Hermann Mauguin Symbol
Number Schoenflies Hermann-Mauguin Hall
1 C$_{1}^{1}$ P1 P 1
2 C$_{i}^{1}$ P-1 -P 1
3:b C$_{2}^{1}$ P2:b = P121 P 2y
3:c C$_{2}^{1}$ P2:c = P112 P 2
3:a C$_{2}^{1}$ P2:a = P211 P 2x
4:b C$_{2}^{2}$ P21:b = P1211 P 2yb
4:c C$_{2}^{2}$ P21:c = P1121 P 2c
4:a C$_{2}^{2}$ P21:a = P2111 P 2xa
5:b1 C$_{2}^{3}$ C2:b1 = C121 C 2y
5:b2 C$_{2}^{3}$ C2:b2 = A121 A 2y
5:b3 C$_{2}^{3}$ C2:b3 = I121 I 2y
5:c1 C$_{2}^{3}$ C2:c1 = A112 A 2
5:c2 C$_{2}^{3}$ C2:c2 = B112 = B2 B 2
5:c3 C$_{2}^{3}$ C2:c3 = I112 I 2
5:a1 C$_{2}^{3}$ C2:a1 = B211 B 2x
5:a2 C$_{2}^{3}$ C2:a2 = C211 C 2x
5:a3 C$_{2}^{3}$ C2:a3 = I211 I 2x
6:b C$_{s}^{1}$ Pm:b = P1m1 P -2y
6:c C$_{s}^{1}$ Pm:c = P11m P -2
6:a C$_{s}^{1}$ Pm:a = Pm11 P -2x
7:b1 C$_{s}^{2}$ Pc:b1 = P1c1 P -2yc
7:b2 C$_{s}^{2}$ Pc:b2 = P1n1 P -2yac
7:b3 C$_{s}^{2}$ Pc:b3 = P1a1 P -2ya
7:c1 C$_{s}^{2}$ Pc:c1 = P11a P -2a
7:c2 C$_{s}^{2}$ Pc:c2 = P11n P -2ab
7:c3 C$_{s}^{2}$ Pc:c3 = P11b = Pb P -2b
7:a1 C$_{s}^{2}$ Pc:a1 = Pb11 P -2xb
7:a2 C$_{s}^{2}$ Pc:a2 = Pn11 P -2xbc
7:a3 C$_{s}^{2}$ Pc:a3 = Pc11 P -2xc
8:b1 C$_{s}^{3}$ Cm:b1 = C1m1 C -2y
8:b2 C$_{s}^{3}$ Cm:b2 = A1m1 A -2y
8:b3 C$_{s}^{3}$ Cm:b3 = I1m1 I -2y
8:c1 C$_{s}^{3}$ Cm:c1 = A11m A -2
8:c2 C$_{s}^{3}$ Cm:c2 = B11m = Bm B -2
8:c3 C$_{s}^{3}$ Cm:c3 = I11m I -2
8:a1 C$_{s}^{3}$ Cm:a1 = Bm11 B -2x
8:a2 C$_{s}^{3}$ Cm:a2 = Cm11 C -2x
8:a3 C$_{s}^{3}$ Cm:a3 = Im11 I -2x
9:b1 C$_{s}^{4}$ Cc:b1 = C1c1 C -2yc
9:b2 C$_{s}^{4}$ Cc:b2 = A1n1 A -2yac
9:b3 C$_{s}^{4}$ Cc:b3 = I1a1 I -2ya
9:-b1 C$_{s}^{4}$ Cc:-b1 = A1a1 A -2ya
9:-b2 C$_{s}^{4}$ Cc:-b2 = C1n1 C -2ybc
9:-b3 C$_{s}^{4}$ Cc:-b3 = I1c1 I -2yc
9:c1 C$_{s}^{4}$ Cc:c1 = A11a A -2a
9:c2 C$_{s}^{4}$ Cc:c2 = B11n B -2bc
9:c3 C$_{s}^{4}$ Cc:c3 = I11b I -2b
9:-c1 C$_{s}^{4}$ Cc:-c1 = B11b = Bb B -2b
9:-c2 C$_{s}^{4}$ Cc:-c2 = A11n A -2ac
9:-c3 C$_{s}^{4}$ Cc:-c3 = I11a I -2a
9:a1 C$_{s}^{4}$ Cc:a1 = Bb11 B -2xb
9:a2 C$_{s}^{4}$ Cc:a2 = Cn11 C -2xbc
9:a3 C$_{s}^{4}$ Cc:a3 = Ic11 I -2xc
9:-a1 C$_{s}^{4}$ Cc:-a1 = Cc11 C -2xc
9:-a2 C$_{s}^{4}$ Cc:-a2 = Bn11 B -2xbc
9:-a3 C$_{s}^{4}$ Cc:-a3 = Ib11 I -2xb
10:b C$_{2h}^{1}$ P2/m:b = P12/m1 -P 2y
10:c C$_{2h}^{1}$ P2/m:c = P112/m -P 2
10:a C$_{2h}^{1}$ P2/m:a = P2/m11 -P 2x
11:b C$_{2h}^{2}$ P21/m:b = P121/m1 -P 2yb
11:c C$_{2h}^{2}$ P21/m:c = P1121/m -P 2c
11:a C$_{2h}^{2}$ P21/m:a = P21/m11 -P 2xa
12:b1 C$_{2h}^{3}$ C2/m:b1 = C12/m1 -C 2y
12:b2 C$_{2h}^{3}$ C2/m:b2 = A12/m1 -A 2y
12:b3 C$_{2h}^{3}$ C2/m:b3 = I12/m1 -I 2y
12:c1 C$_{2h}^{3}$ C2/m:c1 = A112/m -A 2
12:c2 C$_{2h}^{3}$ C2/m:c2 = B112/m = B2/m -B 2
12:c3 C$_{2h}^{3}$ C2/m:c3 = I112/m -I 2
12:a1 C$_{2h}^{3}$ C2/m:a1 = B2/m11 -B 2x
12:a2 C$_{2h}^{3}$ C2/m:a2 = C2/m11 -C 2x
12:a3 C$_{2h}^{3}$ C2/m:a3 = I2/m11 -I 2x
13:b1 C$_{2h}^{4}$ P2/c:b1 = P12/c1 -P 2yc
13:b2 C$_{2h}^{4}$ P2/c:b2 = P12/n1 -P 2yac
13:b3 C$_{2h}^{4}$ P2/c:b3 = P12/a1 -P 2ya
13:c1 C$_{2h}^{4}$ P2/c:c1 = P112/a -P 2a
13:c2 C$_{2h}^{4}$ P2/c:c2 = P112/n -P 2ab
13:c3 C$_{2h}^{4}$ P2/c:c3 = P112/b = P2/b -P 2b
13:a1 C$_{2h}^{4}$ P2/c:a1 = P2/b11 -P 2xb
13:a2 C$_{2h}^{4}$ P2/c:a2 = P2/n11 -P 2xbc
13:a3 C$_{2h}^{4}$ P2/c:a3 = P2/c11 -P 2xc
14:b1 C$_{2h}^{5}$ P21/c:b1 = P121/c1 -P 2ybc
14:b2 C$_{2h}^{5}$ P21/c:b2 = P121/n1 -P 2yn
14:b3 C$_{2h}^{5}$ P21/c:b3 = P121/a1 -P 2yab
14:c1 C$_{2h}^{5}$ P21/c:c1 = P1121/a -P 2ac
14:c2 C$_{2h}^{5}$ P21/c:c2 = P1121/n -P 2n
14:c3 C$_{2h}^{5}$ P21/c:c3 = P1121/b = P21/b -P 2bc
14:a1 C$_{2h}^{5}$ P21/c:a1 = P21/b11 -P 2xab
14:a2 C$_{2h}^{5}$ P21/c:a2 = P21/n11 -P 2xn
14:a3 C$_{2h}^{5}$ P21/c:a3 = P21/c11 -P 2xac
15:b1 C$_{2h}^{6}$ C2/c:b1 = C12/c1 -C 2yc
15:b2 C$_{2h}^{6}$ C2/c:b2 = A12/n1 -A 2yac
15:b3 C$_{2h}^{6}$ C2/c:b3 = I12/a1 -I 2ya
15:-b1 C$_{2h}^{6}$ C2/c:-b1 = A12/a1 -A 2ya
15:-b2 C$_{2h}^{6}$ C2/c:-b2 = C12/n1 -C 2ybc
15:-b3 C$_{2h}^{6}$ C2/c:-b3 = I12/c1 -I 2yc
15:c1 C$_{2h}^{6}$ C2/c:c1 = A112/a -A 2a
15:c2 C$_{2h}^{6}$ C2/c:c2 = B112/n -B 2bc
15:c3 C$_{2h}^{6}$ C2/c:c3 = I112/b -I 2b
15:-c1 C$_{2h}^{6}$ C2/c:-c1 = B112/b = B2/b -B 2b
15:-c2 C$_{2h}^{6}$ C2/c:-c2 = A112/n -A 2ac
15:-c3 C$_{2h}^{6}$ C2/c:-c3 = I112/a -I 2a
15:a1 C$_{2h}^{6}$ C2/c:a1 = B2/b11 -B 2xb
15:a2 C$_{2h}^{6}$ C2/c:a2 = C2/n11 -C 2xbc
15:a3 C$_{2h}^{6}$ C2/c:a3 = I2/c11 -I 2xc
15:-a1 C$_{2h}^{6}$ C2/c:-a1 = C2/c11 -C 2xc
15:-a2 C$_{2h}^{6}$ C2/c:-a2 = B2/n11 -B 2xbc
15:-a3 C$_{2h}^{6}$ C2/c:-a3 = I2/b11 -I 2xb
16 D$_{2}^{1}$ P222 P 2 2
17 D$_{2}^{2}$ P2221 P 2c 2
17:cab D$_{2}^{2}$ P2122 P 2a 2a
17:bca D$_{2}^{2}$ P2212 P 2 2b
18 D$_{2}^{3}$ P21212 P 2 2ab
18:cab D$_{2}^{3}$ P22121 P 2bc 2
18:bca D$_{2}^{3}$ P21221 P 2ac 2ac
19 D$_{2}^{4}$ P212121 P 2ac 2ab
20 D$_{2}^{5}$ C2221 C 2c 2
20:cab D$_{2}^{5}$ A2122 A 2a 2a
20:bca D$_{2}^{5}$ B2212 B 2 2b
21 D$_{2}^{6}$ C222 C 2 2
21:cab D$_{2}^{6}$ A222 A 2 2
21:bca D$_{2}^{6}$ B222 B 2 2
22 D$_{2}^{7}$ F222 F 2 2
23 D$_{2}^{8}$ I222 I 2 2
24 D$_{2}^{9}$ I212121 I 2b 2c
25 C$_{2v}^{1}$ Pmm2 P 2 -2
25:cab C$_{2v}^{1}$ P2mm P -2 2
25:bca C$_{2v}^{1}$ Pm2m P -2 -2
26 C$_{2v}^{2}$ Pmc21 P 2c -2
26:ba-c C$_{2v}^{2}$ Pcm21 P 2c -2c
26:cab C$_{2v}^{2}$ P21ma P -2a 2a
26:-cba C$_{2v}^{2}$ P21am P -2 2a
26:bca C$_{2v}^{2}$ Pb21m P -2 -2b
26:a-cb C$_{2v}^{2}$ Pm21b P -2b -2
27 C$_{2v}^{3}$ Pcc2 P 2 -2c
27:cab C$_{2v}^{3}$ P2aa P -2a 2
27:bca C$_{2v}^{3}$ Pb2b P -2b -2b
28 C$_{2v}^{4}$ Pma2 P 2 -2a
28:ba-c C$_{2v}^{4}$ Pbm2 P 2 -2b
28:cab C$_{2v}^{4}$ P2mb P -2b 2
28:-cba C$_{2v}^{4}$ P2cm P -2c 2
28:bca C$_{2v}^{4}$ Pc2m P -2c -2c
28:a-cb C$_{2v}^{4}$ Pm2a P -2a -2a
29 C$_{2v}^{5}$ Pca21 P 2c -2ac
29:ba-c C$_{2v}^{5}$ Pbc21 P 2c -2b
29:cab C$_{2v}^{5}$ P21ab P -2b 2a
29:-cba C$_{2v}^{5}$ P21ca P -2ac 2a
29:bca C$_{2v}^{5}$ Pc21b P -2bc -2c
29:a-cb C$_{2v}^{5}$ Pb21a P -2a -2ab
30 C$_{2v}^{6}$ Pnc2 P 2 -2bc
30:ba-c C$_{2v}^{6}$ Pcn2 P 2 -2ac
30:cab C$_{2v}^{6}$ P2na P -2ac 2
30:-cba C$_{2v}^{6}$ P2an P -2ab 2
30:bca C$_{2v}^{6}$ Pb2n P -2ab -2ab
30:a-cb C$_{2v}^{6}$ Pn2b P -2bc -2bc
31 C$_{2v}^{7}$ Pmn21 P 2ac -2
31:ba-c C$_{2v}^{7}$ Pnm21 P 2bc -2bc
31:cab C$_{2v}^{7}$ P21mn P -2ab 2ab
31:-cba C$_{2v}^{7}$ P21nm P -2 2ac
31:bca C$_{2v}^{7}$ Pn21m P -2 -2bc
31:a-cb C$_{2v}^{7}$ Pm21n P -2ab -2
32 C$_{2v}^{8}$ Pba2 P 2 -2ab
32:cab C$_{2v}^{8}$ P2cb P -2bc 2
32:bca C$_{2v}^{8}$ Pc2a P -2ac -2ac
33 C$_{2v}^{9}$ Pna21 P 2c -2n
33:ba-c C$_{2v}^{9}$ Pbn21 P 2c -2ab
33:cab C$_{2v}^{9}$ P21nb P -2bc 2a
33:-cba C$_{2v}^{9}$ P21cn P -2n 2a
33:bca C$_{2v}^{9}$ Pc21n P -2n -2ac
33:a-cb C$_{2v}^{9}$ Pn21a P -2ac -2n
34 C$_{2v}^{10}$ Pnn2 P 2 -2n
34:cab C$_{2v}^{10}$ P2nn P -2n 2
34:bca C$_{2v}^{10}$ Pn2n P -2n -2n
35 C$_{2v}^{11}$ Cmm2 C 2 -2
35:cab C$_{2v}^{11}$ A2mm A -2 2
35:bca C$_{2v}^{11}$ Bm2m B -2 -2
36 C$_{2v}^{12}$ Cmc21 C 2c -2
36:ba-c C$_{2v}^{12}$ Ccm21 C 2c -2c
36:cab C$_{2v}^{12}$ A21ma A -2a 2a
36:-cba C$_{2v}^{12}$ A21am A -2 2a
36:bca C$_{2v}^{12}$ Bb21m B -2 -2b
36:a-cb C$_{2v}^{12}$ Bm21b B -2b -2
37 C$_{2v}^{13}$ Ccc2 C 2 -2c
37:cab C$_{2v}^{13}$ A2aa A -2a 2
37:bca C$_{2v}^{13}$ Bb2b B -2b -2b
38 C$_{2v}^{14}$ Amm2 A 2 -2
38:ba-c C$_{2v}^{14}$ Bmm2 B 2 -2
38:cab C$_{2v}^{14}$ B2mm B -2 2
38:-cba C$_{2v}^{14}$ C2mm C -2 2
38:bca C$_{2v}^{14}$ Cm2m C -2 -2
38:a-cb C$_{2v}^{14}$ Am2m A -2 -2
39 C$_{2v}^{15}$ Abm2 A 2 -2c
39:ba-c C$_{2v}^{15}$ Bma2 B 2 -2c
39:cab C$_{2v}^{15}$ B2cm B -2c 2
39:-cba C$_{2v}^{15}$ C2mb C -2b 2
39:bca C$_{2v}^{15}$ Cm2a C -2b -2b
39:a-cb C$_{2v}^{15}$ Ac2m A -2c -2c
40 C$_{2v}^{16}$ Ama2 A 2 -2a
40:ba-c C$_{2v}^{16}$ Bbm2 B 2 -2b
40:cab C$_{2v}^{16}$ B2mb B -2b 2
40:-cba C$_{2v}^{16}$ C2cm C -2c 2
40:bca C$_{2v}^{16}$ Cc2m C -2c -2c
40:a-cb C$_{2v}^{16}$ Am2a A -2a -2a
41 C$_{2v}^{17}$ Aba2 A 2 -2ac
41:ba-c C$_{2v}^{17}$ Bba2 B 2 -2bc
41:cab C$_{2v}^{17}$ B2cb B -2bc 2
41:-cba C$_{2v}^{17}$ C2cb C -2bc 2
41:bca C$_{2v}^{17}$ Cc2a C -2bc -2bc
41:a-cb C$_{2v}^{17}$ Ac2a A -2ac -2ac
42 C$_{2v}^{18}$ Fmm2 F 2 -2
42:cab C$_{2v}^{18}$ F2mm F -2 2
42:bca C$_{2v}^{18}$ Fm2m F -2 -2
43 C$_{2v}^{19}$ Fdd2 F 2 -2d
43:cab C$_{2v}^{19}$ F2dd F -2d 2
43:bca C$_{2v}^{19}$ Fd2d F -2d -2d
44 C$_{2v}^{20}$ Imm2 I 2 -2
44:cab C$_{2v}^{20}$ I2mm I -2 2
44:bca C$_{2v}^{20}$ Im2m I -2 -2
45 C$_{2v}^{21}$ Iba2 I 2 -2c
45:cab C$_{2v}^{21}$ I2cb I -2a 2
45:bca C$_{2v}^{21}$ Ic2a I -2b -2b
46 C$_{2v}^{22}$ Ima2 I 2 -2a
46:ba-c C$_{2v}^{22}$ Ibm2 I 2 -2b
46:cab C$_{2v}^{22}$ I2mb I -2b 2
46:-cba C$_{2v}^{22}$ I2cm I -2c 2
46:bca C$_{2v}^{22}$ Ic2m I -2c -2c
46:a-cb C$_{2v}^{22}$ Im2a I -2a -2a
47 D$_{2h}^{1}$ Pmmm -P 2 2
48:1 D$_{2h}^{2}$ Pnnn:1 P 2 2 -1n
48:2 D$_{2h}^{2}$ Pnnn:2 -P 2ab 2bc
49 D$_{2h}^{3}$ Pccm -P 2 2c
49:cab D$_{2h}^{3}$ Pmaa -P 2a 2
49:bca D$_{2h}^{3}$ Pbmb -P 2b 2b
50:1 D$_{2h}^{4}$ Pban:1 P 2 2 -1ab
50:2 D$_{2h}^{4}$ Pban:2 -P 2ab 2b
50:1cab D$_{2h}^{4}$ Pncb:1 P 2 2 -1bc
50:2cab D$_{2h}^{4}$ Pncb:2 -P 2b 2bc
50:1bca D$_{2h}^{4}$ Pcna:1 P 2 2 -1ac
50:2bca D$_{2h}^{4}$ Pcna:2 -P 2a 2c
51 D$_{2h}^{5}$ Pmma -P 2a 2a
51:ba-c D$_{2h}^{5}$ Pmmb -P 2b 2
51:cab D$_{2h}^{5}$ Pbmm -P 2 2b
51:-cba D$_{2h}^{5}$ Pcmm -P 2c 2c
51:bca D$_{2h}^{5}$ Pmcm -P 2c 2
51:a-cb D$_{2h}^{5}$ Pmam -P 2 2a
52 D$_{2h}^{6}$ Pnna -P 2a 2bc
52:ba-c D$_{2h}^{6}$ Pnnb -P 2b 2n
52:cab D$_{2h}^{6}$ Pbnn -P 2n 2b
52:-cba D$_{2h}^{6}$ Pcnn -P 2ab 2c
52:bca D$_{2h}^{6}$ Pncn -P 2ab 2n
52:a-cb D$_{2h}^{6}$ Pnan -P 2n 2bc
53 D$_{2h}^{7}$ Pmna -P 2ac 2
53:ba-c D$_{2h}^{7}$ Pnmb -P 2bc 2bc
53:cab D$_{2h}^{7}$ Pbmn -P 2ab 2ab
53:-cba D$_{2h}^{7}$ Pcnm -P 2 2ac
53:bca D$_{2h}^{7}$ Pncm -P 2 2bc
53:a-cb D$_{2h}^{7}$ Pman -P 2ab 2
54 D$_{2h}^{8}$ Pcca -P 2a 2ac
54:ba-c D$_{2h}^{8}$ Pccb -P 2b 2c
54:cab D$_{2h}^{8}$ Pbaa -P 2a 2b
54:-cba D$_{2h}^{8}$ Pcaa -P 2ac 2c
54:bca D$_{2h}^{8}$ Pbcb -P 2bc 2b
54:a-cb D$_{2h}^{8}$ Pbab -P 2b 2ab
55 D$_{2h}^{9}$ Pbam -P 2 2ab
55:cab D$_{2h}^{9}$ Pmcb -P 2bc 2
55:bca D$_{2h}^{9}$ Pcma -P 2ac 2ac
56 D$_{2h}^{10}$ Pccn -P 2ab 2ac
56:cab D$_{2h}^{10}$ Pnaa -P 2ac 2bc
56:bca D$_{2h}^{10}$ Pbnb -P 2bc 2ab
57 D$_{2h}^{11}$ Pbcm -P 2c 2b
57:ba-c D$_{2h}^{11}$ Pcam -P 2c 2ac
57:cab D$_{2h}^{11}$ Pmca -P 2ac 2a
57:-cba D$_{2h}^{11}$ Pmab -P 2b 2a
57:bca D$_{2h}^{11}$ Pbma -P 2a 2ab
57:a-cb D$_{2h}^{11}$ Pcmb -P 2bc 2c
58 D$_{2h}^{12}$ Pnnm -P 2 2n
58:cab D$_{2h}^{12}$ Pmnn -P 2n 2
58:bca D$_{2h}^{12}$ Pnmn -P 2n 2n
59:1 D$_{2h}^{13}$ Pmmn:1 P 2 2ab -1ab
59:2 D$_{2h}^{13}$ Pmmn:2 -P 2ab 2a
59:1cab D$_{2h}^{13}$ Pnmm:1 P 2bc 2 -1bc
59:2cab D$_{2h}^{13}$ Pnmm:2 -P 2c 2bc
59:1bca D$_{2h}^{13}$ Pmnm:1 P 2ac 2ac -1ac
59:2bca D$_{2h}^{13}$ Pmnm:2 -P 2c 2a
60 D$_{2h}^{14}$ Pbcn -P 2n 2ab
60:ba-c D$_{2h}^{14}$ Pcan -P 2n 2c
60:cab D$_{2h}^{14}$ Pnca -P 2a 2n
60:-cba D$_{2h}^{14}$ Pnab -P 2bc 2n
60:bca D$_{2h}^{14}$ Pbna -P 2ac 2b
60:a-cb D$_{2h}^{14}$ Pcnb -P 2b 2ac
61 D$_{2h}^{15}$ Pbca -P 2ac 2ab
61:ba-c D$_{2h}^{15}$ Pcab -P 2bc 2ac
62 D$_{2h}^{16}$ Pnma -P 2ac 2n
62:ba-c D$_{2h}^{16}$ Pmnb -P 2bc 2a
62:cab D$_{2h}^{16}$ Pbnm -P 2c 2ab
62:-cba D$_{2h}^{16}$ Pcmn -P 2n 2ac
62:bca D$_{2h}^{16}$ Pmcn -P 2n 2a
62:a-cb D$_{2h}^{16}$ Pnam -P 2c 2n
63 D$_{2h}^{17}$ Cmcm -C 2c 2
63:ba-c D$_{2h}^{17}$ Ccmm -C 2c 2c
63:cab D$_{2h}^{17}$ Amma -A 2a 2a
63:-cba D$_{2h}^{17}$ Amam -A 2 2a
63:bca D$_{2h}^{17}$ Bbmm -B 2 2b
63:a-cb D$_{2h}^{17}$ Bmmb -B 2b 2
64 D$_{2h}^{18}$ Cmca -C 2bc 2
64:ba-c D$_{2h}^{18}$ Ccmb -C 2bc 2bc
64:cab D$_{2h}^{18}$ Abma -A 2ac 2ac
64:-cba D$_{2h}^{18}$ Acam -A 2 2ac
64:bca D$_{2h}^{18}$ Bbcm -B 2 2bc
64:a-cb D$_{2h}^{18}$ Bmab -B 2bc 2
65 D$_{2h}^{19}$ Cmmm -C 2 2
65:cab D$_{2h}^{19}$ Ammm -A 2 2
65:bca D$_{2h}^{19}$ Bmmm -B 2 2
66 D$_{2h}^{20}$ Cccm -C 2 2c
66:cab D$_{2h}^{20}$ Amaa -A 2a 2
66:bca D$_{2h}^{20}$ Bbmb -B 2b 2b
67 D$_{2h}^{21}$ Cmma -C 2b 2
67:ba-c D$_{2h}^{21}$ Cmmb -C 2b 2b
67:cab D$_{2h}^{21}$ Abmm -A 2c 2c
67:-cba D$_{2h}^{21}$ Acmm -A 2 2c
67:bca D$_{2h}^{21}$ Bmcm -B 2 2c
67:a-cb D$_{2h}^{21}$ Bmam -B 2c 2
68:1 D$_{2h}^{22}$ Ccca:1 C 2 2 -1bc
68:2 D$_{2h}^{22}$ Ccca:2 -C 2b 2bc
68:1ba-c D$_{2h}^{22}$ Cccb:1 C 2 2 -1bc
68:2ba-c D$_{2h}^{22}$ Cccb:2 -C 2b 2c
68:1cab D$_{2h}^{22}$ Abaa:1 A 2 2 -1ac
68:2cab D$_{2h}^{22}$ Abaa:2 -A 2a 2c
68:1-cba D$_{2h}^{22}$ Acaa:1 A 2 2 -1ac
68:2-cba D$_{2h}^{22}$ Acaa:2 -A 2ac 2c
68:1bca D$_{2h}^{22}$ Bbcb:1 B 2 2 -1bc
68:2bca D$_{2h}^{22}$ Bbcb:2 -B 2bc 2b
68:1a-cb D$_{2h}^{22}$ Bbab:1 B 2 2 -1bc
68:2a-cb D$_{2h}^{22}$ Bbab:2 -B 2b 2bc
69 D$_{2h}^{23}$ Fmmm -F 2 2
70:1 D$_{2h}^{24}$ Fddd:1 F 2 2 -1d
70:2 D$_{2h}^{24}$ Fddd:2 -F 2uv 2vw
71 D$_{2h}^{25}$ Immm -I 2 2
72 D$_{2h}^{26}$ Ibam -I 2 2c
72:cab D$_{2h}^{26}$ Imcb -I 2a 2
72:bca D$_{2h}^{26}$ Icma -I 2b 2b
73 D$_{2h}^{27}$ Ibca -I 2b 2c
73:ba-c D$_{2h}^{27}$ Icab -I 2a 2b
74 D$_{2h}^{28}$ Imma -I 2b 2
74:ba-c D$_{2h}^{28}$ Immb -I 2a 2a
74:cab D$_{2h}^{28}$ Ibmm -I 2c 2c
74:-cba D$_{2h}^{28}$ Icmm -I 2 2b
74:bca D$_{2h}^{28}$ Imcm -I 2 2a
74:a-cb D$_{2h}^{28}$ Imam -I 2c 2
75 C$_{4}^{1}$ P4 P 4
76 C$_{4}^{2}$ P41 P 4w
77 C$_{4}^{3}$ P42 P 4c
78 C$_{4}^{4}$ P43 P 4cw
79 C$_{4}^{5}$ I4 I 4
80 C$_{4}^{6}$ I41 I 4bw
81 S$_{4}^{1}$ P-4 P -4
82 S$_{4}^{2}$ I-4 I -4
83 C$_{4h}^{1}$ P4/m -P 4
84 C$_{4h}^{2}$ P42/m -P 4c
85:1 C$_{4h}^{3}$ P4/n:1 P 4ab -1ab
85:2 C$_{4h}^{3}$ P4/n:2 -P 4a
86:1 C$_{4h}^{4}$ P42/n:1 P 4n -1n
86:2 C$_{4h}^{4}$ P42/n:2 -P 4bc
87 C$_{4h}^{5}$ I4/m -I 4
88:1 C$_{4h}^{6}$ I41/a:1 I 4bw -1bw
88:2 C$_{4h}^{6}$ I41/a:2 -I 4ad
89 D$_{4}^{1}$ P422 P 4 2
90 D$_{4}^{2}$ P4212 P 4ab 2ab
91 D$_{4}^{3}$ P4122 P 4w 2c
92 D$_{4}^{4}$ P41212 P 4abw 2nw
93 D$_{4}^{5}$ P4222 P 4c 2
94 D$_{4}^{6}$ P42212 P 4n 2n
95 D$_{4}^{7}$ P4322 P 4cw 2c
96 D$_{4}^{8}$ P43212 P 4nw 2abw
97 D$_{4}^{9}$ I422 I 4 2
98 D$_{4}^{10}$ I4122 I 4bw 2bw
99 C$_{4v}^{1}$ P4mm P 4 -2
100 C$_{4v}^{2}$ P4bm P 4 -2ab
101 C$_{4v}^{3}$ P42cm P 4c -2c
102 C$_{4v}^{4}$ P42nm P 4n -2n
103 C$_{4v}^{5}$ P4cc P 4 -2c
104 C$_{4v}^{6}$ P4nc P 4 -2n
105 C$_{4v}^{7}$ P42mc P 4c -2
106 C$_{4v}^{8}$ P42bc P 4c -2ab
107 C$_{4v}^{9}$ I4mm I 4 -2
108 C$_{4v}^{10}$ I4cm I 4 -2c
109 C$_{4v}^{11}$ I41md I 4bw -2
110 C$_{4v}^{12}$ I41cd I 4bw -2c
111 D$_{2d}^{1}$ P-42m P -4 2
112 D$_{2d}^{2}$ P-42c P -4 2c
113 D$_{2d}^{3}$ P-421m P -4 2ab
114 D$_{2d}^{4}$ P-421c P -4 2n
115 D$_{2d}^{5}$ P-4m2 P -4 -2
116 D$_{2d}^{6}$ P-4c2 P -4 -2c
117 D$_{2d}^{7}$ P-4b2 P -4 -2ab
118 D$_{2d}^{8}$ P-4n2 P -4 -2n
119 D$_{2d}^{9}$ I-4m2 I -4 -2
120 D$_{2d}^{10}$ I-4c2 I -4 -2c
121 D$_{2d}^{11}$ I-42m I -4 2
122 D$_{2d}^{12}$ I-42d I -4 2bw
123 D$_{4h}^{1}$ P4/mmm -P 4 2
124 D$_{4h}^{2}$ P4/mcc -P 4 2c
125:1 D$_{4h}^{3}$ P4/nbm:1 P 4 2 -1ab
125:2 D$_{4h}^{3}$ P4/nbm:2 -P 4a 2b
126:1 D$_{4h}^{4}$ P4/nnc:1 P 4 2 -1n
126:2 D$_{4h}^{4}$ P4/nnc:2 -P 4a 2bc
127 D$_{4h}^{5}$ P4/mbm -P 4 2ab
128 D$_{4h}^{6}$ P4/mnc -P 4 2n
129:1 D$_{4h}^{7}$ P4/nmm:1 P 4ab 2ab -1ab
129:2 D$_{4h}^{7}$ P4/nmm:2 -P 4a 2a
130:1 D$_{4h}^{8}$ P4/ncc:1 P 4ab 2n -1ab
130:2 D$_{4h}^{8}$ P4/ncc:2 -P 4a 2ac
131 D$_{4h}^{9}$ P42/mmc -P 4c 2
132 D$_{4h}^{10}$ P42/mcm -P 4c 2c
133:1 D$_{4h}^{11}$ P42/nbc:1 P 4n 2c -1n
133:2 D$_{4h}^{11}$ P42/nbc:2 -P 4ac 2b
134:1 D$_{4h}^{12}$ P42/nnm:1 P 4n 2 -1n
134:2 D$_{4h}^{12}$ P42/nnm:2 -P 4ac 2bc
135 D$_{4h}^{13}$ P42/mbc -P 4c 2ab
136 D$_{4h}^{14}$ P42/mnm -P 4n 2n
137:1 D$_{4h}^{15}$ P42/nmc:1 P 4n 2n -1n
137:2 D$_{4h}^{15}$ P42/nmc:2 -P 4ac 2a
138:1 D$_{4h}^{16}$ P42/ncm:1 P 4n 2ab -1n
138:2 D$_{4h}^{16}$ P42/ncm:2 -P 4ac 2ac
139 D$_{4h}^{17}$ I4/mmm -I 4 2
140 D$_{4h}^{18}$ I4/mcm -I 4 2c
141:1 D$_{4h}^{19}$ I41/amd:1 I 4bw 2bw -1bw
141:2 D$_{4h}^{19}$ I41/amd:2 -I 4bd 2
142:1 D$_{4h}^{20}$ I41/acd:1 I 4bw 2aw -1bw
142:2 D$_{4h}^{20}$ I41/acd:2 -I 4bd 2c
143 C$_{3}^{1}$ P3 P 3
144 C$_{3}^{2}$ P31 P 31
145 C$_{3}^{3}$ P32 P 32
146:H C$_{3}^{4}$ R3:H R 3
146:R C$_{3}^{4}$ R3:R P 3*
147 C$_{3i}^{1}$ P-3 -P 3
148:H C$_{3i}^{2}$ R-3:H -R 3
148:R C$_{3i}^{2}$ R-3:R -P 3*
149 D$_{3}^{1}$ P312 P 3 2
150 D$_{3}^{2}$ P321 P 3 2$''$
151 D$_{3}^{3}$ P3112 P 31 2c (0 0 1)
152 D$_{3}^{4}$ P3121 P 31 2$''$
153 D$_{3}^{5}$ P3212 P 32 2c (0 0 -1)
154 D$_{3}^{6}$ P3221 P 32 2$''$
155:H D$_{3}^{7}$ R32:H R 3 2$''$
155:R D$_{3}^{7}$ R32:R P 3* 2
156 C$_{3v}^{1}$ P3m1 P 3 -2$''$
157 C$_{3v}^{2}$ P31m P 3 -2
158 C$_{3v}^{3}$ P3c1 P 3 -2$''$c
159 C$_{3v}^{4}$ P31c P 3 -2c
160:H C$_{3v}^{5}$ R3m:H R 3 -2$''$
160:R C$_{3v}^{5}$ R3m:R P 3* -2
161:H C$_{3v}^{6}$ R3c:H R 3 -2$''$c
161:R C$_{3v}^{6}$ R3c:R P 3* -2n
162 D$_{3d}^{1}$ P-31m -P 3 2
163 D$_{3d}^{2}$ P-31c -P 3 2c
164 D$_{3d}^{3}$ P-3m1 -P 3 2$''$
165 D$_{3d}^{4}$ P-3c1 -P 3 2$''$c
166:H D$_{3d}^{5}$ R-3m:H -R 3 2$''$
166:R D$_{3d}^{5}$ R-3m:R -P 3* 2
167:H D$_{3d}^{6}$ R-3c:H -R 3 2$''$c
167:R D$_{3d}^{6}$ R-3c:R -P 3* 2n
168 C$_{6}^{1}$ P6 P 6
169 C$_{6}^{2}$ P61 P 61
170 C$_{6}^{3}$ P65 P 65
171 C$_{6}^{4}$ P62 P 62
172 C$_{6}^{5}$ P64 P 64
173 C$_{6}^{6}$ P63 P 6c
174 C$_{3h}^{1}$ P-6 P -6
175 C$_{6h}^{1}$ P6/m -P 6
176 C$_{6h}^{2}$ P63/m -P 6c
177 D$_{6}^{1}$ P622 P 6 2
178 D$_{6}^{2}$ P6122 P 61 2 (0 0 -1)
179 D$_{6}^{3}$ P6522 P 65 2 (0 0 1)
180 D$_{6}^{4}$ P6222 P 62 2c (0 0 1)
181 D$_{6}^{5}$ P6422 P 64 2c (0 0 -1)
182 D$_{6}^{6}$ P6322 P 6c 2c
183 C$_{6v}^{1}$ P6mm P 6 -2
184 C$_{6v}^{2}$ P6cc P 6 -2c
185 C$_{6v}^{3}$ P63cm P 6c -2
186 C$_{6v}^{4}$ P63mc P 6c -2c
187 D$_{3h}^{1}$ P-6m2 P -6 2
188 D$_{3h}^{2}$ P-6c2 P -6c 2
189 D$_{3h}^{3}$ P-62m P -6 -2
190 D$_{3h}^{4}$ P-62c P -6c -2c
191 D$_{6h}^{1}$ P6/mmm -P 6 2
192 D$_{6h}^{2}$ P6/mcc -P 6 2c
193 D$_{6h}^{3}$ P63/mcm -P 6c 2
194 D$_{6h}^{4}$ P63/mmc -P 6c 2c
195 T$_{}^{1}$ P23 P 2 2 3
196 T$_{}^{2}$ F23 F 2 2 3
197 T$_{}^{3}$ I23 I 2 2 3
198 T$_{}^{4}$ P213 P 2ac 2ab 3
199 T$_{}^{5}$ I213 I 2b 2c 3
200 T$_{h}^{1}$ Pm-3 -P 2 2 3
201:1 T$_{h}^{2}$ Pn-3:1 P 2 2 3 -1n
201:2 T$_{h}^{2}$ Pn-3:2 -P 2ab 2bc 3
202 T$_{h}^{3}$ Fm-3 -F 2 2 3
203:1 T$_{h}^{4}$ Fd-3:1 F 2 2 3 -1d
203:2 T$_{h}^{4}$ Fd-3:2 -F 2uv 2vw 3
204 T$_{h}^{5}$ Im-3 -I 2 2 3
205 T$_{h}^{6}$ Pa-3 -P 2ac 2ab 3
206 T$_{h}^{7}$ Ia-3 -I 2b 2c 3
207 O$^{1}$ P432 P 4 2 3
208 O$^{2}$ P4232 P 4n 2 3
209 O$^{3}$ F432 F 4 2 3
210 O$^{4}$ F4132 F 4d 2 3
211 O$^{5}$ I432 I 4 2 3
212 O$^{6}$ P4332 P 4acd 2ab 3
213 O$^{7}$ P4132 P 4bd 2ab 3
214 O$^{8}$ I4132 I 4bd 2c 3
215 T$_{d}^{1}$ P-43m P -4 2 3
216 T$_{d}^{2}$ F-43m F -4 2 3
217 T$_{d}^{3}$ I-43m I -4 2 3
218 T$_{d}^{4}$ P-43n P -4n 2 3
219 T$_{d}^{5}$ F-43c F -4c 2 3
220 T$_{d}^{6}$ I-43d I -4bd 2c 3
221 O$_{h}^{1}$ Pm-3m -P 4 2 3
222:1 O$_{h}^{2}$ Pn-3n:1 P 4 2 3 -1n
222:2 O$_{h}^{2}$ Pn-3n:2 -P 4a 2bc 3
223 O$_{h}^{3}$ Pm-3n -P 4n 2 3
224:1 O$_{h}^{4}$ Pn-3m:1 P 4n 2 3 -1n
224:2 O$_{h}^{4}$ Pn-3m:2 -P 4bc 2bc 3
225 O$_{h}^{5}$ Fm-3m -F 4 2 3
226 O$_{h}^{6}$ Fm-3c -F 4c 2 3
227:1 O$_{h}^{7}$ Fd-3m:1 F 4d 2 3 -1d
227:2 O$_{h}^{7}$ Fd-3m:2 -F 4vw 2vw 3
228:1 O$_{h}^{8}$ Fd-3c:1 F 4d 2 3 -1cd
228:2 O$_{h}^{8}$ Fd-3c:2 -F 4cvw 2vw 3
229 O$_{h}^{9}$ Im-3m -I 4 2 3
230 O$_{h}^{10}$ Ia-3d -I 4bd 2c 3
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