Finite Group Databasebeta

← Group #6978

Character table — Group #6978

Order 252.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size13377133772661414266141439921213992121
order17733214146632121336424266428281212428281212
χ1111111111111111111111111111111
χ2111−1+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+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+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−i7200
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1
χ7111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−i32111−1+i32−1−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+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+i7200-31+i721−i7200-31+i721−i7200
χ103−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i72003−1+i72−1−i7200-31−i721+i7200-31−i721+i7200
χ1111111-1-1-1-1-111111-1-1-1-1-1iiiii−i−i−i−i−i
χ12111−1+i32−1−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−ζ83
χ13111−1−i32−1+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−ζ79
χ143−1−i72−1+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−ζ8300
χ153−1+i72−1−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−ζ7900
χ1611111-1-1-1-1-111111-1-1-1-1-1−i−i−i−i−iiiiii
χ17111−1+i32−1−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
χ18111−1−i32−1+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
χ193−1−i72−1+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
χ203−1+i72−1−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
χ212222222222-1-1-1-1-1-1-1-1-1-10000000000
χ22222−1+i3−1−i3222−1+i3−1−i3-1-1-11−i321+i32-1-1-11−i321+i320000000000
χ23222−1−i3−1+i3222−1−i3−1+i3-1-1-11+i321−i32-1-1-11+i321−i320000000000
χ246−1−i7−1+i7006−1−i7−1+i700-31+i721−i7200-31+i721−i72000000000000
χ256−1+i7−1−i7006−1+i7−1−i700-31−i721+i7200-31−i721+i72000000000000
χ2622222-2-2-2-2-2-1-1-1-1-1111110000000000
χ27222−1+i3−1−i3-2-2-21−i31+i3-1-1-11−i321+i32111−1+i32−1−i320000000000
χ28222−1−i3−1+i3-2-2-21+i31−i3-1-1-11+i321−i32111−1−i32−1+i320000000000
χ296−1−i7−1+i700-61+i71−i700-31+i721−i72003−1−i72−1+i72000000000000
χ306−1+i7−1−i700-61−i71+i700-31−i721+i72003−1+i72−1−i72000000000000

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