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character table of 2D4=Dic2=Q8

linear representation theory of binary dihedral group 2D 42 D_4

== dicyclic group Dic 2Dic_2 == quaternion group Q 8Q_8

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group order: |2D 4|=8{\vert 2D_4\vert} = 8

conjugacy classes:124A4B4C
their cardinality:11222

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

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

irrep124A4B4CSchur index
ρ 1\rho_1111111
ρ 2\rho_211-11-11
ρ 3\rho_3111-1-11
ρ 4\rho_411-1-111
ρ 5\rho_52-20002

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

irrep124A4B4C
ρ 1\rho_111111
ρ 2\rho_211-11-1
ρ 3\rho_3111-1-1
ρ 4\rho_411-1-11
ρ 5ρ 5\rho_5 \oplus \rho_54-4000

References

Last revised on October 8, 2018 at 06:21:59. See the history of this page for a list of all contributions to it.