Categorisation by Class: Hexagonal

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Cubic			(T Th O Td Oh)
Tetragonal			(C4 S4 C4h D4 C4v D2d D4h)
Orthorhombic			(D2 C2v D2h)
Monoclinic			(C2 Cs C2h)
Triclinic			(C1 Ci)
Trigonal			(C3 S6 D3 C3v D3d)
Hexagonal
Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	× i	Isomorph. with
E, C6, C3, C2, C32, C65	6	C6	6	6		⊗	C6h	S6, C3h
E, C3, C32, σh, S3, S32	6	C3h(S3)				⊗	C6h	S6, C6
E, C6, C3, C2, C32, C65, i, S32, S65, σh, 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, 3σv, 3σd	12	C6v	6mm	6mm		⊗	D6h	D6, D3d, D3h
E, 2C3, 3C2, σh, 2S3, 3σv	12	D3h	m2	m2		⊗	D6h	D6, D3d, C6v
E, 2C6, 2C5, C2, 3C2’, 3C2’’, i, 2S3, 2S6, σh, 3σd, 3σv	24	D6h	6/mmm			⊗	D6h
Non-crystallographic			(C∞ C∞h C∞v D∞h C5 S8 D5 C5v C5h D4d D5d D5h D6d I Ih)
All

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.