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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.
If a finite group G has exactly two conjugacy classes of involutions with representatives t and z, then the Thompson order formula (Aschbacher 2000, 45.6) (Suzuki 1986, 5.1.7) states
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Here we consider (homotopy classes of) lifts of paths in the base space X of a fibration : ~. The result has the structure of a groupoid over the base space X. The advantage is that we can drop the condition of connectedness of X.
The set of integer-valued class functions on G, Z([G]), is a commutative ring, finitely generated over . All of its elements are thus integral over Z {\displaystyle \mathbb {Z} } , in particular the mapping u which takes the value 1 on the conjugacy class of g and 0 elsewhere.
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 ...
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)