Finite Group Databasebeta

← Group #66580

Character table — Group #66580

Order 336.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size13377133771337713377266141426614142661414266141426614142661414
order1773321414662141466214146621414662141466428281212428281212428281212428281212
χ111111111111111111111111111111111111111111111111111
χ2111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32
χ3111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32
χ43−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i7200
χ53−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i7200
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ7111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32-1-1-11−i321+i32-1-1-11−i321+i32
χ8111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32-1-1-11+i321−i32-1-1-11+i321−i32
χ93−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i7200-31+i721−i7200-31+i721−i7200
χ103−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i7200-31−i721+i7200-31−i721+i7200
χ1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ12111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32
χ13111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32
χ143−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i7200
χ153−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i7200
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ17111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32111−1+i32−1−i32
χ18111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32111−1−i32−1+i32
χ193−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i72003−1−i72−1+i7200
χ203−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i72003−1+i72−1−i7200
χ211111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i
χ22111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ23111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ243−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300
χ253−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900
χ261111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii
χ27111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ28111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ293−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300
χ303−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900
χ311111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111iiiii−i−i−i−i−i−i−i−i−i−iiiiii
χ32111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ33111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ343−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300
χ353−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900
χ361111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111−i−i−i−i−iiiiiiiiiii−i−i−i−i−i
χ37111−1+i32−1−i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ38111−1−i32−1+i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ393−1−i72−1+i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300
χ403−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900
χ4122222-2-2-2-2-222222-2-2-2-2-2000000000000000000000000000000
χ42222−1+i3−1−i3-2-2-21−i31+i3222−1+i3−1−i3-2-2-21−i31+i3000000000000000000000000000000
χ43222−1−i3−1+i3-2-2-21+i31−i3222−1−i3−1+i3-2-2-21+i31−i3000000000000000000000000000000
χ446−1−i7−1+i700-61+i71−i7006−1−i7−1+i700-61+i71−i700000000000000000000000000000000
χ456−1+i7−1−i700-61−i71+i7006−1+i7−1−i700-61−i71+i700000000000000000000000000000000
χ4622222-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000000
χ47222−1+i3−1−i3-2-2-21−i31+i3-2-2-21−i31+i3222−1+i3−1−i3000000000000000000000000000000
χ48222−1−i3−1+i3-2-2-21+i31−i3-2-2-21+i31−i3222−1−i3−1+i3000000000000000000000000000000
χ496−1−i7−1+i700-61+i71−i700-61+i71−i7006−1−i7−1+i700000000000000000000000000000000
χ506−1+i7−1−i700-61−i71+i700-61−i71+i7006−1+i7−1−i700000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.