Linear representation theory of dihedral group:D16
This article gives specific information, namely, linear representation theory, about a particular group, namely: dihedral group:D16.
View linear representation theory of particular groups | View other specific information about dihedral group:D16
Summary
We shall use the dihedral group with the following presentation:
.
| Item | Value |
|---|---|
| degrees of irreducible representations over a splitting field | 1,1,1,1,2,2,2 maximum: 2, lcm: 2, number: 7, sum of squares: 16 |
| Schur index values of irreducible representations over a splitting field | 1,1,1,1,1,1,1 |
| smallest ring of realization (characteristic zero) | or (not sure -- need to check!) |
| smallest field of realization (characteristic zero) | or |
| condition for a field to be a splitting field | ? |
| smallest size splitting field | ? |
| degrees of irreducible representations over the rational numbers | ? |
![{\displaystyle \mathbb {Z} [{\sqrt {2}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffca8cc80ac2e1bc11dc6429dedfe3239f148019)
![{\displaystyle \mathbb {Z} [x]/(x^{2}-2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b48e19540d0483da53cffe91de9cfa19d3975697)
![{\displaystyle \mathbb {Q} [x]/(x^{2}-2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9f257d51dc9f363db49ba93e03829ab95d444a)
Family contexts
| Family name | Parameter values | General discussion of linear representation theory of family |
|---|---|---|
| dihedral group | degree , order | linear representation theory of dihedral groups |
COMPARE AND CONTRAST: View linear representation theory of groups of order 16 to compare and contrast the linear representation theory with other groups of order 16.