# nLab character table of 2O

linear representation theory of binary octahedral group $2 O$

$\,$

group order: ${\vert 2O\vert} = 48$

conjugacy classes:1-1$i$acefg
their cardinality:116886612

character table over the complex numbers $\mathbb{C}$

irrep1-1$i$acefg
$\rho_1$11111111
$\rho_2$11111-1-1-1
$\rho_3$222-1-1000
$\rho_4$33-10011-1
$\rho_5$33-100-1-11
$\rho_6$2-201-1$\sqrt{2}$$-\sqrt{2}$0
$\rho_7$2-201-1$-\sqrt{2}$$\sqrt{2}$0
$\rho_8$4-40-11000

character table over the real numbers $\mathbb{R}$

irrep1-1$i$acefg
$\rho_1$11111111
$\rho_2$11111-1-1-1
$\rho_3$222-1-1000
$\rho_4$33-10011-1
$\rho_5$33-100-1-11
$\rho_6 \oplus \rho_6$4-402-2$2 \sqrt{2}$$-2 \sqrt{2}$0
$\rho_7 \oplus \rho_7$4-402-2$-2 \sqrt{2}$$2 \sqrt{2}$0
$\rho_8 \oplus \rho_8$8-80-22000

References

• Groupnames, CSU(2,3)

• Bockland, Character tables and McKay quivers (pdf)

Last revised on October 8, 2018 at 06:22:17. See the history of this page for a list of all contributions to it.