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character table of 2T

linear representation theory of binary tetrahedral group 2T2 T

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

conjugacy classes:1-1iiabcd
their cardinality:1164444

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

e.g. ζ 3=12(1+3i)\zeta_3 = \tfrac{1}{2}(-1 + \sqrt{3} i), notice that ζ 3+ζ 3 2=1\zeta_3 + \zeta_3^2 = 1

character table over the complex numbers \mathbb{C}

irrep1-1iiabcd
ρ 1\rho_11111111
ρ 2\rho_2111ζ 3\zeta_3ζ 3 2\zeta_3^2ζ 3 2\zeta_3^2ζ 3\zeta_3
ρ 2 *\rho_2^\ast111ζ 3 2\zeta^2_3ζ 3\zeta_3ζ 3\zeta_3ζ 3 2\zeta_3^2
ρ 3\rho_333-10000
ρ 4\rho_42-20ζ 3\zeta_3ζ 3 2\zeta_3^2ζ 3 2-\zeta_3^2ζ 3-\zeta_3
ρ 4 *\rho_4^\ast2-20ζ 3 2\zeta_3^2ζ 3\zeta_3ζ 3-\zeta_3ζ 3 2-\zeta_3^2
ρ 5\rho_5 2-2011-1-1

character table over the real numbers \mathbb{R}

irrep1-1iiabcd
ρ 1\rho_11111111
ρ 2ρ 2 *\rho_2 \oplus \rho_2^\ast222-1-1-1-1
ρ 3\rho_333-10000
ρ 4ρ 4 *\rho_4 \oplus \rho_4^\ast4-40-1-111
ρ 5ρ 5\rho_5 \oplus \rho_54-4022-2-2

References

Last revised on October 8, 2018 at 06:22:24. See the history of this page for a list of all contributions to it.