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3次元の空間群は230種類あります。軸の交換や原点選択を考慮すると、530種類となります。以下に、この530種類の空間群の一覧を掲載します。

  • Serial No.: 全体の通し番号 (1~530)
  • ITA No.: International Tables for Crystallography, Vol. A (以下ITA) における空間群番号 (1~230)
  • Sub No.: ITA表記に対する枝番号 (1はITA表記そのまま、2以降は軸設定などが異なる)
  • Axis setting, Origin: 主軸/副軸の設定 あるいは 原点選択(Origin Choice)
  • Hall symbol: Hallの記法に従った空間群表記
  • Schoenflies symbol: Schoenfliesの記法に従った空間群表記
  • HM symbol (short): Hermann–Mauguinの記法に従った空間群表記 (省略形)
  • HM symbol (full): Hermann–Mauguinの記法に従った空間群表記 (完全形)
  • No. of Point Group: 点群の通し番号 (1~32)
  • Point Group (HM): Hermann–Mauguinの記法に従った点群表記 (省略形)
  • Point Group (Schoenflies): Schoenfliesの記法に従った点群表記
  • No. of Laue Group: ラウエクラスの通し番号 (1~11)
  • Laue Group (HM): ラウエクラス (HM記法)
  • No. of Crystal System: 結晶系の通し番号 (1~7)
  • Crystal System: 結晶系の名称

Triclinic 三斜晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies symbolHM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
111P 1\(C_1^1\)\(P\ 1\)\(P\ 1\)1\(1\)\(C_1\)1 \( \bar{1} \) 1triclinic
221-P 1\(C_i^1\)\(P\ \bar{1}\)\(P\ \bar{1}\)2\(\bar{1}\)\(C_i\)

Monoclinic 単斜晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies symbolHM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
331\(b\)P 2y\(C_2^1\)\(P\ 2\ =\ P\ 1\ 2\ 1\)\(P\ 1\ 2\ 1\)3\(2\)\(C_2\)2\(2/m\)2monoclinic
42\(c\)P 2\(P\ 2\ =\ P\ 1\ 1\ 2\)\(P\ 1\ 1\ 2\)
53\(a\)P 2x\(P\ 2\ =\ P\ 2\ 1\ 1\)\(P\ 2\ 1\ 1\)
641\(b\)P 2yb\(C_2^2\)\(P\ 2_1\ =\ P\ 1\ 2_1\ 1\)\(P\ 1\ 2_1\ 1\)
72\(c\)P 2c\(P\ 2_1\ =\ P\ 1\ 1\ 2_1\)\(P\ 1\ 1\ 2_1\)
83\(a\)P 2xa\(P\ 2_1\ =\ P\ 2_1\ 1\ 1\)\(P\ 2_1\ 1\ 1\)
951\(b1\)C 2y\(C_2^3\)\(C\ 2\ =\ C\ 1\ 2\ 1\)\(C\ 1\ 2\ 1\)
102\(b2\)A 2y\(C\ 2\ =\ A\ 1\ 2\ 1\)\(A\ 1\ 2\ 1\)
113\(b3\)I 2y\(C\ 2\ =\ I\ 1\ 2\ 1\)\(I\ 1\ 2\ 1\)
124\(c1\)A 2\(C\ 2\ =\ A\ 1\ 1\ 2\)\(A\ 1\ 1\ 2\)
135\(c2\)B 2\(C\ 2\ =\ B\ 1\ 1\ 2\ =\ B\ 2\)\(B\ 1\ 1\ 2\)
146\(c3\)I 2\(C\ 2\ =\ I\ 1\ 1\ 2\)\(I\ 1\ 1\ 2\)
157\(a1\)B 2x\(C\ 2\ =\ B\ 2\ 1\ 1\)\(B\ 2\ 1\ 1\)
168\(a2\)C 2x\(C\ 2\ =\ C\ 2\ 1\ 1\)\(C\ 2\ 1\ 1\)
179\(a3\)I 2x\(C\ 2\ =\ I\ 2\ 1\ 1\)\(I\ 2\ 1\ 1\)
1861\(b\)P -2y\(C_s^1\)\(P\ m\ =\ P\ 1\ m\ 1\)\(P\ 1\ m\ 1\)4\(m\)\(C_s\)
192\(c\)P -2\(P\ m\ =\ P\ 1\ 1\ m\)\(P\ 1\ 1\ m\)
203\(a\)P -2x\(P\ m\ =\ P\ m\ 1\ 1\)\(P\ m\ 1\ 1\)
2171\(b1\)P -2yc\(C_s^2\)\(P\ c\ =\ P\ 1\ c\ 1\)\(P\ 1\ c\ 1\)
222\(b2\)P -2yac\(P\ c\ =\ P\ 1\ n\ 1\)\(P\ 1\ n\ 1\)
233\(b3\)P -2ya\(P\ c\ =\ P\ 1\ a\ 1\)\(P\ 1\ a\ 1\)
244\(c1\)P -2a\(P\ c\ =\ P\ 1\ 1\ a\)\(P\ 1\ 1\ a\)
255\(c2\)P -2ab\(P\ c\ =\ P\ 1\ 1\ n\)\(P\ 1\ 1\ n\)
266\(c3\)P -2b\(P\ c\ =\ P\ 1\ 1\ b\ =\ P\ b\)\(P\ 1\ 1\ b\)
277\(a1\)P -2xb\(P\ c\ =\ P\ b\ 1\ 1\)\(P\ b\ 1\ 1\)
288\(a2\)P -2xbc\(P\ c\ =\ P\ n\ 1\ 1\)\(P\ n\ 1\ 1\)
299\(a3\)P -2xc\(P\ c\ =\ P\ c\ 1\ 1\)\(P\ c\ 1\ 1\)
3081\(b1\)C -2y\(C_s^3\)\(C\ m\ =\ C\ 1\ m\ 1\)\(C\ 1\ m\ 1\)
312\(b2\)A -2y\(C\ m\ =\ A\ 1\ m\ 1\)\(A\ 1\ m\ 1\)
323\(b3\)I -2y\(C\ m\ =\ I\ 1\ m\ 1\)\(I\ 1\ m\ 1\)
334\(c1\)A -2\(C\ m\ =\ A\ 1\ 1\ m\)\(A\ 1\ 1\ m\)
345\(c2\)B -2\(C\ m\ =\ B\ 1\ 1\ m\ =\ B\ m\)\(B\ 1\ 1\ m\)
356\(c3\)I -2\(C\ m\ =\ I\ 1\ 1\ m\)\(I\ 1\ 1\ m\)
367\(a1\)B -2x\(C\ m\ =\ B\ m\ 1\ 1\)\(B\ m\ 1\ 1\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies symbolHM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
3788\(a2\)C -2x\(C_s^3\)\(C\ m\ =\ C\ m\ 1\ 1\)\(C\ m\ 1\ 1\)4\(m\)\(C_s\)2\(2/m\)2monoclinic
389\(a3\)I -2x\(C\ m\ =\ I\ m\ 1\ 1\)\(I\ m\ 1\ 1\)
3991\(b1\)C -2yc\(C_s^4\)\(C\ c\ =\ C\ 1\ c\ 1\)\(C\ 1\ c\ 1\)
402\(b2\)A -2yac\(C\ c\ =\ A\ 1\ n\ 1\)\(A\ 1\ n\ 1\)
413\(b3\)I -2ya\(C\ c\ =\ I\ 1\ a\ 1\)\(I\ 1\ a\ 1\)
424\(\bar{b}1\)A -2ya\(C\ c\ =\ A\ 1\ a\ 1\)\(A\ 1\ a\ 1\)
435\(\bar{b}2\)C -2ybc\(C\ c\ =\ C\ 1\ n\ 1\)\(C\ 1\ n\ 1\)
446\(\bar{b}3\)I -2yc\(C\ c\ =\ I\ 1\ c\ 1\)\(I\ 1\ c\ 1\)
457\(c1\)A -2a\(C\ c\ =\ A\ 1\ 1\ a\)\(A\ 1\ 1\ a\)
468\(c2\)B -2bc\(C\ c\ =\ B\ 1\ 1\ n\)\(B\ 1\ 1\ n\)
479\(c3\)I -2b\(C\ c\ =\ I\ 1\ 1\ b\)\(I\ 1\ 1\ b\)
4810\(\bar{c}1\)B -2b\(C\ c\ =\ B\ 1\ 1\ b\ =\ B\ b\)\(B\ 1\ 1\ b\)
4911\(\bar{c}2\)A -2ac\(C\ c\ =\ A\ 1\ 1\ n\)\(A\ 1\ 1\ n\)
5012\(\bar{c}3\)I -2a\(C\ c\ =\ I\ 1\ 1\ a\)\(I\ 1\ 1\ a\)
5113\(a1\)B -2xb\(C\ c\ =\ B\ b\ 1\ 1\)\(B\ b\ 1\ 1\)
5214\(a2\)C -2xbc\(C\ c\ =\ C\ n\ 1\ 1\)\(C\ n\ 1\ 1\)
5315\(a3\)I -2xc\(C\ c\ =\ I\ c\ 1\ 1\)\(I\ c\ 1\ 1\)
5416\(\bar{a}1\)C -2xc\(C\ c\ =\ C\ c\ 1\ 1\)\(C\ c\ 1\ 1\)
5517\(\bar{a}2\)B -2xbc\(C\ c\ =\ B\ n\ 1\ 1\)\(B\ n\ 1\ 1\)
5618\(\bar{a}3\)I -2xb\(C\ c\ =\ I\ b\ 1\ 1\)\(I\ b\ 1\ 1\)
57101\(b\)-P 2y\(C_{2h}^1\)\(P\ 2/m\ =\ P\ 1\ 2/m\ 1\)\(P\ 1\ 2/m\ 1\)5\(2/m\)\(C_{2h}\)
582\(c\)-P 2\(P\ 2/m\ =\ P\ 1\ 1\ 2/m\)\(P\ 1\ 1\ 2/m\)5
593\(a\)-P 2x\(P\ 2/m\ =\ P\ 2/m\ 1\ 1\)\(P\ 2/m\ 1\ 1\)5
60111\(b\)-P 2yb\(C_{2h}^2\)\(P\ 2_1/m\ =\ P\ 1\ 2_1/m\ 1\)\(P\ 1\ 2_1/m\ 1\)5
612\(c\)-P 2c\(P\ 2_1/m\ =\ P\ 1\ 1\ 2_1/m\)\(P\ 1\ 1\ 2_1/m\)5
623\(a\)-P 2xa\(P\ 2_1/m\ =\ P\ 2_1/m\ 1\ 1\)\(P\ 2_1/m\ 1\ 1\)5
63121\(b1\)-C 2y\(C_{2h}^3\)\(C\ 2/m\ =\ C\ 1\ 2/m\ 1\)\(C\ 1\ 2/m\ 1\)5
642\(b2\)-A 2y\(C\ 2/m\ =\ A\ 1\ 2/m\ 1\)\(A\ 1\ 2/m\ 1\)5
653\(b3\)-I 2y\(C\ 2/m\ =\ I\ 1\ 2/m\ 1\)\(I\ 1\ 2/m\ 1\)5
664\(c1\)-A 2\(C\ 2/m\ =\ A\ 1\ 1\ 2/m\)\(A\ 1\ 1\ 2/m\)5
675\(c2\)-B 2\(C\ 2/m\ =\ B\ 1\ 1\ 2/m\ =\ B\ 2/m\)\(B\ 1\ 1\ 2/m\)5
686\(c3\)-I 2\(C\ 2/m\ =\ I\ 1\ 1\ 2/m\)\(I\ 1\ 1\ 2/m\)5
697\(a1\)-B 2x\(C\ 2/m\ =\ B\ 2/m\ 1\ 1\)\(B\ 2/m\ 1\ 1\)5
708\(a2\)-C 2x\(C\ 2/m\ =\ C\ 2/m\ 1\ 1\)\(C\ 2/m\ 1\ 1\)5
719\(a3\)-I 2x\(C\ 2/m\ =\ I\ 2/m\ 1\ 1\)\(I\ 2/m\ 1\ 1\)5
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies symbolHM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
72131\(b1\)-P 2yc\(C_{2h}^4\)\(P\ 2/c\ =\ P\ 1\ 2/c\ 1\)\(P\ 1\ 2/c\ 1\)5\(2/m\)\(C_{2h}\)2\(2/m\)2monoclinic
732\(b2\)-P 2yac\(P\ 2/c\ =\ P\ 1\ 2/n\ 1\)\(P\ 1\ 2/n\ 1\)
743\(b3\)-P 2ya\(P\ 2/c\ =\ P\ 1\ 2/a\ 1\)\(P\ 1\ 2/a\ 1\)
754\(c1\)-P 2a\(P\ 2/c\ =\ P\ 1\ 1\ 2/a\)\(P\ 1\ 1\ 2/a\)
765\(c2\)-P 2ab\(P\ 2/c\ =\ P\ 1\ 1\ 2/n\)\(P\ 1\ 1\ 2/n\)
776\(c3\)-P 2b\(P\ 2/c\ =\ P\ 1\ 1\ 2/b\ =\ P\ 2/b\)\(P\ 1\ 1\ 2/b\)
787\(a1\)-P 2xb\(P\ 2/c\ =\ P\ 2/b\ 1\ 1\)\(P\ 2/b\ 1\ 1\)
798\(a2\)-P 2xbc\(P\ 2/c\ =\ P\ 2/n\ 1\ 1\)\(P\ 2/n\ 1\ 1\)
809\(a3\)-P 2xc\(P\ 2/c\ =\ P\ 2/c\ 1\ 1\)\(P\ 2/c\ 1\ 1\)
81141\(b1\)-P 2ybc\(C_{2h}^5\)\(P\ 2_1/c\ =\ P\ 1\ 2_1/c\ 1\)\(P\ 1\ 2_1/c\ 1\)
822\(b2\)-P 2yn\(P\ 2_1/c\ =\ P\ 1\ 2_1/n\ 1\)\(P\ 1\ 2_1/n\ 1\)
833\(b3\)-P 2yab\(P\ 2_1/c\ =\ P\ 1\ 2_1/a\ 1\)\(P\ 1\ 2_1/a\ 1\)
844\(c1\)-P 2ac\(P\ 2_1/c\ =\ P\ 1\ 1\ 2_1/a\)\(P\ 1\ 1\ 2_1/a\)
855\(c2\)-P 2n\(P\ 2_1/c\ =\ P\ 1\ 1\ 2_1/n\)\(P\ 1\ 1\ 2_1/n\)
866\(c3\)-P 2bc\(P\ 2_1/c\ =\ P\ 1\ 1\ 2_1/b\ =\ P\ 2_1/b\)\(P\ 1\ 1\ 2_1/b\)
877\(a1\)-P 2xab\(P\ 2_1/c\ =\ P\ 2_1/b\ 1\ 1\)\(P\ 2_1/b\ 1\ 1\)
888\(a2\)-P 2xn\(P\ 2_1/c\ =\ P\ 2_1/n\ 1\ 1\)\(P\ 2_1/n\ 1\ 1\)
899\(a3\)-P 2xac\(P\ 2_1/c\ =\ P\ 2_1/c\ 1\ 1\)\(P\ 2_1/c\ 1\ 1\)
90151\(b1\)-C 2yc\(C_{2h}^6\)\(C\ 2/c\ =\ C\ 1\ 2/c\ 1\)\(C\ 1\ 2/c\ 1\)
912\(b2\)-A 2yac\(C\ 2/c\ =\ A\ 1\ 2/n\ 1\)\(A\ 1\ 2/n\ 1\)
923\(b3\)-I 2ya\(C\ 2/c\ =\ I\ 1\ 2/a\ 1\)\(I\ 1\ 2/a\ 1\)
934\(\bar{b}1\)-A 2ya\(C\ 2/c\ =\ A\ 1\ 2/a\ 1\)\(A\ 1\ 2/a\ 1\)
945\(\bar{b}2\)-C 2ybc\(C\ 2/c\ =\ C\ 1\ 2/n\ 1\)\(C\ 1\ 2/n\ 1\)
956\(\bar{b}3\)-I 2yc\(C\ 2/c\ =\ I\ 1\ 2/c\ 1\)\(I\ 1\ 2/c\ 1\)
967\(c1\)-A 2a\(C\ 2/c\ =\ A\ 1\ 1\ 2/a\)\(A\ 1\ 1\ 2/a\)
978\(c2\)-B 2bc\(C\ 2/c\ =\ B\ 1\ 1\ 2/n\)\(B\ 1\ 1\ 2/n\)
989\(c3\)-I 2b\(C\ 2/c\ =\ I\ 1\ 1\ 2/b\)\(I\ 1\ 1\ 2/b\)
9910\(\bar{c}1\)-B 2b\(C\ 2/c\ =\ B\ 1\ 1\ 2/b\ =\ B\ 2/b\)\(B\ 1\ 1\ 2/b\)
10011\(\bar{c}2\)-A 2ac\(C\ 2/c\ =\ A\ 1\ 1\ 2/n\)\(A\ 1\ 1\ 2/n\)
10112\(\bar{c}3\)-I 2a\(C\ 2/c\ =\ I\ 1\ 1\ 2/a\)\(I\ 1\ 1\ 2/a\)
10213\(a1\)-B 2xb\(C\ 2/c\ =\ B\ 2/b\ 1\ 1\)\(B\ 2/b\ 1\ 1\)
10314\(a2\)-C 2xbc\(C\ 2/c\ =\ C\ 2/n\ 1\ 1\)\(C\ 2/n\ 1\ 1\)
10415\(a3\)-I 2xc\(C\ 2/c\ =\ I\ 2/c\ 1\ 1\)\(I\ 2/c\ 1\ 1\)
10516\(\bar{a}1\)-C 2xc\(C\ 2/c\ =\ C\ 2/c\ 1\ 1\)\(C\ 2/c\ 1\ 1\)
10617\(\bar{a}2\)-B 2xbc\(C\ 2/c\ =\ B\ 2/n\ 1\ 1\)\(B\ 2/n\ 1\ 1\)
10718\(\bar{a}3\)-I 2xb\(C\ 2/c\ =\ I\ 2/b\ 1\ 1\)\(I\ 2/b\ 1\ 1\)

Orthorhombic 直方晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
108161P 2 2\(D_2^1\)\(P\ 2\ 2\ 2\)\(P\ 2\ 2\ 2\)6\(2\ 2\ 2\)\(D_2\)3\(mmm\)3orthorhombic
109171P 2c 2\(D_2^2\)\(P\ 2\ 2\ 2_1\)\(P\ 2\ 2\ 2_1\)
1102\(cab\)P 2a 2a\(P\ 2_1\ 2\ 2\)\(P\ 2_1\ 2\ 2\)
1113\(bca\)P 2 2b\(P\ 2\ 2_1\ 2\)\(P\ 2\ 2_1\ 2\)
112181P 2 2ab\(D_2^3\)\(P\ 2_1\ 2_1\ 2\)\(P\ 2_1\ 2_1\ 2\)
1132\(cab\)P 2bc 2\(P\ 2\ 2_1\ 2_1\)\(P\ 2\ 2_1\ 2_1\)
1143\(bca\)P 2ac 2ac\(P\ 2_1\ 2\ 2_1\)\(P\ 2_1\ 2\ 2_1\)
115191P 2ac 2ab\(D_2^4\)\(P\ 2_1\ 2_1\ 2_1\)\(P\ 2_1\ 2_1\ 2_1\)
116201C 2c 2\(D_2^5\)\(C\ 2\ 2\ 2_1\)\(C\ 2\ 2\ 2_1\)
1172\(cab\)A 2a 2a\(A\ 2_1\ 2\ 2\)\(A\ 2_1\ 2\ 2\)
1183\(bca\)B 2 2b\(B\ 2\ 2_1\ 2\)\(B\ 2\ 2_1\ 2\)
119211C 2 2\(D_2^6\)\(C\ 2\ 2\ 2\)\(C\ 2\ 2\ 2\)
1202\(cab\)A 2 2\(A\ 2\ 2\ 2\)\(A\ 2\ 2\ 2\)
1213\(bca\)B 2 2\(B\ 2\ 2\ 2\)\(B\ 2\ 2\ 2\)
122221F 2 2\(D_2^7\)\(F\ 2\ 2\ 2\)\(F\ 2\ 2\ 2\)
123231I 2 2\(D_2^8\)\(I\ 2\ 2\ 2\)\(I\ 2\ 2\ 2\)
124241I 2b 2c\(D_2^9\)\(I\ 2_1\ 2_1\ 2_1\)\(I\ 2_1\ 2_1\ 2_1\)
125251P 2 -2\(C_{2v}^1\)\(P\ m\ m\ 2\)\(P\ m\ m\ 2\)7\(m\ m\ 2\)\(C_{2v}\)
1262\(cab\)P -2 2\(P\ 2\ m\ m\)\(P\ 2\ m\ m\)
1273\(bca\)P -2 -2\(P\ m\ 2\ m\)\(P\ m\ 2\ m\)
128261P 2c -2\(C_{2v}^2\)\(P\ m\ c\ 2_1\)\(P\ m\ c\ 2_1\)
1292\(ba\bar{c}\)P 2c -2c\(P\ c\ m\ 2_1\)\(P\ c\ m\ 2_1\)
1303\(cab\)P -2a 2a\(P\ 2_1\ m\ a\)\(P\ 2_1\ m\ a\)
1314\(\bar{c}ba\)P -2 2a\(P\ 2_1\ a\ m\)\(P\ 2_1\ a\ m\)
1325\(bca\)P -2 -2b\(P\ b\ 2_1\ m\)\(P\ b\ 2_1\ m\)
1336\(a\bar{c}b\)P -2b -2\(P\ m\ 2_1\ b\)\(P\ m\ 2_1\ b\)
134271P 2 -2c\(C_{2v}^3\)\(P\ c\ c\ 2\)\(P\ c\ c\ 2\)
1352\(cab\)P -2a 2\(P\ 2\ a\ a\)\(P\ 2\ a\ a\)
1363\(bca\)P -2b -2b\(P\ b\ 2\ b\)\(P\ b\ 2\ b\)
137281P 2 -2a\(C_{2v}^4\)\(P\ m\ a\ 2\)\(P\ m\ a\ 2\)
1382\(ba\bar{c}\)P 2 -2b\(P\ b\ m\ 2\)\(P\ b\ m\ 2\)
1393\(cab\)P -2b 2\(P\ 2\ m\ b\)\(P\ 2\ m\ b\)
1404\(\bar{c}ba\)P -2c 2\(P\ 2\ c\ m\)\(P\ 2\ c\ m\)
1415\(bca\)P -2c -2c\(P\ c\ 2\ m\)\(P\ c\ 2\ m\)
1426\(a\bar{c}b\)P -2a -2a\(P\ m\ 2\ a\)\(P\ m\ 2\ a\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
143291P 2c -2ac\(C_{2v}^5\)\(P\ c\ a\ 2_1\)\(P\ c\ a\ 2_1\)7\(m\ m\ 2\)\(C_{2v}\)3\(mmm\)3orthorhombic
1442\(ba\bar{c}\)P 2c -2b\(P\ b\ c\ 2_1\)\(P\ b\ c\ 2_1\)
1453\(cab\)P -2b 2a\(P\ 2_1\ a\ b\)\(P\ 2_1\ a\ b\)
1464\(\bar{c}ba\)P -2ac 2a\(P\ 2_1\ c\ a\)\(P\ 2_1\ c\ a\)
1475\(bca\)P -2bc -2c\(P\ c\ 2_1\ b\)\(P\ c\ 2_1\ b\)
1486\(a\bar{c}b\)P -2a -2ab\(P\ b\ 2_1\ a\)\(P\ b\ 2_1\ a\)
149301P 2 -2bc\(C_{2v}^6\)\(P\ n\ c\ 2\)\(P\ n\ c\ 2\)
1502\(ba\bar{c}\)P 2 -2ac\(P\ c\ n\ 2\)\(P\ c\ n\ 2\)
1513\(cab\)P -2ac 2\(P\ 2\ n\ a\)\(P\ 2\ n\ a\)
1524\(\bar{c}ba\)P -2ab 2\(P\ 2\ a\ n\)\(P\ 2\ a\ n\)
1535\(bca\)P -2ab -2ab\(P\ b\ 2\ n\)\(P\ b\ 2\ n\)
1546\(a\bar{c}b\)P -2bc -2bc\(P\ n\ 2\ b\)\(P\ n\ 2\ b\)
155311P 2ac -2\(C_{2v}^7\)\(P\ m\ n\ 2_1\)\(P\ m\ n\ 2_1\)
1562\(ba\bar{c}\)P 2bc -2bc\(P\ n\ m\ 2_1\)\(P\ n\ m\ 2_1\)
1573\(cab\)P -2ab 2ab\(P\ 2_1\ m\ n\)\(P\ 2_1\ m\ n\)
1584\(\bar{c}ba\)P -2 2ac\(P\ 2_1\ n\ m\)\(P\ 2_1\ n\ m\)
1595\(bca\)P -2 -2bc\(P\ n\ 2_1\ m\)\(P\ n\ 2_1\ m\)
1606\(a\bar{c}b\)P -2ab -2\(P\ m\ 2_1\ n\)\(P\ m\ 2_1\ n\)
161321P 2 -2ab\(C_{2v}^8\)\(P\ b\ a\ 2\)\(P\ b\ a\ 2\)
1622\(cab\)P -2bc 2\(P\ 2\ c\ b\)\(P\ 2\ c\ b\)
1633\(bca\)P -2ac -2ac\(P\ c\ 2\ a\)\(P\ c\ 2\ a\)
164331P 2c -2n\(C_{2v}^9\)\(P\ n\ a\ 2_1\)\(P\ n\ a\ 2_1\)
1652\(ba\bar{c}\)P 2c -2ab\(P\ b\ n\ 2_1\)\(P\ b\ n\ 2_1\)
1663\(cab\)P -2bc 2a\(P\ 2_1\ n\ b\)\(P\ 2_1\ n\ b\)
1674\(\bar{c}ba\)P -2n 2a\(P\ 2_1\ c\ n\)\(P\ 2_1\ c\ n\)
1685\(bca\)P -2n -2ac\(P\ c\ 2_1\ n\)\(P\ c\ 2_1\ n\)
1696\(a\bar{c}b\)P -2ac -2n\(P\ n\ 2_1\ a\)\(P\ n\ 2_1\ a\)
170341P 2 -2n\(C_{2v}^{10}\)\(P\ n\ n\ 2\)\(P\ n\ n\ 2\)
1712\(cab\)P -2n 2\(P\ 2\ n\ n\)\(P\ 2\ n\ n\)
1723\(bca\)P -2n -2n\(P\ n\ 2\ n\)\(P\ n\ 2\ n\)
173351C 2 -2\(C_{2v}^{11}\)\(C\ m\ m\ 2\)\(C\ m\ m\ 2\)
1742\(cab\)A -2 2\(A\ 2\ m\ m\)\(A\ 2\ m\ m\)
1753\(bca\)B -2 -2\(B\ m\ 2\ m\)\(B\ m\ 2\ m\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
176361C 2c -2\(C_{2v}^{12}\)\(C\ m\ c\ 2_1\)\(C\ m\ c\ 2_1\)7\(m\ m\ 2\)\(C_{2v}\)3\(mmm\)3orthorhombic
1772\(ba\bar{c}\)C 2c -2c\(C\ c\ m\ 2_1\)\(C\ c\ m\ 2_1\)
1783\(cab\)A -2a 2a\(A\ 2_1\ m\ a\)\(A\ 2_1\ m\ a\)
1794\(\bar{c}ba\)A -2 2a\(A\ 2_1\ a\ m\)\(A\ 2_1\ a\ m\)
1805\(bca\)B -2 -2b\(B\ b\ 2_1\ m\)\(B\ b\ 2_1\ m\)
1816\(a\bar{c}b\)B -2b -2\(B\ m\ 2_1\ b\)\(B\ m\ 2_1\ b\)
182371C 2 -2c\(C_{2v}^{13}\)\(C\ c\ c\ 2\)\(C\ c\ c\ 2\)
1832\(cab\)A -2a 2\(A\ 2\ a\ a\)\(A\ 2\ a\ a\)
1843\(bca\)B -2b -2b\(B\ b\ 2\ b\)\(B\ b\ 2\ b\)
185381A 2 -2\(C_{2v}^{14}\)\(A\ m\ m\ 2\)\(A\ m\ m\ 2\)
1862\(ba\bar{c}\)B 2 -2\(B\ m\ m\ 2\)\(B\ m\ m\ 2\)
1873\(cab\)B -2 2\(B\ 2\ m\ m\)\(B\ 2\ m\ m\)
1884\(\bar{c}ba\)C -2 2\(C\ 2\ m\ m\)\(C\ 2\ m\ m\)
1895\(bca\)C -2 -2\(C\ m\ 2\ m\)\(C\ m\ 2\ m\)
1906\(a\bar{c}b\)A -2 -2\(A\ m\ 2\ m\)\(A\ m\ 2\ m\)
191391A 2 -2c\(C_{2v}^{15}\)\(A\ b\ m\ 2\)\(A\ b\ m\ 2\)
1922\(ba\bar{c}\)B 2 -2c\(B\ m\ a\ 2\)\(B\ m\ a\ 2\)
1933\(cab\)B -2c 2\(B\ 2\ c\ m\)\(B\ 2\ c\ m\)
1944\(\bar{c}ba\)C -2b 2\(C\ 2\ m\ b\)\(C\ 2\ m\ b\)
1955\(bca\)C -2b -2b\(C\ m\ 2\ a\)\(C\ m\ 2\ a\)
1966\(a\bar{c}b\)A -2c -2c\(A\ c\ 2\ m\)\(A\ c\ 2\ m\)
197401A 2 -2a\(C_{2v}^{16}\)\(A\ m\ a\ 2\)\(A\ m\ a\ 2\)
1982\(ba\bar{c}\)B 2 -2b\(B\ b\ m\ 2\)\(B\ b\ m\ 2\)
1993\(cab\)B -2b 2\(B\ 2\ m\ b\)\(B\ 2\ m\ b\)
2004\(\bar{c}ba\)C -2c 2\(C\ 2\ c\ m\)\(C\ 2\ c\ m\)
2015\(bca\)C -2c -2c\(C\ c\ 2\ m\)\(C\ c\ 2\ m\)
2026\(a\bar{c}b\)A -2a -2a\(A\ m\ 2\ a\)\(A\ m\ 2\ a\)
203411A 2 -2ac\(C_{2v}^{17}\)\(A\ b\ a\ 2\)\(A\ b\ a\ 2\)
2042\(ba\bar{c}\)B 2 -2bc\(B\ b\ a\ 2\)\(B\ b\ a\ 2\)
2053\(cab\)B -2bc 2\(B\ 2\ c\ b\)\(B\ 2\ c\ b\)
2064\(\bar{c}ba\)C -2bc 2\(C\ 2\ c\ b\)\(C\ 2\ c\ b\)
2075\(bca\)C -2bc -2bc\(C\ c\ 2\ a\)\(C\ c\ 2\ a\)
2086\(a\bar{c}b\)A -2ac -2ac\(A\ c\ 2\ a\)\(A\ c\ 2\ a\)
209421F 2 -2\(C_{2v}^{18}\)\(F\ m\ m\ 2\)\(F\ m\ m\ 2\)
2102\(cab\)F -2 2\(F\ 2\ m\ m\)\(F\ 2\ m\ m\)
2113\(bca\)F -2 -2\(F\ m\ 2\ m\)\(F\ m\ 2\ m\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
212431F 2 -2d\(C_{2v}^{19}\)\(F\ d\ d\ 2\)\(F\ d\ d\ 2\)7\(m\ m\ 2\)\(C_{2v}\)3\(mmm\)3orthorhombic
2132\(cab\)F -2d 2\(F\ 2\ d\ d\)\(F\ 2\ d\ d\)
2143\(bca\)F -2d -2d\(F\ d\ 2\ d\)\(F\ d\ 2\ d\)
215441I 2 -2\(C_{2v}^{20}\)\(I\ m\ m\ 2\)\(I\ m\ m\ 2\)
2162\(cab\)I -2 2\(I\ 2\ m\ m\)\(I\ 2\ m\ m\)
2173\(bca\)I -2 -2\(I\ m\ 2\ m\)\(I\ m\ 2\ m\)
218451I 2 -2c\(C_{2v}^{21}\)\(I\ b\ a\ 2\)\(I\ b\ a\ 2\)
2192\(cab\)I -2a 2\(I\ 2\ c\ b\)\(I\ 2\ c\ b\)
2203\(bca\)I -2b -2b\(I\ c\ 2\ a\)\(I\ c\ 2\ a\)
221461I 2 -2a\(C_{2v}^{22}\)\(I\ m\ a\ 2\)\(I\ m\ a\ 2\)
2222\(ba\bar{c}\)I 2 -2b\(I\ b\ m\ 2\)\(I\ b\ m\ 2\)
2233\(cab\)I -2b 2\(I\ 2\ m\ b\)\(I\ 2\ m\ b\)
2244\(\bar{c}ba\)I -2c 2\(I\ 2\ c\ m\)\(I\ 2\ c\ m\)
2255\(bca\)I -2c -2c\(I\ c\ 2\ m\)\(I\ c\ 2\ m\)
2266\(a\bar{c}b\)I -2a -2a\(I\ m\ 2\ a\)\(I\ m\ 2\ a\)
227471-P 2 2\(D_{2h}^1\)\(P\ m\ m\ m\)\(P\ 2/m\ 2/m\ 2/m\)8\(m\ m\ m\)\(D_{2h}\)
228481\(1\)P 2 2 -1n\(D_{2h}^2\)\(P\ n\ n\ n\)\(P\ 2/n\ 2/n\ 2/n\)
2292\(2\)-P 2ab 2bc
230491-P 2 2c\(D_{2h}^3\)\(P\ c\ c\ m\)\(P\ 2/c\ 2/c\ 2/m\)
2312\(cab\)-P 2a 2\(P\ m\ a\ a\)\(P\ 2/m\ 2/a\ 2/a\)
2323\(bca\)-P 2b 2b\(P\ b\ m\ b\)\(P\ 2/b\ 2/m\ 2/b\)
233501\(1\)P 2 2 -1ab\(D_{2h}^4\)\(P\ b\ a\ n\)\(P\ 2/b\ 2/a\ 2/n\)
2342\(2\)-P 2ab 2b
2353\(1cab\)P 2 2 -1bc\(P\ n\ c\ b\)\(P\ 2/n\ 2/c\ 2/b\)
2364\(2cab\)-P 2b 2bc
2375\(1bca\)P 2 2 -1ac\(P\ c\ n\ a\)\(P\ 2/c\ 2/n\ 2/a\)
2386\(2bca\)-P 2a 2c
239511-P 2a 2a\(D_{2h}^5\)\(P\ m\ m\ a\)\(P\ 2_1/m\ 2/m\ 2/a\)
2402\(ba\bar{c}\)-P 2b 2\(P\ m\ m\ b\)\(P\ 2/m\ 2_1/m\ 2/b\)
2413\(cab\)-P 2 2b\(P\ b\ m\ m\)\(P\ 2/b\ 2_1/m\ 2/m\)
2424\(\bar{c}ba\)-P 2c 2c\(P\ c\ m\ m\)\(P\ 2/c\ 2/m\ 2_1/m\)
2435\(bca\)-P 2c 2\(P\ m\ c\ m\)\(P\ 2/m\ 2/c\ 2_1/m\)
2446\(a\bar{c}b\)-P 2 2a\(P\ m\ a\ m\)\(P\ 2_1/m\ 2/a\ 2/m\)
245521-P 2a 2bc\(D_{2h}^6\)\(P\ n\ n\ a\)\(P\ 2/n\ 2_1/n\ 2/a\)
2462\(ba\bar{c}\)-P 2b 2n\(P\ n\ n\ b\)\(P\ 2_1/n\ 2/n\ 2/b\)
2473\(cab\)-P 2n 2b\(P\ b\ n\ n\)\(P\ 2/b\ 2/n\ 2_1/n\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
248524\(\bar{c}ba\)-P 2ab 2c\(D_{2h}^6\)\(P\ c\ n\ n\)\(P\ 2/c\ 2_1/n\ 2/n\)8\(m\ m\ m\)\(D_{2h}\)3\(mmm\)3orthorhombic
2495\(bca\)-P 2ab 2n\(P\ n\ c\ n\)\(P\ 2_1/n\ 2/c\ 2/n\)
2506\(a\bar{c}b\)-P 2n 2bc\(P\ n\ a\ n\)\(P\ 2/n\ 2/a\ 2_1/n\)
251531-P 2ac 2\(D_{2h}^7\)\(P\ m\ n\ a\)\(P\ 2/m\ 2/n\ 2_1/a\)
2522\(ba\bar{c}\)-P 2bc 2bc\(P\ n\ m\ b\)\(P\ 2/n\ 2/m\ 2_1/b\)
2533\(cab\)-P 2ab 2ab\(P\ b\ m\ n\)\(P\ 2_1/b\ 2/m\ 2/n\)
2544\(\bar{c}ba\)-P 2 2ac\(P\ c\ n\ m\)\(P\ 2_1/c\ 2/n\ 2/m\)
2555\(bca\)-P 2 2bc\(P\ n\ c\ m\)\(P\ 2/n\ 2_1/c\ 2/m\)
2566\(a\bar{c}b\)-P 2ab 2\(P\ m\ a\ n\)\(P\ 2/m\ 2_1/a\ 2/n\)
257541-P 2a 2ac\(D_{2h}^8\)\(P\ c\ c\ a\)\(P\ 2_1/c\ 2/c\ 2/a\)
2582\(ba\bar{c}\)-P 2b 2c\(P\ c\ c\ b\)\(P\ 2/c\ 2_1/c\ 2/b\)
2593\(cab\)-P 2a 2b\(P\ b\ a\ a\)\(P\ 2/b\ 2_1/a\ 2/a\)
2604\(\bar{c}ba\)-P 2ac 2c\(P\ c\ a\ a\)\(P\ 2/c\ 2/a\ 2_1/a\)
2615\(bca\)-P 2bc 2b\(P\ b\ c\ b\)\(P\ 2/b\ 2/c\ 2_1/b\)
2626\(a\bar{c}b\)-P 2b 2ab\(P\ b\ a\ b\)\(P\ 2_1/b\ 2/a\ 2/b\)
263551-P 2 2ab\(D_{2h}^9\)\(P\ b\ a\ m\)\(P\ 2_1/b\ 2_1/a\ 2/m\)
2642\(cab\)-P 2bc 2\(P\ m\ c\ b\)\(P\ 2/m\ 2_1/c\ 2_1/b\)
2653\(bca\)-P 2ac 2ac\(P\ c\ m\ a\)\(P\ 2_1/c\ 2/m\ 2_1/a\)
266561-P 2ab 2ac\(D_{2h}^{10}\)\(P\ c\ c\ n\)\(P\ 2_1/c\ 2_1/c\ 2/n\)
2672\(cab\)-P 2ac 2bc\(P\ n\ a\ a\)\(P\ 2/n\ 2_1/a\ 2_1/a\)
2683\(bca\)-P 2bc 2ab\(P\ b\ n\ b\)\(P\ 2_1/b\ 2/n\ 2_1/b\)
269571-P 2c 2b\(D_{2h}^{11}\)\(P\ b\ c\ m\)\(P\ 2/b\ 2_1/c\ 2_1/m\)
2702\(ba\bar{c}\)-P 2c 2ac\(P\ c\ a\ m\)\(P\ 2_1/c\ 2/a\ 2_1/m\)
2713\(cab\)-P 2ac 2a\(P\ m\ c\ a\)\(P\ 2_1/m\ 2/c\ 2_1/a\)
2724\(\bar{c}ba\)-P 2b 2a\(P\ m\ a\ b\)\(P\ 2_1/m\ 2_1/a\ 2/b\)
2735\(bca\)-P 2a 2ab\(P\ b\ m\ a\)\(P\ 2_1/b\ 2_1/m\ 2/a\)
2746\(a\bar{c}b\)-P 2bc 2c\(P\ c\ m\ b\)\(P\ 2/c\ 2_1/m\ 2_1/b\)
275581-P 2 2n\(D_{2h}^{12}\)\(P\ n\ n\ m\)\(P\ 2_1/n\ 2_1/n\ 2/m\)
2762\(cab\)-P 2n 2\(P\ m\ n\ n\)\(P\ 2/m\ 2_1/n\ 2_1/n\)
2773\(bca\)-P 2n 2n\(P\ n\ m\ n\)\(P\ 2_1/n\ 2/m\ 2_1/n\)
278591\(1\)P 2 2ab -1ab\(D_{2h}^{13}\)\(P\ m\ m\ n\)\(P\ 2_1/m\ 2_1/m\ 2/n\)
2792\(2\)-P 2ab 2a
2803\(1cab\)P 2bc 2 -1bc\(P\ n\ m\ m\)\(P\ 2/n\ 2_1/m\ 2_1/m\)
2814\(2cab\)-P 2c 2bc
2825\(1bca\)P 2ac 2ac -1ac\(P\ m\ n\ m\)\(P\ 2_1/m\ 2/n\ 2_1/m\)
2836\(2bca\)-P 2c 2a
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
284601-P 2n 2ab\(D_{2h}^{14}\)\(P\ b\ c\ n\)\(P\ 2_1/b\ 2/c\ 2_1/n\)8\(m\ m\ m\)\(D_{2h}\)3\(mmm\)3orthorhombic
2852\(ba\bar{c}\)-P 2n 2c\(P\ c\ a\ n\)\(P\ 2/c\ 2_1/a\ 2_1/n\)
2863\(cab\)-P 2a 2n\(P\ n\ c\ a\)\(P\ 2_1/n\ 2_1/c\ 2/a\)
2874\(\bar{c}ba\)-P 2bc 2n\(P\ n\ a\ b\)\(P\ 2_1/n\ 2/a\ 2_1/b\)
2885\(bca\)-P 2ac 2b\(P\ b\ n\ a\)\(P\ 2/b\ 2_1/n\ 2_1/a\)
2896\(a\bar{c}b\)-P 2b 2ac\(P\ c\ n\ b\)\(P\ 2_1/c\ 2_1/n\ 2/b\)
290611-P 2ac 2ab\(D_{2h}^{15}\)\(P\ b\ c\ a\)\(P\ 2_1/b\ 2_1/c\ 2_1/a\)
2912\(ba\bar{c}\)-P 2bc 2ac\(P\ c\ a\ b\)\(P\ 2_1/c\ 2_1/a\ 2_1/b\)
292621-P 2ac 2n\(D_{2h}^{16}\)\(P\ n\ m\ a\)\(P\ 2_1/n\ 2_1/m\ 2_1/a\)
2932\(ba\bar{c}\)-P 2bc 2a\(P\ m\ n\ b\)\(P\ 2_1/m\ 2_1/n\ 2_1/b\)
2943\(cab\)-P 2c 2ab\(P\ b\ n\ m\)\(P\ 2_1/b\ 2_1/n\ 2_1/m\)
2954\(\bar{c}ba\)-P 2n 2ac\(P\ c\ m\ n\)\(P\ 2_1/c\ 2_1/m\ 2_1/n\)
2965\(bca\)-P 2n 2a\(P\ m\ c\ n\)\(P\ 2_1/m\ 2_1/c\ 2_1/n\)
2976\(a\bar{c}b\)-P 2c 2n\(P\ n\ a\ m\)\(P\ 2_1/n\ 2_1/a\ 2_1/m\)
298631-C 2c 2\(D_{2h}^{17}\)\(C\ m\ c\ m\)\(C\ 2/m\ 2/c\ 2_1/m\)
2992\(ba\bar{c}\)-C 2c 2c\(C\ c\ m\ m\)\(C\ 2/c\ 2/m\ 2_1/m\)
3003\(cab\)-A 2a 2a\(A\ m\ m\ a\)\(A\ 2_1/m\ 2/m\ 2/a\)
3014\(\bar{c}ba\)-A 2 2a\(A\ m\ a\ m\)\(A\ 2_1/m\ 2/a\ 2/m\)
3025\(bca\)-B 2 2b\(B\ b\ m\ m\)\(B\ 2/b\ 2_1/m\ 2/m\)
3036\(a\bar{c}b\)-B 2b 2\(B\ m\ m\ b\)\(B\ 2/m\ 2_1/m\ 2/b\)
304641-C 2bc 2\(D_{2h}^{18}\)\(C\ m\ c\ a\)\(C\ 2/m\ 2/c\ 2_1/a\)
3052\(ba\bar{c}\)-C 2bc 2bc\(C\ c\ m\ b\)\(C\ 2/c\ 2/m\ 2_1/b\)
3063\(cab\)-A 2ac 2ac\(A\ b\ m\ a\)\(A\ 2_1/b\ 2/m\ a\)
3074\(\bar{c}ba\)-A 2 2ac\(A\ c\ a\ m\)\(A\ 2_1/c\ 2/a\ 2/m\)
3085\(bca\)-B 2 2bc\(B\ b\ c\ m\)\(B\ 2/b\ 2_1/c\ 2/m\)
3096\(a\bar{c}b\)-B 2bc 2\(B\ m\ a\ b\)\(B\ 2/m\ 2_1/a\ 2/b\)
310651-C 2 2\(D_{2h}^{19}\)\(C\ m\ m\ m\)\(C\ 2/m\ 2/m\ 2/m\)
3112\(cab\)-A 2 2\(A\ m\ m\ m\)\(A\ 2/m\ 2/m\ 2/m\)
3123\(bca\)-B 2 2\(B\ m\ m\ m\)\(B\ 2/m\ 2/m\ 2/m\)
313661-C 2 2c\(D_{2h}^{20}\)\(C\ c\ c\ m\)\(C\ 2/c\ 2/c\ 2/m\)
3142\(cab\)-A 2a 2\(A\ m\ a\ a\)\(A\ 2/m\ 2/a\ 2/a\)
3153\(bca\)-B 2b 2b\(B\ b\ m\ b\)\(B\ 2/b\ 2/m\ 2/b\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
316671-C 2b 2\(D_{2h}^{21}\)\(C\ m\ m\ a\)\(C\ 2/m\ 2/m\ 2/a\)8\(m\ m\ m\)\(D_{2h}\)3\(mmm\)3orthorhombic
3172\(ba\bar{c}\)-C 2b 2b\(C\ m\ m\ b\)\(C\ 2/m\ 2/m\ 2/b\)
3183\(cab\)-A 2c 2c\(A\ b\ m\ m\)\(A\ 2/b\ 2/m\ 2/m\)
3194\(\bar{c}ba\)-A 2 2c\(A\ c\ m\ m\)\(A\ 2/c\ 2/m\ 2/m\)
3205\(bca\)-B 2 2c\(B\ m\ c\ m\)\(B\ 2/m\ 2/c\ 2/m\)
3216\(a\bar{c}b\)-B 2c 2\(B\ m\ a\ m\)\(B\ 2/m\ 2/a\ 2/m\)
322681\(1\)C 2 2 -1bc\(D_{2h}^{22}\)\(C\ c\ c\ a\)\(C\ 2/c\ 2/c\ 2/a\)
3232\(2\)-C 2b 2bc
3243\(1ba\bar{c}\)C 2 2 -1bc\(C\ c\ c\ b\)\(C\ 2/c\ 2/c\ 2/b\)
3254\(2ba\bar{c}\)-C 2b 2c
3265\(1cab\)A 2 2 -1ac\(A\ b\ a\ a\)\(A\ 2/b\ 2/a\ 2/a\)
3276\(2cab\)-A 2a 2c
3287\(1\bar{c}ba\)A 2 2 -1ac\(A\ c\ a\ a\)\(A\ 2/c\ 2/a\ 2/a\)
3298\(2\bar{c}ba\)-A 2ac 2c
3309\(1bca\)B 2 2 -1bc\(B\ b\ c\ b\)\(B\ 2/b\ 2/c\ 2/b\)
33110\(2bca\)-B 2bc 2b
33211\(1a\bar{c}b\)B 2 2 -1bc\(B\ b\ a\ b\)\(B\ 2/b\ 2/a\ 2/b\)
33312\(2a\bar{c}b\)-B 2b 2bc
334691-F 2 2\(D_{2h}^{23}\)\(F\ m\ m\ m\)\(F\ 2/m\ 2/m\ 2/m\)
335701\(1\)F 2 2 -1d\(D_{2h}^{24}\)\(F\ d\ d\ d\)\(F\ 2/d\ 2/d\ 2/d\)
3362\(2\)-F 2uv 2vw
337711-I 2 2\(D_{2h}^{25}\)\(I\ m\ m\ m\)\(I\ 2/m\ 2/m\ 2/m\)
338721-I 2 2c\(D_{2h}^{26}\)\(I\ b\ a\ m\)\(I\ 2/b\ 2/a\ 2/m\)
3392\(cab\)-I 2a 2\(I\ m\ c\ b\)\(I\ 2/m\ 2/c\ 2/b\)
3403\(bca\)-I 2b 2b\(I\ c\ m\ a\)\(I\ 2/c\ 2/m\ 2/a\)
341731-I 2b 2c\(D_{2h}^{27}\)\(I\ b\ c\ a\)\(I\ 2/b\ 2/c\ 2/a\)
3422\(ba\bar{c}\)-I 2a 2b\(I\ c\ a\ b\)\(I\ 2/c\ 2/a\ 2/b\)
343741-I 2b 2\(D_{2h}^{28}\)\(I\ m\ m\ a\)\(I\ 2/m\ 2/m\ 2/a\)
3442\(ba\bar{c}\)-I 2a 2a\(I\ m\ m\ b\)\(I\ 2/m\ 2/m\ 2/b\)
3453\(cab\)-I 2c 2c\(I\ b\ m\ m\)\(I\ 2/b\ 2/m\ 2/m\)
3464\(\bar{c}ba\)-I 2 2b\(I\ c\ m\ m\)\(I\ 2/c\ 2/m\ 2/m\)
3475\(bca\)-I 2 2a\(I\ m\ c\ m\)\(I\ 2/m\ 2/c\ 2/m\)
3486\(a\bar{c}b\)-I 2c 2\(I\ m\ a\ m\)\(I\ 2/m\ 2/a\ 2/m\)

Tetragonal 正方晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
349751P 4\(C_4^1\)\(P\ 4\)\(P\ 4\)9\(4\)\(C_4\)4\(4/m\)4tetragonal
350761P 4w\(C_4^2\)\(P\ 4_1\)\(P\ 4_1\)
351771P 4c\(C_4^3\)\(P\ 4_2\)\(P\ 4_2\)
352781P 4cw\(C_4^4\)\(P\ 4_3\)\(P\ 4_3\)
353791I 4\(C_4^5\)\(I\ 4\)\(I\ 4\)
354801I 4bw\(C_4^6\)\(I\ 4_1\)\(I\ 4_1\)
355811P -4\(S_4^1\)\(P\ \bar{4}\)\(P\ \bar{4}\)10\(\bar{4}\)\(S_4\)
356821I -4\(S_4^2\)\(I\ \bar{4}\)\(I\ \bar{4}\)
357831-P 4\(C_{4h}^1\)\(P\ 4/m\)\(P\ 4/m\)11\(4/m\)\(C_{4h}\)
358841-P 4c\(C_{4h}^2\)\(P\ 4_2/\ m\)\(P\ 4_2/m\)
359851\(1\)P 4ab -1ab\(C_{4h}^3\)\(P\ 4/n\)\(P\ 4/n\)
3602\(2\)-P 4a
361861\(1\)P 4n -1n\(C_{4h}^4\)\(P\ 4_2/\ n\)\(P\ 4_2/n\)
3622\(2\)-P 4bc
363871-I 4\(C_{4h}^5\)\(I\ 4/m\)\(I\ 4/m\)
364881\(1\)I 4bw -1bw\(C_{4h}^6\)\(I\ 4_1/\ a\)\(I\ 4_1/a\)
3652\(2\)-I 4ad
366891P 4 2\(D_4^1\)\(P\ 4\ 2\ 2\)\(P\ 4\ 2\ 2\)12\(4\ 2\ 2\)\(D_4\)5\(4/mmm\)
367901P 4ab 2ab\(D_4^2\)\(P\ 4\ 2_1\ 2\)\(P\ 4\ 2_1\ 2\)
368911P 4w 2c\(D_4^3\)\(P\ 4_1\ 2\ 2\)\(P\ 4_1\ 2\ 2\)
369921P 4abw 2nw\(D_4^4\)\(P\ 4_1\ 2_1\ 2\)\(P\ 4_1\ 2_1\ 2\)
370931P 4c 2\(D_4^5\)\(P\ 4_2\ 2\ 2\)\(P\ 4_2\ 2\ 2\)
371941P 4n 2n\(D_4^6\)\(P\ 4_2\ 2_1\ 2\)\(P\ 4_2\ 2_1\ 2\)
372951P 4cw 2c\(D_4^7\)\(P\ 4_3\ 2\ 2\)\(P\ 4_3\ 2\ 2\)
373961P 4nw 2abw\(D_4^8\)\(P\ 4_3\ 2_1\ 2\)\(P\ 4_3\ 2_1\ 2\)
374971I 4 2\(D_4^9\)\(I\ 4\ 2\ 2\)\(I\ 4\ 2\ 2\)
375981I 4bw 2bw\(D_4^{10}\)\(I\ 4_1\ 2\ 2\)\(I\ 4_1\ 2\ 2\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbol_Schoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
376991P 4 -2\(C_{4v}^1\)\(P\ 4\ m\ m\)\(P\ 4\ m\ m\)13\(4\ m\ m\)\(C_{4v}\)5\(4/mmm\)4tetragonal
3771001P 4 -2ab\(C_{4v}^2\)\(P\ 4\ b\ m\)\(P\ 4\ b\ m\)
3781011P 4c -2c\(C_{4v}^3\)\(P\ 4_2\ c\ m\)\(P\ 4_2\ c\ m\)
3791021P 4n -2n\(C_{4v}^4\)\(P\ 4_2\ n\ m\)\(P\ 4_2\ n\ m\)
3801031P 4 -2c\(C_{4v}^5\)\(P\ 4\ c\ c\)\(P\ 4\ c\ c\)
3811041P 4 -2n\(C_{4v}^6\)\(P\ 4\ n\ c\)\(P\ 4\ n\ c\)
3821051P 4c -2\(C_{4v}^7\)\(P\ 4_2\ m\ c\)\(P\ 4_2\ m\ c\)
3831061P 4c -2ab\(C_{4v}^8\)\(P\ 4_2\ b\ c\)\(P\ 4_2\ b\ c\)
3841071I 4 -2\(C_{4v}^9\)\(I\ 4\ m\ m\)\(I\ 4\ m\ m\)
3851081I 4 -2c\(C_{4v}^{10}\)\(I\ 4\ c\ m\)\(I\ 4\ c\ m\)
3861091I 4bw -2\(C_{4v}^{11}\)\(I\ 4_1\ m\ d\)\(I\ 4_1\ m\ d\)
3871101I 4bw -2c\(C_{4v}^{12}\)\(I\ 4_1\ c\ d\)\(I\ 4_1\ c\ d\)
3881111P -4 2\(D_{2d}^1\)\(P\ \bar{4}\ 2\ m\)\(P\ \bar{4}\ 2\ m\)14\(\bar{4}\ 2\ m\)\(D_{2d}\)
3891121P -4 2c\(D_{2d}^2\)\(P\ \bar{4}\ 2\ c\)\(P\ \bar{4}\ 2\ c\)
3901131P -4 2ab\(D_{2d}^3\)\(P\ \bar{4}\ 2_1\ m\)\(P\ \bar{4}\ 2_1\ m\)
3911141P -4 2n\(D_{2d}^4\)\(P\ \bar{4}\ 2_1\ c\)\(P\ \bar{4}\ 2_1\ c\)
3921151P -4 -2\(D_{2d}^5\)\(P\ \bar{4}\ m\ 2\)\(P\ \bar{4}\ m\ 2\)
3931161P -4 -2c\(D_{2d}^6\)\(P\ \bar{4}\ c\ 2\)\(P\ \bar{4}\ c\ 2\)
3941171P -4 -2ab\(D_{2d}^7\)\(P\ \bar{4}\ b\ 2\)\(P\ \bar{4}\ b\ 2\)
3951181P -4 -2n\(D_{2d}^8\)\(P\ \bar{4}\ n\ 2\)\(P\ \bar{4}\ n\ 2\)
3961191I -4 -2\(D_{2d}^9\)\(I\ \bar{4}\ m\ 2\)\(I\ \bar{4}\ m\ 2\)
3971201I -4 -2c\(D_{2d}^{10}\)\(I\ \bar{4}\ c\ 2\)\(I\ \bar{4}\ c\ 2\)
3981211I -4 2\(D_{2d}^{11}\)\(I\ \bar{4}\ 2\ m\)\(I\ \bar{4}\ 2\ m\)
3991221I -4 2bw\(D_{2d}^{12}\)\(I\ \bar{4}\ 2\ d\)\(I\ \bar{4}\ 2\ d\)
4001231-P 4 2\(D_{4h}^1\)\(P\ 4/m\ m\ m\)\(P\ 4/m\ 2/m\ 2/m\)15\(4/m\ m\ m\)\(D_{4h}\)
4011241-P 4 2c\(D_{4h}^2\)\(P\ 4/m\ c\ c\)\(P\ 4/m\ 2/c\ 2/c\)
4021251\(1\)P 4 2 -1ab\(D_{4h}^3\)\(P\ 4/n\ b\ m\)\(P\ 4/n\ 2/b\ 2/m\)
4032\(2\)-P 4a 2b
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
4041261\(1\)P 4 2 -1n\(D_{4h}^4\)\(P\ 4/n\ n\ c\)\(P\ 4/n\ 2/n\ 2/c\)15\(4/m\ m\ m\)\(D_{4h}\)5\(4/mmm\)4tetragonal
4052\(2\)-P 4a 2bc
4061271-P 4 2ab\(D_{4h}^5\)\(P\ 4/m\ b\ m\)\(P\ 4/m\ 2_1/b\ m\)
4071281-P 4 2n\(D_{4h}^6\)\(P\ 4/m\ n\ c\)\(P\ 4/m\ 2_1/n\ c\)
4081291\(1\)P 4ab 2ab -1ab\(D_{4h}^7\)\(P\ 4/n\ m\ m\)\(P\ 4/n\ 2_1/m\ m\)
4092\(2\)-P 4a 2a
4101301\(1\)P 4ab 2n -1ab\(D_{4h}^8\)\(P\ 4/n\ c\ c\)\(P\ 4/n\ 2_1/c\ c\)
4112\(2\)-P 4a 2ac
4121311-P 4c 2\(D_{4h}^9\)\(P\ 4_2/\ m\ m\ c\)\(P\ 4_2/m\ 2/m\ 2/c\)
4131321-P 4c 2c\(D_{4h}^{10}\)\(P\ 4_2/\ m\ c\ m\)\(P\ 4_2/m\ 2/c\ 2/m\)
4141331\(1\)P 4n 2c -1n\(D_{4h}^{11}\)\(P\ 4_2/\ n\ b\ c\)\(P\ 4_2/n\ 2/b\ 2/c\)
4152\(2\)-P 4ac 2b
4161341\(1\)P 4n 2 -1n\(D_{4h}^{12}\)\(P\ 4_2/\ n\ n\ m\)\(P\ 4_2/n\ 2/n\ 2/m\)
4172\(2\)-P 4ac 2bc
4181351-P 4c 2ab\(D_{4h}^{13}\)\(P\ 4_2/\ m\ b\ c\)\(P\ 4_2/m\ 2_1/b\ 2/c\)
4191361-P 4n 2n\(D_{4h}^{14}\)\(P\ 4_2/\ m\ n\ m\)\(P\ 4_2/m\ 2_1/n\ 2/m\)
4201371\(1\)P 4n 2n -1n\(D_{4h}^{15}\)\(P\ 4_2/\ n\ m\ c\)\(P\ 4_2/n\ 2_1/m\ 2/c\)
4212\(2\)-P 4ac 2a
4221381\(1\)P 4n 2ab -1n\(D_{4h}^{16}\)\(P\ 4_2/\ n\ c\ m\)\(P\ 4_2/n\ 2_1/c\ 2/m\)
4232\(2\)-P 4ac 2ac
4241391-I 4 2\(D_{4h}^{17}\)\(I\ 4/m\ m\ m\)\(I\ 4/m\ 2/m\ 2/m\)
4251401-I 4 2c\(D_{4h}^{18}\)\(I\ 4/m\ c\ m\)\(I\ 4/m\ 2/c\ 2/m\)
4261411\(1\)I 4bw 2bw -1bw\(D_{4h}^{19}\)\(I\ 4_1/\ a\ m\ d\)\(I\ 4_1/a\ 2/m\ 2/d\)
4272\(2\)-I 4bd 2
4281421\(1\)I 4bw 2aw -1bw\(D_{4h}^{20}\)\(I\ 4_1/\ a\ c\ d\)\(I\ 4_1/a\ 2/c\ 2/d\)
4292\(2\)-I 4bd 2c

Trigonal 三方晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
4301431P 3\(C_3^1\)\(P\ 3\)\(P\ 3\)16\(3\)\(C_{3}\)6\(\bar{3}\)5trigonal
4311441P 31\(C_3^2\)\(P\ 3_1\)\(P\ 3_1\)
4321451P 32\(C_3^3\)\(P\ 3_2\)\(P\ 3_2\)
4331461\(H\)R 3\(C_3^4\)\(R\ 3\)\(R\ 3\)
4342\(R\)P 3*
4351471-P 3\(C_{3i}^1\)\(P\ \bar{3}\)\(P\ \bar{3}\)17\(\bar{3}\)
4361481\(H\)-R 3\(C_{3i}^2\)\(R\ \bar{3}\)\(R\ \bar{3}\)
4372\(R\)-P 3*
4381491P 3 2\(D_3^1\)\(P\ 3\ 1\ 2\)\(P\ 3\ 1\ 2\)18\(3\ 2\)\(D_3\)7\(\bar{3}2m\)
4391501P 3 2\\(D_3^2\)\(P\ 3\ 2\ 1\)\(P\ 3\ 2\ 1\)
4401511P 31 2c (0 0 1)\(D_3^3\)\(P\ 3_1\ 1\ 2\)\(P\ 3_1\ 1\ 2\)
4411521P 31 2\\(D_3^4\)\(P\ 3_1\ 2\ 1\)\(P\ 3_1\ 2\ 1\)
4421531P 32 2c (0 0 -1)\(D_3^5\)\(P\ 3_2\ 1\ 2\)\(P\ 3_2\ 1\ 2\)
4431541P 32 2\\(D_3^6\)\(P\ 3_2\ 2\ 1\)\(P\ 3_2\ 2\ 1\)
4441551\(H\)R 3 2\\(D_3^7\)\(R\ 3\ 2\)\(R\ 3\ 2\)
4452\(R\)P 3* 2
4461561P 3 -2\\(C_{3v}^1\)\(P\ 3\ m\ 1\)\(P\ 3\ m\ 1\)19\(3\ m\)\(C_{3v}\)
4471571P 3 -2\(C_{3v}^2\)\(P\ 3\ 1\ m\)\(P\ 3\ 1\ m\)
4481581P 3 -2\c\(C_{3v}^3\)\(P\ 3\ c\ 1\)\(P\ 3\ c\ 1\)
4491591P 3 -2c\(C_{3v}^4\)\(P\ 3\ 1\ c\)\(P\ 3\ 1\ c\)
4501601\(H\)R 3 -2\\(C_{3v}^5\)\(R\ 3\ m\)\(R\ 3\ m\)
4512\(R\)P 3* -2
4521611\(H\)R 3 -2\c\(C_{3v}^6\)\(R\ 3\ c\)\(R\ 3\ c\)
4532\(R\)P 3* -2n
4541621-P 3 2\(D_{3d}^1\)\(P\ \bar{3}\ \ 1\ m\)\(P\ \bar{3}\ 1\ 2/m\)20\(\bar{3}\ m\)\(D_{3d}\)
4551631-P 3 2c\(D_{3d}^2\)\(P\ \bar{3}\ \ 1\ c\)\(P\ \bar{3}\ 1\ 2/c\)
4561641-P 3 2\\(D_{3d}^3\)\(P\ \bar{3}\ \ m\ 1\)\(P\ \bar{3}\ 2/m\ 1\)
4571651-P 3 2\c\(D_{3d}^4\)\(P\ \bar{3}\ \ c\ 1\)\(P\ \bar{3}\ 2/c\ 1\)
4581661\(H\)-R 3 2\\(D_{3d}^5\)\(R\ \bar{3}\ \ m\)\(R\ \bar{3}\ 2/m\)
4592\(R\)-P 3* 2
4601671\(H\)-R 3 2\c\(D_{3d}^6\)\(R\ \bar{3}\ \ c\)\(R\ \bar{3}\ 2/c\)
4612\(R\)-P 3* 2n

Hexagonal 六方晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. o5f
Crystal
System
Crystal System
4621681P 6\(C_61\)\(P\ 6\)\(P\ 6\)21\(6\)\(C_6\)8\(6/m\)6hexagonal
4631691P 61\(C_62\)\(P\ 6_1\)\(P\ 6_1\)
4641701P 65\(C_63\)\(P\ 6_5\)\(P\ 6_5\)
4651711P 62\(C_64\)\(P\ 6_2\)\(P\ 6_2\)
4661721P 64\(C_65\)\(P\ 6_4\)\(P\ 6_4\)
4671731P 6c\(C_66\)\(P\ 6_3\)\(P\ 6_3\)
4681741P -6\(C_{3h}^1\)\(P\ \bar{6}\)\(P\ \bar{6}\)22\(\bar{6}\)\(C_{3}h\)
4691751-P 6\(C_{6h}^1\)\(P\ 6/m\)\(P\ 6/m\)23\(6/m\)\(C_6h\)
4701761-P 6c\(C_{6h}^2\)\(P\ 6_3/m\)\(P\ 6_3/m\)
4711771P 6 2\(D_61\)\(P\ 6\ 2\ 2\)\(P\ 6\ 2\ 2\)24\(6\ 2\ 2\)\(D_6\)9\(6/mmm\)
4721781P 61 2 (0 0 -1)\(D_62\)\(P\ 6_1\ 2\ 2\)\(P\ 6_1\ 2\ 2\)
4731791P 65 2 (0 0 1)\(D_63\)\(P\ 6_5\ 2\ 2\)\(P\ 6_5\ 2\ 2\)
4741801P 62 2c (0 0 1)\(D_64\)\(P\ 6_2\ 2\ 2\)\(P\ 6_2\ 2\ 2\)
4751811P 64 2c (0 0 -1)\(D_65\)\(P\ 6_4\ 2\ 2\)\(P\ 6_4\ 2\ 2\)
4761821P 6c 2c\(D_66\)\(P\ 6_3\ 2\ 2\)\(P\ 6_3\ 2\ 2\)
4771831P 6 -2\(C_6v1\)\(P\ 6\ m\ m\)\(P\ 6\ m\ m\)25\(6\ m\ m\)\(C_{6v}\)
4781841P 6 -2c\(C_6v2\)\(P\ 6\ c\ c\)\(P\ 6\ c\ c\)
4791851P 6c -2\(C_6v3\)\(P\ 6_3\ c\ m\)\(P\ 6_3\ c\ m\)
4801861P 6c -2c\(C_6v4\)\(P\ 6_3\ m\ c\)\(P\ 6_3\ m\ c\)
4811871P -6 2\(D_{3h}^1\)\(P\ \bar{6}\ m\ 2\)\(P\ \bar{6}\ m\ 2\)26\(\bar{6}\ m\ 2\)\(D_{3h}\)
4821881P -6c 2\(D_{3h}^2\)\(P\ \bar{6}\ c\ 2\)\(P\ \bar{6}\ c\ 2\)
4831891P -6 -2\(D_{3h}^3\)\(P\ \bar{6}\ 2\ m\)\(P\ \bar{6}\ 2\ m\)
4841901P -6c -2c\(D_{3h}^4\)\(P\ \bar{6}\ 2\ c\)\(P\ \bar{6}\ 2\ c\)
4851911-P 6 2\(D_{6h}^1\)\(P\ 6/m\ m\ m\)\(P\ 6/m\ 2/m\ 2/m\)27\(6/m\ m\ m\)\(D_{6h}\)
4861921-P 6 2c\(D_{6h}^2\)\(P\ 6/m\ c\ c\)\(P\ 6/m\ 2/c\ 2/c\)
4871931-P 6c 2\(D_{6h}^3\)\(P\ 6_3/m\ c\ m\)\(P\ 6_3/m\ 2/c\ 2/m\)
4881941-P 6c 2c\(D_{6h}^4\)\(P\ 6_3/m\ m\ c\)\(P\ 6_3/m\ 2/m\ 2/c\)

Cubic 立方晶系

Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
4891951P 2 2 3\(T^1\)\(P\ 2\ 3\)\(P\ 2\ 3\)28\(2\ 3\)\(T\)10\(m\bar{3}\)7cubic
4901961F 2 2 3\(T^2\)\(F\ 2\ 3\)\(F\ 2\ 3\)
4911971I 2 2 3\(T^3\)\(I\ 2\ 3\)\(I\ 2\ 3\)
4921981P 2ac 2ab 3\(T^4\)\(P\ 2_1\ 3\)\(P\ 2_1\ 3\)
4931991I 2b 2c 3\(T^5\)\(I\ 2_1\ 3\)\(I\ 2_1\ 3\)
4942001-P 2 2 3\(T_h^1\)\(P\ m\ \bar{3}\)\(P\ 2/m\ \bar{3}\)29\(m\ \bar{3}\)\(T_h\)
4952011\(1\)P 2 2 3 -1n\(T_h^2\)\(P\ n\ \bar{3}\)\(P\ 2/n\ \bar{3}\)
4962\(2\)-P 2ab 2bc 3
4972021-F 2 2 3\(T_h^3\)\(F\ m\ \bar{3}\)\(F\ 2/m\ \bar{3}\)
4982031\(1\)F 2 2 3 -1d\(T_h^4\)\(F\ d\ \bar{3}\)\(F\ 2/d\ \bar{3}\)
4992\(2\)-F 2uv 2vw 3
5002041-I 2 2 3\(T_h^5\)\(I\ m\ \bar{3}\)\(I\ 2/m\ \bar{3}\)
5012051-P 2ac 2ab 3\(T_h^6\)\(P\ a\ \bar{3}\)\(P\ 2_1/a\ \bar{3}\)
5022061-I 2b 2c 3\(T_h^7\)\(I\ a\ \bar{3}\)\(I\ 2_1/a\ \bar{3}\)
5032071P 4 2 3\(O^1\)\(P\ 4\ 3\ 2\)\(P\ 4\ 3\ 2\)30\(4\ 3\ 2\)\(O\)11\(m\bar{3}m\)
5042081P 4n 2 3\(O^2\)\(P\ 4_2\ 3\ 2\)\(P\ 4_2\ 3\ 2\)
5052091F 4 2 3\(O^3\)\(F\ 4\ 3\ 2\)\(F\ 4\ 3\ 2\)
5062101F 4d 2 3\(O^4\)\(F\ 4_1\ 3\ 2\)\(F\ 4_1\ 3\ 2\)
5072111I 4 2 3\(O^5\)\(I\ 4\ 3\ 2\)\(I\ 4\ 3\ 2\)
5082121P 4acd 2ab 3\(O^6\)\(P\ 4_3\ 3\ 2\)\(P\ 4_3\ 3\ 2\)
Serial No.ITA No.Sub No.Axis
setting,
Origin
Hall symbolSchoenflies
symbol
HM symbol
(short)
HM symbol
(full)
No. of
Point
Group
Point
group
(HM)
Point
group
(Schoenflies)
No. of
Laue
Group
Laue
Group

(HM)
No. of
Crystal
System
Crystal System
5092131P 4bd 2ab 3\(O^7\)\(P\ 4_1\ 3\ 2\)\(P\ 4_1\ 3\ 2\)30\(4\ 3\ 2\)\(O\)11\(m\bar{3}m\)7cubic
5102141I 4bd 2c 3\(O^8\)\(I\ 4_1\ 3\ 2\)\(I\ 4_1\ 3\ 2\)
5112151P -4 2 3\(T_d^1\)\(P\ \bar{4}\ 3\ m\)\(P\ \bar{4}\ 3\ m\)31\(\bar{4}\ 3\ m\)\(T_d\)
5122161F -4 2 3\(T_d^2\)\(F\ \bar{4}\ 3\ m\)\(F\ \bar{4}\ 3\ m\)
5132171I -4 2 3\(T_d^3\)\(I\ \bar{4}\ 3\ m\)\(I\ \bar{4}\ 3\ m\)
5142181P -4n 2 3\(T_d^4\)\(P\ \bar{4}\ 3\ n\)\(P\ \bar{4}\ 3\ n\)
5152191F -4c 2 3\(T_d^5\)\(F\ \bar{4}\ 3\ c\)\(F\ \bar{4}\ 3\ c\)
5162201I -4bd 2c 3\(T_d^6\)\(I\ \bar{4}\ 3\ d\)\(I\ \bar{4}\ 3\ d\)
5172211-P 4 2 3\(O_h^1\)\(P\ m\ \bar{3}\ \ m\)\(P\ 4/m\ \bar{3}\ 2/m\)32\(m\ \bar{3}\ m\)\(O_h\)
5182221\(1\)P 4 2 3 -1n\(O_h^2\)\(P\ n\ \bar{3}\ \ n\)\(P\ 4/n\ \bar{3}\ 2/n\)
5192\(2\)-P 4a 2bc 3
5202231-P 4n 2 3\(O_h^3\)\(P\ m\ \bar{3}\ \ n\)\(P\ 4_2/m\ \bar{3}\ 2/n\)
5212241\(1\)P 4n 2 3 -1n\(O_h^4\)\(P\ n\ \bar{3}\ \ m\)\(P\ 4_2/n\ \bar{3}\ 2/m\)
5222\(2\)-P 4bc 2bc 3
5232251-F 4 2 3\(O_h^5\)\(F\ m\ \bar{3}\ \ m\)\(F\ 4/m\ \bar{3}\ 2/m\)
5242261-F 4c 2 3\(O_h^6\)\(F\ m\ \bar{3}\ \ c\)\(F\ 4/m\ \bar{3}\ 2/c\)
5252271\(1\)F 4d 2 3 -1d\(O_h^7\)\(F\ d\ \bar{3}\ \ m\)\(F\ 4_1/d\ \bar{3}\ 2/m\)
5262\(2\)-F 4vw 2vw 3
5272281\(1\)F 4d 2 3 -1cd\(O_h^8\)\(F\ d\ \bar{3}\ \ c\)\(F\ 4_1/d\ \bar{3}\ 2/c\)
5282\(2\)-F 4cvw 2vw 3
5292291-I 4 2 3\(O_h^9\)\(I\ m\ \bar{3}\ \ m\)\(I\ 4/m\ \bar{3}\ 2/m\)
5302301-I 4bd 2c 3\(O_h^{10}\)\(I\ a\ \bar{3}\ \ d\)\(I\ 4_1/a\ \bar{3}\ 2/d\)

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Stupidity has a certain charm; ignorance does not. Frank Zappa