# nLab character table of 2T

linear representation theory of binary tetrahedral group $2 T$

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group order: $\vert 2T\vert = 24$

conjugacy classes:1-1$i$abcd
their cardinality:1164444

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let $\zeta_3$ be a third root of unity, $(\zeta_3)^3 = 1$

e.g. $\zeta_3 = \tfrac{1}{2}(-1 + \sqrt{3} i)$, notice that $\zeta_3 + \zeta_3^2 = 1$

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

irrep1-1$i$abcd
$\rho_1$1111111
$\rho_2$111$\zeta_3$$\zeta_3^2$$\zeta_3^2$$\zeta_3$
$\rho_2^\ast$111$\zeta^2_3$$\zeta_3$$\zeta_3$$\zeta_3^2$
$\rho_3$33-10000
$\rho_4$2-20$\zeta_3$$\zeta_3^2$$-\zeta_3^2$$-\zeta_3$
$\rho_4^\ast$2-20$\zeta_3^2$$\zeta_3$$-\zeta_3$$-\zeta_3^2$
$\rho_5$2-2011-1-1

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

irrep1-1$i$abcd
$\rho_1$1111111
$\rho_2 \oplus \rho_2^\ast$222-1-1-1-1
$\rho_3$33-10000
$\rho_4 \oplus \rho_4^\ast$4-40-1-111
$\rho_5 \oplus \rho_5$4-4022-2-2

References

• Bockland, Character tables and McKay quivers (pdf)

Last revised on September 2, 2021 at 08:43:09. See the history of this page for a list of all contributions to it.