List of 230 3D symmetry space groups

This page presents the list of the 230 3D symmetry space groups with characteristics, and also, if applicable, derivatives of the space group.

This list of symmetry groups is part of the on-line help of the ABINIT code. Besides classical crystallographic information, it provides the values of certain symmetry-related variables used in the input file of the ABINIT code.

The table entries are as follows:

SPGROUP

SPace GROUP number as found in the International Tables of Crystallography, 1983 edition [Hahn1983].

SPGAXOR

SPace Group AXis ORientation, the orientation of the unit cell axis. The allowed values are:

• Trigonal groups:
  • 1 represents the hexagonal axes
  • 2 represents the rhombohedral axes
• Orthorhombic groups:
  • 1 abc -> abc
  • 2 abc -> cab
  • 3 abc -> bca
  • 4 abc -> acb
  • 5 abc -> bac
  • 6 abc -> cba
• Monoclinic: 3 or 9 possibilities depending on the space group

SPGORIG

SPace Group ORIGin, the position of the origin in the unit cell. The allowed values are 1 and 2. they correspond to the actual choices in the International Tables of Crystallography, 1986 edition.

BRVLTT

BRaVais LaTTice, the type of Bravais lattice. The allowed values are:

• 1 = Primitive with no associated translations
• 2 = Inner centered with (a/2 + b/2 + c/2) associated translation
• 3 = Face centered with (a/2 + b/2; b/2 + c/2; c/2 + a/2) associated translations
• 4 = C - centered with (a/2 + b/2) associated translation
• 5 = A - centered with (b/2 + c/2) associated translation
• 6 = B - centered with (c/2 + a/2) associated translation
• 7 = Rhombohedral lattice

INTERNATIONAL

the INTERNATIONAL notation of the space group

SCHOENFLIES

the equivalent SCHOENFLIES notation of the space group

MULTIPLICITY (x y z)

the maximum multiplicity, after applying Bravais lattice translations, corresponding to a general position (x y z)

List of 230 3D symmetry space groups

This section presents the list of the 230 3D symmetry space groups with characteristics, and also, if applicable, derivatives of the space group.

SPGROUP	SPGAXOR	SPGORIG	BRVLTT	INTERNATIONAL	SCHOENFLIES	ORDER
1	1	1	1	P1	C11	1
2	1	1	1	P-1	Ci1	2
3	1	1	1	P2_b = P121	C21	2
3	3	1	1	P2_c = P112	C21	2
3	2	1	1	P2_a = P211	C21	2
4	1	1	1	P21_b = P1211	C22	2
4	3	1	1	P21_c = P1121	C22	2
4	2	1	1	P21_a = P2111	C22	2
5	1	1	4	C2_b1 = C121	C23	4
5	5	1	5	C2_b2 = A121	C23	4
5	6	1	2	C2_b3 = I121	C23	4
5	7	1	5	C2_c1 = A112	C23	4
5	8	1	6	C2_c2 = B112 = B2	C23	4
5	9	1	2	C2_c3 = I112	C23	4
5	2	1	6	C2_a1 = B211	C23	4
5	3	1	4	C2_a2 = C211	C23	4
5	4	1	2	C2_a3 = I211	C23	4
6	1	1	1	Pm_b = P1m1	Cs1	2
6	3	1	1	Pm_c = P11m	Cs1	2
6	2	1	1	Pm_a = Pm11	Cs1	2
7	1	1	1	Pc_b1 = P1c1	Cs2	2
7	5	1	1	Pc_b2 = P1n1	Cs2	2
7	6	1	1	Pc_b3 = P1a1	Cs2	2
7	7	1	1	Pc_c1 = P11a	Cs2	2
7	8	1	1	Pc_c2 = P11n	Cs2	2
7	9	1	1	Pc_c3 = P11b = Pb	Cs2	2
7	2	1	1	Pc_a1 = Pb11	Cs2	2
7	3	1	1	Pc_a2 = Pn11	Cs2	2
7	4	1	1	Pc_a3 = Pc11	Cs2	2
8	1	1	4	Cm_b1 = C1m1	Cs3	4
8	5	1	5	Cm_b2 = A1m1	Cs3	4
8	6	1	2	Cm_b3 = I1m1	Cs3	4
8	7	1	5	Cm_c1 = A11m	Cs3	4
8	8	1	6	Cm_c2 = B11m = Bm	Cs3	4
8	9	1	2	Cm_c3 = I11m	Cs3	4
8	2	1	6	Cm_a1 = Bm11	Cs3	4
8	3	1	4	Cm_a2 = Cm11	Cs3	4
8	4	1	2	Cm_a3 = Im11	Cs3	4
9	1	1	4	Cc_b1 = C1c1	Cs4	4
9	5	1	5	Cc_b2 = A1n1	Cs4	4
9	6	1	2	Cc_b3 = I1a1	Cs4	4
9	7	1	5	Cc_c1 = A11a	Cs4	4
9	8	1	6	Cc_c2 = B11n	Cs4	4
9	9	1	2	Cc_c3 = I11b	Cs4	4
9	2	1	6	Cc_a1 = Bb11	Cs4	4
9	3	1	4	Cc_a2 = Cn11	Cs4	4
9	4	1	2	Cc_a3 = Ic11	Cs4	4
10	1	1	1	P2/m_b = P12/m1	C2h1	4
10	3	1	1	P2/m_c = P112/m	C2h1	4
10	2	1	1	P2/m_a = P2/m11	C2h1	4
11	1	1	1	P21/m_b = P121/m1	C2h2	4
11	3	1	1	P21/m_c = P1121/m	C2h2	4
11	2	1	1	P21/m_a = P21/m11	C2h2	4
12	1	1	4	C2/m_b1 = C12/m1	C2h3	8
12	5	1	5	C2/m_b2 = A12/m1	C2h3	8
12	6	1	2	C2/m_b3 = I12/m1	C2h3	8
12	7	1	5	C2/m_c1 = A112/m	C2h3	8
12	8	1	6	C2/m_c2 = B112/m = B2/m	C2h3	8
12	9	1	2	C2/m_c3 = I112/m	C2h3	8
12	2	1	6	C2/m_a1 = B2/m11	C2h3	8
12	3	1	4	C2/m_a2 = C2/m11	C2h3	8
12	4	1	2	C2/m_a3 = I2/m11	C2h3	8
13	1	1	1	P2/c_b1 = P12/c1	C2h4	4
13	5	1	1	P2/c_b2 = P12/n1	C2h4	4
13	6	1	1	P2/c_b3 = P12/a1	C2h4	4
13	7	1	1	P2/c_c1 = P112/a	C2h4	4
13	8	1	1	P2/c_c2 = P112/n	C2h4	4
13	9	1	1	P2/c_c3 = P112/b = P2/b	C2h4	4
13	2	1	1	P2/c_a1 = P2/b11	C2h4	4
13	3	1	1	P2/c_a2 = P2/n11	C2h4	4
13	4	1	1	P2/c_a3 = P2/c11	C2h4	4
14	1	1	1	P21/c_b1 = P121/c1	C2h5	4
14	5	1	1	P21/c_b2 = P121/n1	C2h5	4
14	6	1	1	P21/c_b3 = P121/a1	C2h5	4
14	7	1	1	P21/c_c1 = P1121/a	C2h5	4
14	8	1	1	P21/c_c2 = P1121/n	C2h5	4
14	9	1	1	P21/c_c3 = P1121/b = P21/b	C2h5	4
14	2	1	1	P21/c_a1 = P21/b11	C2h5	4
14	3	1	1	P21/c_a2 = P21/n11	C2h5	4
14	4	1	1	P21/c_a3 = P21/c11	C2h5	4
15	1	1	4	C2/c_b1 = C12/c1	C2h6	8
15	5	1	5	C2/c_b2 = A12/n1	C2h6	8
15	6	1	2	C2/c_b3 = I12/a1	C2h6	8
15	7	1	4	C2/c_c1 = A112/a	C2h6	8
15	8	1	6	C2/c_c2 = B112/n	C2h6	8
15	9	1	2	C2/c_c3 = I112/b	C2h6	8
15	2	1	6	C2/c_a1 = B2/b11	C2h6	8
15	3	1	4	C2/c_a2 = C2/n11	C2h6	8
15	4	1	2	C2/c_a3 = I2/c11	C2h6	8
16	1	1	1	P222	D21	4
17	1	1	1	P2221	D22	4
17	2	1	1	P2122	D22	4
17	3	1	1	P2212	D22	4
18	1	1	1	P21212	D23	4
18	2	1	1	P22121	D23	4
18	3	1	1	P21221	D23	4
19	1	1	1	P212121	D24	4
20	1	1	4	C2221	D25	8
20	2	1	5	A2122	D25	8
20	3	1	6	B2212	D25	8
21	1	1	4	C222	D26	8
21	2	1	5	A222	D26	8
21	3	1	6	B222	D26	8
22	1	1	3	F222	D27	16
23	1	1	2	I222	D28	8
24	1	1	2	I212121	D29	8
25	1	1	1	Pmm2	C2v1	4
25	2	1	1	P2mm	C2v1	4
25	3	1	1	Pm2m	C2v1	4
26	1	1	1	Pmc21	C2v2	4
26	5	1	1	Pcm21	C2v2	4
26	2	1	1	P21ma	C2v2	4
26	6	1	1	P21am	C2v2	4
26	3	1	1	Pb21m	C2v2	4
26	4	1	1	Pm21b	C2v2	4
27	1	1	1	Pcc2	C2v3	4
27	2	1	1	P2aa	C2v3	4
27	3	1	1	Pb2b	C2v3	4
28	1	1	1	Pma2	C2v4	4
28	5	1	1	Pbm2	C2v4	4
28	2	1	1	P2mb	C2v4	4
28	6	1	1	P2cm	C2v4	4
28	3	1	1	Pc2m	C2v4	4
28	4	1	1	Pm2a	C2v4	4
29	1	1	1	Pca21	C2v5	4
29	5	1	1	Pbc21	C2v5	4
29	2	1	1	P21ab	C2v5	4
29	6	1	1	P21ca	C2v5	4
29	3	1	1	Pc21b	C2v5	4
29	4	1	1	Pb21a	C2v5	4
30	1	1	1	Pnc2	C2v6	4
30	5	1	1	Pcn2	C2v6	4
30	2	1	1	P2na	C2v6	4
30	6	1	1	P2an	C2v6	4
30	3	1	1	Pb2n	C2v6	4
30	4	1	1	Pn2b	C2v6	4
31	1	1	1	Pmn21	C2v7	4
31	5	1	1	Pnm21	C2v7	4
31	2	1	1	P21mn	C2v7	4
31	6	1	1	P21nm	C2v7	4
31	3	1	1	Pn21m	C2v7	4
31	4	1	1	Pm21n	C2v7	4
32	1	1	1	Pba2	C2v8	4
32	2	1	1	P2cb	C2v8	4
32	3	1	1	Pc2a	C2v8	4
33	1	1	1	Pna21	C2v9	4
33	5	1	1	Pbn21	C2v9	4
33	2	1	1	P21nb	C2v9	4
33	6	1	1	P21cn	C2v9	4
33	3	1	1	Pc21n	C2v9	4
33	4	1	1	Pn21a	C2v9	4
34	1	1	1	Pnn2	C2v10	4
34	2	1	1	P2nn	C2v10	4
34	3	1	1	Pn2n	C2v10	4
35	1	1	4	Cmm2	C2v11	8
35	2	1	5	A2mm	C2v11	8
35	3	1	6	Bm2m	C2v11	8
36	1	1	4	Cmc21	C2v12	8
36	5	1	4	Ccm21	C2v12	8
36	2	1	5	A21ma	C2v12	8
36	6	1	5	A21am	C2v12	8
36	3	1	6	Bb21m	C2v12	8
36	4	1	6	Bm21b	C2v12	8
37	1	1	4	Ccc2	C2v13	8
37	2	1	5	A2aa	C2v13	8
37	3	1	6	Bb2b	C2v13	8
38	1	1	5	Amm2	C2v14	8
38	5	1	6	Bmm2	C2v14	8
38	2	1	6	B2mm	C2v14	8
38	6	1	4	C2mm	C2v14	8
38	3	1	4	Cm2m	C2v14	8
38	4	1	5	Am2m	C2v14	8
39	1	1	5	Abm2	C2v15	8
39	5	1	6	Bma2	C2v15	8
39	2	1	6	B2cm	C2v15	8
39	6	1	4	C2mb	C2v15	8
39	3	1	4	Cm2a	C2v15	8
39	4	1	5	Ac2m	C2v15	8
40	1	1	5	Ama2	C2v16	8
40	5	1	6	Bbm2	C2v16	8
40	2	1	6	B2mb	C2v16	8
40	6	1	4	C2cm	C2v16	8
40	3	1	4	Cc2m	C2v16	8
40	4	1	5	Am2a	C2v16	8
41	1	1	5	Aba2	C2v17	8
41	5	1	6	Bba2	C2v17	8
41	2	1	6	B2cb	C2v17	8
41	6	1	4	C2cb	C2v17	8
41	3	1	4	Cc2a	C2v17	8
41	4	1	5	Ac2a	C2v17	8
42	1	1	3	Fmm2	C2v18	16
42	2	1	3	F2mm	C2v18	16
42	3	1	3	Fm2m	C2v18	16
43	1	1	3	Fdd2	C2v19	16
43	2	1	3	F2dd	C2v19	16
43	3	1	3	Fd2d	C2v19	16
44	1	1	2	Imm2	C2v20	8
44	2	1	2	I2mm	C2v20	8
44	3	1	2	Im2m	C2v20	8
45	1	1	2	Iba2	C2v21	8
45	2	1	2	I2cb	C2v21	8
45	3	1	2	Ic2a	C2v21	8
46	1	1	2	Ima2	C2v22	8
46	5	1	2	Ibm2	C2v22	8
46	2	1	2	I2mb	C2v22	8
46	6	1	2	I2cm	C2v22	8
46	3	1	2	Ic2m	C2v22	8
46	4	1	2	Im2a	C2v22	8
47	1	1	1	Pmmm	D2h1	8
48	1	1	1	Pnnn_1	D2h2	8
48	1	2	1	Pnnn_2	D2h2	8
49	1	1	1	Pccm	D2h3	8
49	2	1	1	Pmaa	D2h3	8
49	3	1	1	Pbmb	D2h3	8
50	1	1	1	Pban_1	D2h4	8
50	5	2	1	Pban_2	D2h4	8
50	2	1	1	Pncb_1	D2h4	8
50	6	2	1	Pncb_2	D2h4	8
50	3	1	1	Pcna_1	D2h4	8
50	4	2	1	Pcna_2	D2h4	8
51	1	1	1	Pmma	D2h5	8
51	5	1	1	Pmmb	D2h5	8
51	2	1	1	Pbmm	D2h5	8
51	6	1	1	Pcmm	D2h5	8
51	3	1	1	Pmcm	D2h5	8
51	4	1	1	Pmam	D2h5	8
52	1	1	1	Pnna	D2h6	8
52	5	1	1	Pnnb	D2h6	8
52	2	1	1	Pbnn	D2h6	8
52	6	1	1	Pcnn	D2h6	8
52	3	1	1	Pncn	D2h6	8
52	4	1	1	Pnan	D2h6	8
53	1	1	1	Pmna	D2h7	8
53	5	1	1	Pnmb	D2h7	8
53	2	1	1	Pbmn	D2h7	8
53	6	1	1	Pcnm	D2h7	8
53	3	1	1	Pncm	D2h7	8
53	4	1	1	Pman	D2h7	8
54	1	1	1	Pcca	D2h8	8
54	5	1	1	Pccb	D2h8	8
54	2	1	1	Pbaa	D2h8	8
54	6	1	1	Pcaa	D2h8	8
54	3	1	1	Pbcb	D2h8	8
54	4	1	1	Pbab	D2h8	8
55	1	1	1	Pbam	D2h9	8
55	2	1	1	Pmcb	D2h9	8
55	3	1	1	Pcma	D2h9	8
56	1	1	1	Pccn	D2h10	8
56	2	1	1	Pnaa	D2h10	8
56	3	1	1	Pbnb	D2h10	8
57	1	1	1	Pbcm	D2h11	8
57	5	1	1	Pcam	D2h11	8
57	2	1	1	Pmca	D2h11	8
57	6	1	1	Pmab	D2h11	8
57	3	1	1	Pbma	D2h11	8
57	4	1	1	Pcmb	D2h11	8
58	1	1	1	Pnnm	D2h12	8
58	2	1	1	Pmnn	D2h12	8
58	3	1	1	Pnmn	D2h12	8
59	1	1	1	Pmmn_1	D2h13	8
59	5	2	1	Pmmn_2	D2h13	8
59	2	1	1	Pnmm_1	D2h13	8
59	6	2	1	Pnmm_2	D2h13	8
59	3	1	1	Pmnm_1	D2h13	8
59	4	2	1	Pmnm_2	D2h13	8
60	1	1	1	Pbcn	D2h14	8
60	5	1	1	Pcan	D2h14	8
60	2	1	1	Pnca	D2h14	8
60	6	1	1	Pnab	D2h14	8
60	3	1	1	Pbna	D2h14	8
60	4	1	1	Pcnb	D2h14	8
61	1	1	1	Pbca	D2h15	8
61	2	1	1	Pcab	D2h15	8
62	1	1	1	Pnma	D2h16	8
62	5	1	1	Pmnb	D2h16	8
62	2	1	1	Pbnm	D2h16	8
62	6	1	1	Pcmn	D2h16	8
62	3	1	1	Pmcn	D2h16	8
62	4	1	1	Pnam	D2h16	8
63	1	1	4	Cmcm	D2h17	16
63	5	1	4	Ccmm	D2h17	16
63	2	1	5	Amma	D2h17	16
63	6	1	5	Amam	D2h17	16
63	3	1	6	Bbmm	D2h17	16
63	4	1	6	Bmmb	D2h17	16
64	1	1	4	Cmca	D2h18	16
64	5	1	4	Ccmb	D2h18	16
64	2	1	5	Abma	D2h18	16
64	6	1	5	Acam	D2h18	16
64	3	1	6	Bbcm	D2h18	16
64	4	1	6	Bmab	D2h18	16
65	1	1	4	Cmmm	D2h19	16
65	2	1	5	Ammm	D2h19	16
65	3	1	6	Bmmm	D2h19	16
66	1	1	6	Cccm	D2h20	16
66	2	1	5	Amaa	D2h20	16
66	3	1	6	Bbmb	D2h20	16
67	1	1	4	Cmma	D2h21	16
67	5	1	4	Cmmb	D2h21	16
67	2	1	5	Abmm	D2h21	16
67	6	1	5	Acmm	D2h21	16
67	3	1	6	Bmcm	D2h21	16
67	4	1	6	Bmam	D2h21	16
68	1	1	4	Ccca_1	D2h22	16
68	1	2	4	Ccca_2	D2h22	16
68	5	1	4	Cccb_1	D2h22	16
68	5	2	4	Cccb_2	D2h22	16
68	2	1	5	Abaa_1	D2h22	16
68	2	2	5	Abaa_2	D2h22	16
68	6	1	5	Acaa_1	D2h22	16
68	6	2	5	Acaa_2	D2h22	16
68	3	1	6	Bbcb_1	D2h22	16
68	3	2	6	Bbcb_2	D2h22	16
68	4	1	6	Bbab_1	D2h22	16
68	4	2	6	Bbab_2	D2h22	16
69	1	1	3	Fmmm	D2h23	32
70	1	1	3	Fddd_1	D2h24	32
70	1	2	3	Fddd_2	D2h24	32
71	1	1	2	Immm	D2h25	16
72	1	1	2	Ibam	D2h26	16
72	2	1	2	Imcb	D2h26	16
72	3	1	2	Icma	D2h26	16
73	1	1	2	Ibca	D2h27	16
73	2	1	2	Icab	D2h27	16
74	1	1	2	Imma	D2h28	16
74	5	1	2	Immb	D2h28	16
74	2	1	2	Ibmm	D2h28	16
74	6	1	2	Icmm	D2h28	16
74	3	1	2	Imcm	D2h28	16
74	4	1	2	Imam	D2h28	16
75	1	1	1	P4	C41	4
76	1	1	1	P41	C42	4
77	1	1	1	P42	C43	4
78	1	1	1	P43	C44	4
79	1	1	2	I4	C45	8
80	1	1	2	I41	C46	8
81	1	1	1	P-4	S41	4
82	1	1	2	I-4	S42	8
83	1	1	1	P4/m	C4h1	8
84	1	1	1	P42/m	C4h2	8
85	1	1	1	P4/n_1	C4h3	8
85	1	2	1	P4/n_2	C4h3	8
86	1	1	1	P42/n_1	C4h4	8
86	1	2	1	P42/n_2	C4h4	8
87	1	1	2	I4/m	C4h5	16
88	1	1	2	I41/a_1	C4h6	16
88	1	2	2	I41/a_2	C4h6	16
89	1	1	1	P422	D41	8
90	1	1	1	P4212	D42	8
91	1	1	1	P4122	D43	8
92	1	1	1	P41212	D44	8
93	1	1	1	P4222	D45	8
94	1	1	1	P42212	D46	8
95	1	1	1	P4322	D47	8
96	1	1	1	P43212	D48	8
97	1	1	2	I422	D49	16
98	1	1	2	I4122	D410	16
99	1	1	1	P4mm	C4v1	8
100	1	1	1	P4bm	C4v2	8
101	1	1	1	P42cm	C4v3	8
102	1	1	1	P42nm	C4v4	8
103	1	1	1	P4cc	C4v5	8
104	1	1	1	P4nc	C4v6	8
105	1	1	1	P42mc	C4v7	8
106	1	1	1	P42bc	C4v8	8
107	1	1	2	I4mm	C4v9	16
108	1	1	2	I4cm	C4v10	16
109	1	1	2	I41md	C4v11	16
110	1	1	2	I41cd	C4v12	16
111	1	1	1	P-42m	D2d1	8
112	1	1	1	P-42c	D2d2	8
113	1	1	1	P-421m	D2d3	8
114	1	1	1	P-421c	D2d4	8
115	1	1	1	P-4m2	D2d5	8
116	1	1	1	P-4c2	D2d6	8
117	1	1	1	P-4b2	D2d7	8
118	1	1	1	P-4n2	D2d8	8
119	1	1	2	I-4m2	D2d9	16
120	1	1	2	I-4c2	D2d10	16
121	1	1	2	I-42m	D2d11	16
122	1	1	2	I-42d	D2d12	16
123	1	1	1	P4/mmm	D4h1	16
124	1	1	1	P4/mcc	D4h2	16
125	1	1	1	P4/nbm_1	D4h3	16
125	1	2	1	P4/nbm_2	D4h3	16
126	1	1	1	P4/nnc_1	D4h4	16
126	1	2	1	P4/nnc_2	D4h4	16
127	1	1	1	P4/mbm	D4h5	16
128	1	1	1	P4/mnc	D4h6	16
129	1	1	1	P4/nmm_1	D4h7	16
129	1	2	1	P4/nmm_2	D4h7	16
130	1	1	1	P4/ncc_1	D4h8	16
130	1	2	1	P4/ncc_2	D4h8	16
131	1	1	1	P42/mmc	D4h9	16
132	1	1	1	P42/mcm	D4h10	16
133	1	1	1	P42/nbc_1	D4h11	16
133	1	2	1	P42/nbc_2	D4h11	16
134	1	1	1	P42/nnm_1	D4h12	16
134	1	2	1	P42/nnm_2	D4h12	16
135	1	1	1	P42/mbc	D4h13	16
136	1	1	1	P42/mnm	D4h14	16
137	1	1	1	P42/nmc_1	D4h15	16
137	1	2	1	P42/nmc_2	D4h15	16
138	1	1	1	P42/ncm_1	D4h16	16
138	1	2	1	P42/ncm_2	D4h16	16
139	1	1	2	I4/mmm	D4h17	32
140	1	1	2	I4/mcm	D4h18	32
141	1	1	2	I41/amd_1	D4h19	32
141	1	2	2	I41/amd_2	D4h19	32
142	1	1	2	I41/acd_1	D4h20	32
142	1	2	2	I41/acd_2	D4h20	32
143	1	1	1	P3	C31	3
144	1	1	1	P31	C32	3
145	1	1	1	P32	C33	3
146	1	1	7	R3_H	C34	9
146	2	1	7	R3_R	C34	3
147	1	1	1	P-3	C3i1	6
148	1	1	7	R-3_H	C3i2	18
148	2	1	7	R-3_R	C3i2	6
149	1	1	1	P312	D31	6
150	1	1	1	P321	D32	6
151	1	1	1	P3112	D33	6
152	1	1	1	P3121	D34	6
153	1	1	1	P3212	D35	6
154	1	1	1	P3221	D36	6
155	1	1	7	R32_H	D37	18
155	2	1	7	R32_R	D37	6
156	1	1	1	P3m1	C3v1	6
157	1	1	1	P31m	C3v2	6
158	1	1	1	P3c1	C3v3	6
159	1	1	1	P31c	C3v4	6
160	1	1	7	R3m_H	C3v5	18
160	2	1	7	R3m_R	C3v5	6
161	1	1	7	R3c_H	C3v6	18
161	2	1	7	R3c_R	C3v6	6
162	1	1	1	P-31m	D3d1	12
163	1	1	1	P-31c	D3d2	12
164	1	1	1	P-3m1	D3d3	12
165	1	1	1	P-3c1	D3d4	12
166	1	1	7	R-3m_H	D3d5	36
166	2	1	7	R-3m_R	D3d5	12
167	1	1	7	R-3c_H	D3d6	36
167	2	1	7	R-3c_R	D3d6	12
168	1	1	1	P6	C61	6
169	1	1	1	P61	C62	6
170	1	1	1	P65	C63	6
171	1	1	1	P62	C64	6
172	1	1	1	P64	C65	6
173	1	1	1	P63	C66	6
174	1	1	1	P-6	C3h1	6
175	1	1	1	P6/m	C6h1	12
176	1	1	1	P63/m	C6h2	12
177	1	1	1	P622	D61	12
178	1	1	1	P6122	D62	12
179	1	1	1	P6522	D63	12
180	1	1	1	P6222	D64	12
181	1	1	1	P6422	D65	12
182	1	1	1	P6322	D66	12
183	1	1	1	P6mm	C6v1	12
184	1	1	1	P6cc	C6v2	12
185	1	1	1	P63cm	C6v3	12
186	1	1	1	P63mc	C6v4	12
187	1	1	1	P-6m2	D3h1	12
188	1	1	1	P-6c2	D3h2	12
189	1	1	1	P-62m	D3h3	12
190	1	1	1	P-62c	D3h4	12
191	1	1	1	P6/mmm	D6h1	24
192	1	1	1	P6/mcc	D6h2	24
193	1	1	1	P63/mcm	D6h3	24
194	1	1	1	P63/mmc	D6h4	24
195	1	1	1	P23	T1	12
196	1	1	3	F23	T2	48
197	1	1	2	I23	T3	24
198	1	1	1	P213	T4	12
199	1	1	2	I213	T5	24
200	1	1	1	Pm-3	Th1	24
201	1	1	1	Pn-3_1	Th2	24
201	1	2	1	Pn-3_2	Th2	24
202	1	1	3	Fm-3	Th3	96
203	1	1	3	Fd-3_1	Th4	96
203	1	2	3	Fd-3_2	Th4	96
204	1	1	2	Im-3	Th5	48
205	1	1	1	Pa-3	Th6	24
206	1	1	2	Ia-3	Th7	48
207	1	1	1	P432	O1	24
208	1	1	1	P4232	O2	24
209	1	1	3	F432	O3	96
210	1	1	3	F4132	O4	96
211	1	1	2	I432	O5	48
212	1	1	1	P4332	O6	24
213	1	1	1	P4132	O7	24
214	1	1	2	I4132	O8	48
215	1	1	1	P-43m	Td1	24
216	1	1	3	F-43m	Td2	96
217	1	1	2	I-43m	Td3	48
218	1	1	1	P-43n	Td4	24
219	1	1	3	F-43c	Td5	96
220	1	1	2	I-43d	Td6	48
221	1	1	1	Pm-3m	Oh1	48
222	1	1	1	Pn-3n_1	Oh2	48
222	1	2	1	Pn-3n_2	Oh2	48
223	1	1	1	Pm-3n	Oh3	48
224	1	1	1	Pn-3m_1	Oh4	48
224	1	2	1	Pn-3m_2	Oh4	48
225	1	1	3	Fm-3m	Oh5	192
226	1	1	3	Fm-3c	Oh6	192
227	1	1	3	Fd-3m_1	Oh7	192
227	1	2	3	Fd-3m_2	Oh7	192
228	1	1	3	Fd-3c_1	Oh8	192
228	1	2	3	Fd-3c_2	Oh8	192
229	1	1	2	Im-3m	Oh9	96
230	1	1	2	Ia-3d	Oh10	96