# Categorisation of point groups by symmetry operations

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 "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.

 Cubic Tetragonal Orthorhombic Monoclinic Triclinic Trigonal Hexagonal Non-Crystallographic Operations Order SchönfliesSymbol InternationalSymbol FullSymmetrySymbol CorrelationTable Irred. Rep.products x i Isomorph.with 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 All