Table 1.4.2.1

Wilson, A. J. C.

doi:10.1107/97809553602060000575

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 1.4, pp. 16-19

Table 1.4.2.1

A. J. C. Wilson^a ^‡

^a St John's College, Cambridge CB2 1TP, England

Table 1.4.2.1 | top | pdf |
The three-dimensional space groups, arranged by arithmetic crystal class ; in a few geometric crystal classes this differs somewhat from the conventional numerical order; see International Tables Volume A, Table 8.3.4.1

Crystal system	Crystal class			Space group
	Geometric	Arithmetic		Space group
	Geometric	Number	Symbol	Number	Symbol
Triclinic	1	1	1P	1	P1
Triclinic	$[\bar1]$	2	$[\bar1P]$	2	$[P\bar1]$
Monoclinic	2	3	2P	3
		3	2P	4
		4	2C	5	C2
	m	5	mP	6	Pm
		5	mP	7	Pc
		6	mC	8	Cm
		6	mC	9	Cc
	2/m	7	2/mP	10
				11
				13
				14
		8	2/mC	12
		8	2/mC	15
Orthorhombic	222	9	222P	16	P222
				17
				18
				19
		10	222C	20
		10	222C	21	C222
		11	222F	22	F222
		12	222I	23	I222
		12	222I	24
	mm	13	mm2P	25	Pmm2
				26
				27	Pcc2
				28	Pma2
				29
				30	Pnc2
				31
				32	Pba2
				33
				34	Pnn2
		14	mm2C	35	Cmm2
				36
				37	Ccc2
		15	2mmC (Amm2)	38	C2mm (Amm2)
				39	(Aem2)
				40
				41	(Aea2)
		16	mm2F	42	Fmm2
		16	mm2F	43	Fdd2
		17	mm2I	44	Imm2
				45	Iba2
				46	Ima2
	mmm	18	mmmP	47	Pmmm
				48	Pnnn
				49	Pccm
				50	Pban
				51	Pmma
				52	Pnna
				53	Pmna
				54	Pcca
				55	Pbam
				56	Pccn
				57	Pbcm
				58	Pnnm
				59	Pmmn
				60	Pbcn
				61	Pbca
				62	Pnma
		19	mmmC	63	Cmcm
				64	Cmce
				65	Cmmm
				66	Cccm
				67	Cmme
				68	Ccce
		20	mmmF	69	Fmmm
		20	mmmF	70	Fddd
		21	mmmI	71	Immm
				72	Ibam
				73	Ibca
				74	Imma
Tetragonal	4	22	4P	75	P4
				76
				77
				78
		23	4I	79	I4
		23	4I	80
	$[\bar4]$	24	$[\bar4P]$	81	$[P\bar4]$
	$[\bar4]$	25	$[\bar4I]$	82	$[I\bar4]$
	4/m	26	4/mP	83
				84
				85
				86
		27	4/mI	87
		27	4/mI	88
	422	28	422P	89	P422
				90
				91
				92
				93
				94
				95
				96
		29	422I	97
		29	422I	98
	4mm	30	4mmP	99
				100
				101
				102
				103
				104
				105
				106
		31	4mmI	107
				108
				109
				110
	$[\bar4m]$	32	$[\bar42mP]$	111	$[P\bar42m]$
				112	$[P\bar42c]$
				113	$[P\bar42_1m]$
				114	$[P\bar42_1c]$
		33	$[\bar4m2P]$	115	$[P\bar4m2]$
				116	$[P\bar4c2]$
				117	$[P\bar4b2]$
				118	$[P\bar4n2]$
		34	$[\bar4m2I]$	119	$[I\bar4m2]$
		34	$[\bar4m2I]$	120	$[I\bar4c2]$
		35	$[\bar42mI]$	121	$[I\bar42m]$
		35	$[\bar42mI]$	122	$[I\bar42d]$
	4/mmm	36	4/mmmP	123
				124
				125
				126
				127
				128
				129
				130
				131
				132
				133
				134
				135
				136
				137
				138
37		4/mmmI	139	I4/mmm
			140	I4/mcm
			141
			142
Trigonal	3	38	3P	143	P3
				144
				145
		39	3R	146	R3
	$[\bar3]$	40	$[\bar3P]$	147	$[P\bar3]$
	$[\bar3]$	41	$[\bar3R]$	148	$[R\bar3]$
	32	42	312P	149	P312
				151
				153
		43	321P	150	P321
				152
				154
		44	32R	155	R32
	3m	45	3m1P	156
		45	3m1P	158
		46	31mP	157
		46	31mP	159
		47	3mR	160
		47	3mR	161
	$[\bar3m]$	48	$[\bar31mP]$	162	$[P\bar31m]$
		48	$[\bar31mP]$	163	$[P\bar31c]$
		49	$[\bar3m1P]$	164	$[P\bar3m1]$
		49	$[\bar3m1P]$	165	$[P\bar3c1]$
		50	$[\bar3mR]$	166	$[R\bar3m]$
		50	$[\bar3mR]$	167	$[R\bar3c]$
Hexagonal	6	51	6P	168	P6
				169
				170
				171
				172
				173
	$[\bar6]$	52	$[\bar6P]$	174	$[P\bar6]$
	6/m	53	6/mP	175
	6/m	53	6/mP	176
	622	54	622P	177
				178
				179
				180
				181
				182
	6mm	55	6mmP	183	P6mm
				184
				185
				186
	$[\bar6m]$	56	$[\bar6m2P]$	187	$[P\bar6m2]$
		56	$[\bar6m2P]$	188	$[P\bar6c2]$
		57	$[\bar62mP]$	189	$[P\bar62m]$
		57	$[\bar62mP]$	190	$[P\bar62c]$
	6/mmm	58	6/mmmP	191
				192
				193
				194
Cubic	23	59	23P	195	P23
		59	23P	198
		60	23F	196	F23
		61	23I	197	I23
		61	23I	199
	$[m\bar3]$	62	$[m\bar3P]$	200	$[Pm\bar3]$
				201	$[Pn\bar3]$
				205	$[Pa\bar3]$
		63	$[m\bar3F]$	202	$[Fm\bar3]$
		63	$[m\bar3F]$	203	$[Fd\bar3]$
		64	$[m\bar3I]$	204	$[Im\bar3]$
		64	$[m\bar3I]$	206	$[Ia\bar3]$
	432	65	432P	207	P432
				208
				213
				212
		66	432F	209
		66	432F	210
		67	432I	211	I432
		67	432I	214
	$[\bar43m]$	68	$[\bar43mP]$	215	$[P\bar43m]$
		68	$[\bar43mP]$	218	$[P\bar43n]$
		69	$[\bar43mF]$	216	$[F\bar43m]$
		69	$[\bar43mF]$	219	$[F\bar43c]$
		70	$[\bar43mI]$	217	$[I\bar43m]$
		70	$[\bar43mI]$	220	$[I\bar43d]$
	$[m\bar3m]$	71	$[m\bar3mP]$	221	$[Pm\bar3m]$
				222	$[Pn\bar3n]$
				223	$[Pm\bar3n]$
				224	$[Pn\bar3m]$
		72	$[m\bar3mF]$	225	$[Fm\bar3m]$
				226	$[Fm\bar3c]$
				227	$[Fd\bar3m]$
				228	$[Fd\bar3c]$
		73	$[m\bar3mI]$	229	$[Im\bar3m]$
		73	$[m\bar3mI]$	230	$[Ia\bar3d]$