# nLab character table of 2D4=Dic2=Q8

linear representation theory of binary dihedral group $2 D_4$

$=$ dicyclic group $Dic_2$ $=$ quaternion group $Q_8$

$\,$

group order: ${\vert 2D_4\vert} = 8$

conjugacy classes:124A4B4C
their cardinality:11222

$\,$

splitting field$\mathbb{Q}(\alpha, \beta)$ with $\alpha^2 + \beta^2 = -1$
field generated by characters$\mathbb{Q}$

character table over splitting field $\mathbb{Q}(\alpha,\beta)$/complex numbers $\mathbb{C}$

irrep124A4B4CSchur index
$\rho_1$111111
$\rho_2$11-11-11
$\rho_3$111-1-11
$\rho_4$11-1-111
$\rho_5$2-20002

character table over rational numbers $\mathbb{Q}$/real numbers $\mathbb{R}$

irrep124A4B4C
$\rho_1$11111
$\rho_2$11-11-1
$\rho_3$111-1-1
$\rho_4$11-1-11
$\rho_5 \oplus \rho_5$4-4000

References

Last revised on September 2, 2021 at 04:38:31. See the history of this page for a list of all contributions to it.