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Conjugacy classes may be referred to by describing them, or more briefly by abbreviations such as "6A", meaning "a certain conjugacy class with elements of order 6", and "6B" would be a different conjugacy class with elements of order 6; the conjugacy class 1A is the conjugacy class of the identity which has order 1.
All the reflections are conjugate to each other whenever n is odd, but they fall into two conjugacy classes if n is even. If we think of the isometries of a regular n-gon: for odd n there are rotations in the group between every pair of mirrors, while for even n only half of the mirrors can be reached from one by these rotations. Geometrically ...
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The manipulations of the Rubik's Cube form the Rubik's Cube group. The Rubik's Cube group (,) represents the structure of the Rubik's Cube mechanical puzzle.Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces.
Thus the conjugacy class within the Euclidean group E(n) of inversion in a point is the set of inversions in all points. Since a combination of two inversions is a translation, the conjugate closure of a singleton containing inversion in a point is the set of all translations and the inversions in all points.
After a controversial couple of years in the Chapin-Irmo area school district, nine candidates are running for seats on the Lexington-Richland 5 school board.
The symmetric group S4, consisting of all 24 permutations of four elements, has five conjugacy classes. And you can compute that there are five conjugacy classes by taking the integer partition of 4. But how can you compute how many elements each conjugacy class has? PJ Geest 14:56, 1 June 2009 (UTC)
Interval class Play ⓘ.. In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes.