Categorisation by Class: Cubic

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• Jon Goss
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Cubic*
Operations	Order	Schönflies Symbol	International Symbol	Full Symmetry Symbol	Correlation Table	Irred. Rep. products	× i	Isomorph. with
E, 4C3, 4C32, 3C2	12	T	23	23		⊗	Th
E, 8C3, 3C2, 3σv, i, 8S6	24	Th	m3			⊗	Th
E, 6C4, 8C3, 3C2, 6C2’	24	O	432	432		⊗	Oh	Td
E, 8C3, 3C2, 6S4, 6σd	24	Td	3m	3m		⊗	Oh	O
E, 8C3, 6C2, 6C4, 3C2’, i, 6S4, 8S6, 3σh, 6σd	48	Oh	m3m			⊗	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			(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.