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