Finite Group Databasebeta

← Group #4249

Character table — Group #4249

Order 168.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size1337713377133771337713377133771337713377
order17733428281212214146642828121221414664282812122141466428281212
χ11111111111111111111111111111111111111111
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−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+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+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−i7200
χ611111iiiii-1-1-1-1-1−i−i−i−i−i11111iiiii-1-1-1-1-1−i−i−i−i−i
χ7111−1+i32−1−i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83-1-1-11−i321+i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83111−1+i32−1−i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83-1-1-11−i321+i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ8111−1−i32−1+i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79-1-1-11+i321−i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79111−1−i32−1+i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79-1-1-11+i321−i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ93−1−i72−1+i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300-31+i721−i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003−1−i72−1+i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300-31+i721−i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300
χ103−1+i72−1−i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900-31−i721+i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003−1+i72−1−i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900-31−i721+i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900
χ1111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-1
χ12111−1+i32−1−i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32
χ13111−1−i32−1+i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32
χ143−1−i72−1+i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i7200
χ153−1+i72−1−i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i7200
χ1611111−i−i−i−i−i-1-1-1-1-1iiiii11111−i−i−i−i−i-1-1-1-1-1iiiii
χ17111−1+i32−1−i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83-1-1-11−i321+i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83111−1+i32−1−i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83-1-1-11−i321+i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ18111−1−i32−1+i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79-1-1-11+i321−i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79111−1−i32−1+i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79-1-1-11+i321−i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ193−1−i72−1+i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300-31+i721−i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83003−1−i72−1+i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300-31+i721−i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300
χ203−1+i72−1−i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900-31−i721+i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79003−1+i72−1−i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900-31−i721+i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900
χ2111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ22111−1+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
χ23111−1−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
χ243−1−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
χ253−1+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
χ2611111iiiii-1-1-1-1-1−i−i−i−i−i-1-1-1-1-1−i−i−i−i−i11111iiiii
χ27111−1+i32−1−i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83-1-1-11−i321+i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83-1-1-11−i321+i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83111−1+i32−1−i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ28111−1−i32−1+i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79-1-1-11+i321−i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79-1-1-11+i321−i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79111−1−i32−1+i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ293−1−i72−1+i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300-31+i721−i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300-31+i721−i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83003−1−i72−1+i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300
χ303−1+i72−1−i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900-31−i721+i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900-31−i721+i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79003−1+i72−1−i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900
χ3111111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111111
χ32111−1+i32−1−i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32-1-1-11−i321+i32111−1+i32−1−i32-1-1-11−i321+i32111−1+i32−1−i32
χ33111−1−i32−1+i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32-1-1-11+i321−i32111−1−i32−1+i32-1-1-11+i321−i32111−1−i32−1+i32
χ343−1−i72−1+i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i7200-31+i721−i72003−1−i72−1+i7200-31+i721−i72003−1−i72−1+i7200
χ353−1+i72−1−i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i72003−1+i72−1−i7200-31−i721+i72003−1+i72−1−i7200
χ3611111−i−i−i−i−i-1-1-1-1-1iiiii-1-1-1-1-1iiiii11111−i−i−i−i−i
χ37111−1+i32−1−i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83-1-1-11−i321+i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83-1-1-11−i321+i32iiiζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83111−1+i32−1−i32−i−i−i−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ38111−1−i32−1+i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79-1-1-11+i321−i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79-1-1-11+i321−i32iiiζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79111−1−i32−1+i32−i−i−i−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ393−1−i72−1+i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300-31+i721−i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300-31+i721−i72003iζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83003−1−i72−1+i7200−3i−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300
χ403−1+i72−1−i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900-31−i721+i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ7900-31−i721+i72003iζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79003−1+i72−1−i7200−3i−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900

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