Linear representation theory of cyclic group:Z5
This article gives specific information, namely, linear representation theory, about a particular group, namely: cyclic group:Z5.
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|degrees of irreducible representations over a splitting field|| 1,1,1,1,1|
maximum: 1, lcm: 1, number: 5, sum of squares: 5
|Schur index values of irreducible representations||1,1,1,1,1|
|condition for a field to be a splitting field|| characteristic not equal to 5, must contain a primitive fifth root of unity, or equivalently, the polynomial must split.|
For a finite field of size , equivalent formulation: 5 must divide .
|smallest ring of realization (characteristic zero)||or , integral extension of the ring of integers of degree 4|
|smallest field of realization (characteristic zero)||or , cyclotomicextension of of degree 4|
|smallest size splitting field||field:F11, i.e., field of 11 elements|
|degrees of irreducible representations over the field of real numbers , and more generally over a field where splits as a product of two irreducible quadratics|| 1,2,2|
maximum: 2, lcm: 2, number: 3
|degrees of irreducible representations over the field of rational numbers , and more generally over a field where is irreducible||1,4|
|Family name||Parameter values||General discussion of linear representation theory of family|
|finite cyclic group||5||linear representation theory of finite cyclic groups|