmc2_1\))

27: \(C_{\rm 2v}^{3}\) (\(Pcc2\))

28: \(C_{\rm 2v}^{4}\) (\(Pma2\))

29: \(C_{\rm 2v}^{5}\) (\(Pca2_1\))

30: \(C_{\rm 2v}^{6}\) (\(Pnc2\))

31: \(C_{\rm 2v}^{7}\) (\(Pmn2_1\))

32: \(C_{\rm 2v}^{8}\) (\(Pba2\))

33: \(C_{\rm 2v}^{9}\) (\(Pna2_1\))

34: \(C_{\rm 2v}^{10}\) (\(Pnn2\))

35: \(C_{\rm 2v}^{11}\) (\(Cmm2\))

36: \(C_{\rm 2v}^{12}\) (\(Cmc2_1\))

37: \(C_{\rm 2v}^{13}\) (\(Ccc2\))

38: \(C_{\rm 2v}^{14}\) (\(Amm2\))

39: \(C_{\rm 2v}^{15}\) (\(Aem2\))

40: \(C_{\rm 2v}^{16}\) (\(Ama2\))

41: \(C_{\rm 2v}^{17}\) (\(Aea2\))

42: \(C_{\rm 2v}^{18}\) (\(Fmm2\))

43: \(C_{\rm 2v}^{19}\) (\(Fdd2\))

44: \(C_{\rm 2v}^{20}\) (\(Imm2\))

45: \(C_{\rm 2v}^{21}\) (\(Iba2\))

46: \(C_{\rm 2v}^{22}\) (\(Ima2\))

47: \(D_{\rm 2h}^{1}\) (\(Pmmm\))

48: \(D_{\rm 2h}^{2}\) (\(Pnnn\))

49: \(D_{\rm 2h}^{3}\) (\(Pccm\))

50: \(D_{\rm 2h}^{4}\) (\(Pban\))

51: \(D_{\rm 2h}^{5}\) (\(Pmma\))

52: \(D_{\rm 2h}^{6}\) (\(Pnna\))

53: \(D_{\rm 2h}^{7}\) (\(Pmna\))

54: \(D_{\rm 2h}^{8}\) (\(Pcca\))

55: \(D_{\rm 2h}^{9}\) (\(Pbam\))

56: \(D_{\rm 2h}^{10}\) (\(Pccn\))

57: \(D_{\rm 2h}^{11}\) (\(Pbcm\))

58: \(D_{\rm 2h}^{12}\) (\(Pnnm\))

59: \(D_{\rm 2h}^{13}\) (\(Pmmn\))

60: \(D_{\rm 2h}^{14}\) (\(Pbcn\))

61: \(D_{\rm 2h}^{15}\) (\(Pbca\))

62: \(D_{\rm 2h}^{16}\) (\(Pnma\))

63: \(D_{\rm 2h}^{17}\) (\(Cmcm\))

64: \(D_{\rm 2h}^{18}\) (\(Cmce\))

65: \(D_{\rm 2h}^{19}\) (\(Cmmm\))

66: \(D_{\rm 2h}^{20}\) (\(Cccm\))

67: \(D_{\rm 2h}^{21}\) (\(Cmme\))

68: \(D_{\rm 2h}^{22}\) (\(Ccce\))

69: \(D_{\rm 2h}^{23}\) (\(Fmmm\))

70: \(D_{\rm 2h}^{24}\) (\(Fddd\))

71: \(D_{\rm 2h}^{25}\) (\(Immm\))

72: \(D_{\rm 2h}^{26}\) (\(Ibam\))

73: \(D_{\rm 2h}^{27}\) (\(Ibca\))

74: \(D_{\rm 2h}^{28}\) (\(Imma\))

75: \(C_{\rm 4}^{1}\) (\(P4\))

76: \(C_{\rm 4}^{2}\) (\(P4_1\))

77: \(C_{\rm 4}^{3}\) (\(P4_2\))

78: \(C_{\rm 4}^{4}\) (\(P4_3\))

79: \(C_{\rm 4}^{5}\) (\(I4\))

80: \(C_{\rm 4}^{6}\) (\(I4_1\))

81: \(S_{\rm 4}^{1}\) (\(P\bar{4}\))

82: \(S_{\rm 4}^{2}\) (\(I\bar{4}\))

83: \(C_{\rm 4h}^{1}\) (\(P4/m\))

84: \(C_{\rm 4h}^{2}\) (\(P4_2/m\))

85: \(C_{\rm 4h}^{3}\) (\(P4/n\))

86: \(C_{\rm 4h}^{4}\) (\(P4_2/n\))

87: \(C_{\rm 4h}^{5}\) (\(I4/m\))

88: \(C_{\rm 4h}^{6}\) (\(I4_1/a\))

89: \(D_{\rm 4}^{1}\) (\(P422\))

90: \(D_{\rm 4}^{2}\) (\(P42_12\))

91: \(D_{\rm 4}^{3}\) (\(P4_122\))

92: \(D_{\rm 4}^{4}\) (\(P4_12_12\))

93: \(D_{\rm 4}^{5}\) (\(P4_222\))

94: \(D_{\rm 4}^{6}\) (\(P4_22_12\))

95: \(D_{\rm 4}^{7}\) (\(P4_322\))

96: \(D_{\rm 4}^{8}\) (\(P4_32_12\))

97: \(D_{\rm 4}^{9}\) (\(I422\))

98: \(D_{\rm 4}^{10}\) (\(I4_122\))

99: \(C_{\rm 4v}^{1}\) (\(P4mm\))

100: \(C_{\rm 4v}^{2}\) (\(P4bm\))

101: \(C_{\rm 4v}^{3}\) (\(P4_2cm\))

102: \(C_{\rm 4v}^{4}\) (\(P4_2nm\))

103: \(C_{\rm 4v}^{5}\) (\(P4cc\))

104: \(C_{\rm 4v}^{6}\) (\(P4nc\))

105: \(C_{\rm 4v}^{7}\) (\(P4_2mc\))

106: \(C_{\rm 4v}^{8}\) (\(P4_2bc\))

107: \(C_{\rm 4v}^{9}\) (\(I4mm\))

108: \(C_{\rm 4v}^{10}\) (\(I4cm\))

109: \(C_{\rm 4v}^{11}\) (\(I4_1md\))

110: \(C_{\rm 4v}^{12}\) (\(I4_1cd\))

111: \(D_{\rm 2d}^{1}\) (\(P\bar{4}2m\))

112: \(D_{\rm 2d}^{2}\) (\(P\bar{4}2c\))

113: \(D_{\rm 2d}^{3}\) (\(P\bar{4}2_1m\))

114: \(D_{\rm 2d}^{4}\) (\(P\bar{4}2_1c\))

115: \(D_{\rm 2d}^{5}\) (\(P\bar{4}m2\))

116: \(D_{\rm 2d}^{6}\) (\(P\bar{4}c2\))

117: \(D_{\rm 2d}^{7}\) (\(P\bar{4}b2\))

118: \(D_{\rm 2d}^{8}\) (\(P\bar{4}n2\))

119: \(D_{\rm 2d}^{9}\) (\(I\bar{4}m2\))

120: \(D_{\rm 2d}^{10}\) (\(I\bar{4}c2\))

121: \(D_{\rm 2d}^{11}\) (\(I\bar{4}2m\))

122: \(D_{\rm 2d}^{12}\) (\(I\bar{4}2d\))

123: \(D_{\rm 4h}^{1}\) (\(P4/mmm\))

124: \(D_{\rm 4h}^{2}\) (\(P4/mcc\))

125: \(D_{\rm 4h}^{3}\) (\(P4/nbm\))

126: \(D_{\rm 4h}^{4}\) (\(P4/nnc\))

127: \(D_{\rm 4h}^{5}\) (\(P4/mbm\))

128: \(D_{\rm 4h}^{6}\) (\(P4/mnc\))

129: \(D_{\rm 4h}^{7}\) (\(P4/nmm\))

130: \(D_{\rm 4h}^{8}\) (\(P4/ncc\))

131: \(D_{\rm 4h}^{9}\) (\(P4_2/mmc\))

132: \(D_{\rm 4h}^{10}\) (\(P4_2/mcm\))

133: \(D_{\rm 4h}^{11}\) (\(P4_2/nbc\))

134: \(D_{\rm 4h}^{12}\) (\(P4_2/nnm\))

135: \(D_{\rm 4h}^{13}\) (\(P4_2/mbc\))

136: \(D_{\rm 4h}^{14}\) (\(P4_2/mnm\))

137: \(D_{\rm 4h}^{15}\) (\(P4_2/nmc\))

138: \(D_{\rm 4h}^{16}\) (\(P4_2/ncm\))

139: \(D_{\rm 4h}^{17}\) (\(I4/mmm\))

140: \(D_{\rm 4h}^{18}\) (\(I4/mcm\))

141: \(D_{\rm 4h}^{19}\) (\(I4_1/amd\))

142: \(D_{\rm 4h}^{20}\) (\(I4_1/acd\))

143: \(C_{\rm 3}^{1}\) (\(P3\))

144: \(C_{\rm 3}^{2}\) (\(P3_1\))

145: \(C_{\rm 3}^{3}\) (\(P3_2\))

146: \(C_{\rm 3}^{4}\) (\(R3\))

147: \(C_{\rm 3i}^{1}\) (\(P\bar{3}\))

148: \(C_{\rm 3i}^{2}\) (\(R\bar{3}\))

149: \(D_{\rm 3}^{1}\) (\(P312\))

150: \(D_{\rm 3}^{2}\) (\(P321\))

151: \(D_{\rm 3}^{3}\) (\(P3_112\))

152: \(D_{\rm 3}^{4}\) (\(P3_121\))

153: \(D_{\rm 3}^{5}\) (\(P3_212\))

154: \(D_{\rm 3}^{6}\) (\(P3_221\))

155: \(D_{\rm 3}^{7}\) (\(R32\))

156: \(C_{\rm 3v}^{1}\) (\(P3m1\))

157: \(C_{\rm 3v}^{2}\) (\(P31m\))

158: \(C_{\rm 3v}^{3}\) (\(P3c1\))

159: \(C_{\rm 3v}^{4}\) (\(P31c\))

160: \(C_{\rm 3v}^{5}\) (\(R3m\))

161: \(C_{\rm 3v}^{6}\) (\(R3c\))

162: \(D_{\rm 3d}^{1}\) (\(P\bar{3}1m\))

163: \(D_{\rm 3d}^{2}\) (\(P\bar{3}1c\))

164: \(D_{\rm 3d}^{3}\) (\(P\bar{3}m1\))

165: \(D_{\rm 3d}^{4}\) (\(P\bar{3}c1\))

166: \(D_{\rm 3d}^{5}\) (\(R\bar{3}m\))

167: \(D_{\rm 3d}^{6}\) (\(R\bar{3}c\))

168: \(C_{\rm 6}^{1}\) (\(P6\))

169: \(C_{\rm 6}^{2}\) (\(P6_1\))

170: \(C_{\rm 6}^{3}\) (\(P6_5\))

171: \(C_{\rm 6}^{4}\) (\(P6_2\))

172: \(C_{\rm 6}^{5}\) (\(P6_4\))

173: \(C_{\rm 6}^{6}\) (\(P6_3\))

174: \(C_{\rm 3h}^{1}\) (\(P\bar{6}\))

175: \(C_{\rm 6h}^{1}\) (\(P6/m\))

176: \(C_{\rm 6h}^{2}\) (\(P6_3/m\))

177: \(D_{\rm 6}^{1}\) (\(P622\))

178: \(D_{\rm 6}^{2}\) (\(P6_122\))

179: \(D_{\rm 6}^{3}\) (\(P6_522\))

180: \(D_{\rm 6}^{4}\) (\(P6_222\))

181: \(D_{\rm 6}^{5}\) (\(P6_422\))

182: \(D_{\rm 6}^{6}\) (\(P6_322\))

183: \(C_{\rm 6v}^{1}\) (\(P6mm\))

184: \(C_{\rm 6v}^{2}\) (\(P6cc\))

185: \(C_{\rm 6v}^{3}\) (\(P6_3cm\))

186: \(C_{\rm 6v}^{4}\) (\(P6_3mc\))

187: \(D_{\rm 3h}^{1}\) (\(P\bar{6}m2\))

188: \(D_{\rm 3h}^{2}\) (\(P\bar{6}c2\))

189: \(D_{\rm 3h}^{3}\) (\(P\bar{6}2m\))

190: \(D_{\rm 3h}^{4}\) (\(P\bar{6}2c\))

191: \(D_{\rm 6h}^{1}\) (\(P6/mmm\))

192: \(D_{\rm 6h}^{2}\) (\(P6/mcc\))

193: \(D_{\rm 6h}^{3}\) (\(P6_3/mcm\))

194: \(D_{\rm 6h}^{4}\) (\(P6_3/mmc\))

195: \(T_{\rm }^{1}\) (\(P23\))

196: \(T_{\rm }^{2}\) (\(F23\))

197: \(T_{\rm }^{3}\) (\(I23\))

198: \(T_{\rm }^{4}\) (\(P2_13\))

199: \(T_{\rm }^{5}\) (\(I2_13\))

200: \(T_{\rm h}^{1}\) (\(Pm\bar{3}\))

201: \(T_{\rm h}^{2}\) (\(Pn\bar{3}\))

202: \(T_{\rm h}^{3}\) (\(Fm\bar{3}\))

203: \(T_{\rm h}^{4}\) (\(Fd\bar{3}\))

204: \(T_{\rm h}^{5}\) (\(Im\bar{3}\))

205: \(T_{\rm h}^{6}\) (\(Pa\bar{3}\))

206: \(T_{\rm h}^{7}\) (\(Ia\bar{3}\))

207: \(O_{\rm }^{1}\) (\(P432\))

208: \(O_{\rm }^{2}\) (\(P4_232\))

209: \(O_{\rm }^{3}\) (\(F432\))

210: \(O_{\rm }^{4}\) (\(F4_132\))

211: \(O_{\rm }^{5}\) (\(I432\))

212: \(O_{\rm }^{6}\) (\(P4_332\))

213: \(O_{\rm }^{7}\) (\(P4_132\))

214: \(O_{\rm }^{8}\) (\(I4_132\))

215: \(T_{\rm d}^{1}\) (\(P\bar{4}3m\))

216: \(T_{\rm d}^{2}\) (\(F\bar{4}3m\))

217: \(T_{\rm d}^{3}\) (\(I\bar{4}3m\))

218: \(T_{\rm d}^{4}\) (\(P\bar{4}3n\))

219: \(T_{\rm d}^{5}\) (\(F\bar{4}3c\))

220: \(T_{\rm d}^{6}\) (\(I\bar{4}3d\))

221: \(O_{\rm h}^{1}\) (\(Pm\bar{3}m\))

222: \(O_{\rm h}^{2}\) (\(Pn\bar{3}n\))

223: \(O_{\rm h}^{3}\) (\(Pm\bar{3}n\))

224: \(O_{\rm h}^{4}\) (\(Pn\bar{3}m\))

225: \(O_{\rm h}^{5}\) (\(Fm\bar{3}m\))

226: \(O_{\rm h}^{6}\) (\(Fm\bar{3}c\))

227: \(O_{\rm h}^{7}\) (\(Fd\bar{3}m\))

228: \(O_{\rm h}^{8}\) (\(Fd\bar{3}c\))

229: \(O_{\rm h}^{9}\) (\(Im\bar{3}m\))

230: \(O_{\rm h}^{10}\) (\(Ia\bar{3}d\))

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