Piezoelectric Crystal Classes

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Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	× i	Isomorph. with
Piezoelectric Classes
E	1	C1	1	1		⊗	Ci
E, C2	2	C2	2	2		⊗	C2h	Cs, Ci
E, σh	2	Cs(C1h)	m	m		⊗	C2h	C2, Ci
E, C3, C32	3	C3	3	3		⊗	S6
E, C4, C2, C43	4	C4	4	4		⊗	C4h	S4
E, S4, C2, S43	4	S4				⊗	C4h	C4
E, C2, C2’, C2’’	4	D2(V)	222	222		⊗	D2h	C2v, C2h
E, C2, σv, σv’	4	C2v	mm2	mm2		⊗	D2h	D2, C2h
E, C3, C32, σh, S3, S32	6	C3h(S3)				⊗	C6h	S6, C6
E, 2C3, 3C2	6	D3	32	32		⊗	D3d	C3v
E, 2C3, 3σv	6	C3v	3m	3m		⊗	D3d	D3
E, C6, C3, C2, C32, C65	6	C6	6	6		⊗	C6h	S6, C3h
E, 2C4, C2, 2C2’, 2C2’’	8	D4	422	422		⊗	D4h	C4v, D2d
E, 2C4, C2, 2σv, 2σd	8	C4v	4mm	4mm		⊗	D4h	D4, D2d
E, 2S4, C2, 2C2’, 2σd	8	D2d(Vd)	2m	2m		⊗	D4h	D4, C4v
E, 2C3, 3C2, σh, 2S3, 3σv	12	D3h	m2	m2		⊗	D6h	D6, D3d, C6v
E, 2C6, 2C3, C2, 3C2’, 3C2’’	12	D6	622	622		⊗	D6h	C6v, D3d, D3h
E, 2C6, 2C3, C2, 3σv, 3σd	12	C6v	6mm	6mm		⊗	D6h	D6, D3d, D3h
E, 4C3, 4C32, 3C2	12	T	23	23		⊗	Th
E, 8C3, 3C2, 6S4, 6σd	24	Td	3m	3m		⊗	Oh	O
Pyroelectric Classes

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, and ⊗ links to tables of products of irreducible representations. The group produced by combination with inversion is listed under "× 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.