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Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	xi	Isomorph. with
Cubic
E, 4C3, 4C32, 3C2	12	T	23	23			Th
E, 8C3, 3C2, 3v, i, 8S6	24	Th	m3				Th
E, 6C4, 8C3, 3C2, 6C2’	24	O	432	432			Oh	Td
E, 8C3, 3C2, 6S4, 6d	24	Td	3m	3m			Oh	O
E, 8C3, 6C2, 6C4, 3C2’, i, 6S4, 8S6, 3h, 6d	48	Oh	m3m				Oh
Tetragonal
E, C4, C2, C43	4	C4	4	4			C4h	S4
E, S4, C2, S43	4	S4					C4h	C4
E, C4, C2, C43, i, S43, h, S4	8	C4h	4/m				C4h
E, 2C4, C2, 2C2’, 2C2’’	8	D4	422	422			D4h	C4v, D2d
E, 2C4, C2, 2v, 2d	8	C4v	4mm	4mm			D4h	D4, D2d
E, 2S4, C2, 2C2’, 2d	8	D2d(Vd)	2m	2m			D4h	D4, C4v
E, 2C4, C2, 2C2’, 2C2’’, i, 2S4, h, 2v, 2d	16	D4h	4/mmm				D4h
Orthorhombic
E, C2, C2’, C2’’	4	D2(V)	222	222			D2h	C2v, C2h
E, C2, v, v’	4	C2v	mm2	mm2			D2h	D2, C2h
E, C2, C2’, C2’’, i, , ’, ’’	8	D2h(Vh)	mmm				D2h
Rhombic symmetry for defects in crystals is often divided into two types: Type I:C2 coincides with the [110] direction and C2’ and C2’’ with [001] and [1-10] directions respectively (or, v andv’ coincide with the planes (1-10) and (001)). Also belonging to type I are centres for which C2 coincides with [001] andv andv’ with (110) and (1-10). Type II:C2 axis coincides with [001] and the axes C2’ and C2’’ with [100] and [010], (or, alternatively, v andv’ coincide with (010) and (100)).
Monoclinic
E, C2	2	C2	2	2			C2h	Cs, Ci
E, h	2	Cs(C1h)	m	m			C2h	C2, Ci
E, C2, i, h	4	C2h	2/m				C2h	D2, C2v
Monoclinic symmetry for defects in crystals is often divided into two types: Type I:C2 coincides with<110>orh with (110) Type II:C2 coincides with<100>orh with (100)
Triclinic
E	1	C1	1	1			Ci
E, i	2	Ci(S2)					Ci	Cs, C2
Trigonal
E, C3, C32	3	C3	3	3			S6
E, C3, C32, i, S65, S6	6	S6(C3i)					S6	C6, C3h
E, 2C3, 3C2	6	D3	32	32			D3d	C3v
E, 2C3, 3v	6	C3v	3m	3m			D3d	D3
E, 2C3, 3C2, i, 2S6, 3d	12	D3d	m				D3d	C6v, D6, D3h
Hexagonal
E, C6, C3, C2, C32, C65	6	C6	6	6			C6h	S6, C3h
E, C3, C32, h, S3, S32	6	C3h(S3)					C6h	S6, C6
E, C6, C3, C2, C32, C65, i, S32, S65, h, S6, S3	12	C6h	6/m				C6h
E, 2C6, 2C3, C2, 3C2’, 3C2’’	12	D6	622	622			D6h	C6v, D3d, D3h
E, 2C6, 2C3, C2, 3v, 3d	12	C6v	6mm	6mm			D6h	D6, D3d, D3h
E, 2C3, 3C2, h, 2S3, 3v	12	D3h	m2	m2			D6h	D6, D3d, C6v
E, 2C6, 2C5, C2, 3C2’, 3C2’’, i, 2S3, 2S6, h, 3d, 3v	24	D6h	6/mmm				D6h
Non-Crystallographic
E, 2		C		-		-	Ch
E, 2, i, 2		Ch	/m	-		-	Ch
E, 2, v		Cv	m	-		-	Dh
E, 2, v, i, 2, C2		Dh	/mm	-		-	Dh
E, C5, C52, C53,  C54	5	C5	5	-			S10
E, S8, C4, S83, C2, S85, C43, S87	8	S8	-	-			C8h
E, 2C5, 2C52, 5C2	10	D5	-	-			D5d	C5v
E, 2C5, 2C52, 5v	10	C5v	-	-			D5d	D5
E, C5, C52, C53, C54, h, S5, S57, S53, S59	10	C5h	-	-			C10h
E, 2S8, 2C4, 2S83, C2, 4C2’, 4d	16	D4d	-	-			D8h
E, 2C5, 2C52, 5C2, i, 2S10, 2S103, 5d	20	D5d	-	-			D5d	D5h
E, 2C5, 2C52, 5C2, h, 2S5, 2S52, 5d	20	D5h	-	-			D10h	D5d
E, 2S12, 2C6, 2S4, 2C3, 2S125, C2, 6C2’, 6d	24	D6d	-	-			D12h
E, 12C5, 12C52, 20C3, 15C2	60	I	-	-			Ih
E, 12C5, 12C52, 20C3, 15C2, i, 12S10, 12S103, 20S6, 15	120	Ih	-	-			Ih

This table lists point group symmetries along with their symmetry operations, the order of the group (i.e. the number of symmetry operations) and common notations.links to a correlation table, andlinks to tables of products of irreducible representations. The group produced by combination with inversion is listed under "x i". This, in the case of crystolographic point groups, is the Laue class which corresponds to the symmetry of reciprocal space. Isomorphic groups are also listed where character tables are available.