Categorisation by Class: Tetragonal

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• Jon Goss
• AIMPRO

Cubic			(T Th O Td Oh)
Tetragonal
Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	× i	Isomorph. with
E, C4, C2, C43	4	C4	4	4		⊗	C4h	S4
E, S4, C2, S43	4	S4				⊗	C4h	C4
E, C4, C2, C43, i, S43, σh, S4	8	C4h	4/m			⊗	C4h
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, 2C4, C2, 2C2’, 2C2’’, i, 2S4, σh, 2σv, 2σd	16	D4h	4/mmm			⊗	D4h
Orthorhombic			(D2 C2v D2h)
Monoclinic			(C2 Cs C2h)
Triclinic			(C1 Ci)
Trigonal			(C3 S6 D3 C3v D3d)
Hexagonal			(C6 C3h C6h D6 C6v D3h 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.