character table of 2I

**linear representation theory of binary icosahedral group $2 I$**

$\,$

group order: ${\vert 2I\vert} = 120$

conjugacy classes: | 1 | 2 | 3 | 4 | 5A | 5B | 6 | 10A | 10B |
---|---|---|---|---|---|---|---|---|---|

their cardinality: | 1 | 1 | 20 | 30 | 12 | 12 | 20 | 12 | 12 |

let $\phi \coloneqq \tfrac{1}{2}( 1 + \sqrt{5} )$ (the golden ratio)

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

irrep | 1 | 2 | 3 | 4 | 5A | 5B | 6 | 10A | 10B |
---|---|---|---|---|---|---|---|---|---|

$\rho_1$ | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

$\rho_2$ | 2 | -2 | -1 | 0 | $\phi - 1$ | $-\phi$ | 1 | $\phi$ | $1 - \phi$ |

$\rho_3$ | 2 | -2 | -1 | 0 | $-\phi$ | $\phi - 1$ | 1 | $1-\phi$ | $\phi$ |

$\rho_4$ | 3 | 3 | 0 | -1 | $1 - \phi$ | $\phi$ | 0 | $\phi$ | $1-\phi$ |

$\rho_5$ | 3 | 3 | 0 | -1 | $\phi$ | $1-\phi$ | 0 | $1-\phi$ | $\phi$ |

$\rho_6$ | 4 | 4 | 1 | 0 | -1 | -1 | 1 | -1 | -1 |

$\rho_7$ | 4 | -4 | 1 | 0 | -1 | -1 | -1 | 1 | 1 |

$\rho_8$ | 5 | 5 | -1 | 1 | 0 | 0 | -1 | 0 | 0 |

$\rho_9$ | 6 | -6 | 0 | 0 | 1 | 1 | 0 | -1 | -1 |

**References**

category: character tables

Last revised on October 9, 2018 at 05:16:58. See the history of this page for a list of all contributions to it.