Maximum conjugacy class size does not give bound on maximum degree of irreducible representation
For a prime number
Suppose is a prime number. Then, for any positive integer , it is possible to construct a finite p-group such that the maximum degree of irreducible representation for is but the maximum conjugacy class size in is .
More general versionPLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
- Maximum degree of irreducible representation does not give bound on maximum conjugacy class size
- Degrees of irreducible representations need not determine conjugacy class size statistics
- Conjugacy class size statistics need not determine degrees of irreducible representations
For more related facts, see the facts section of the degrees of irreducible representations page.
Further information: element structure of extraspecial groups, linear representation theory of extraspecial groups
Take the extraspecial group of order (there are two such groups and either will do). The maximum degree of irreducible representation for this group is , and the maximum conjugacy class size is .