Finite Group Databasebeta

← Group #66546

Character table — Group #66546

Order 336.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size111122666666667777777714141414141414141414141414141414
order122244714141428282828336666664444121212121212121212121212
χ111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ511111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ611111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ71111-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1
χ81111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ91111-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ101111-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ111111-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ121111-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ131-11-1i−i11-1-1ii−i−i11-1-111-1-11-1i−i1-11-1i−ii−ii−ii−i
χ141-11-1i−i11-1-1ii−i−i11-1-111-1-1-11−ii-11-11i−ii−i−ii−ii
χ151-11-1i−i11-1-1ii−i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1i−i−1−i321+i32−1+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ161-11-1i−i11-1-1ii−i−i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-11−ii1+i32−1−i321−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ171-11-1i−i11-1-1ii−i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1i−i−1+i321−i32−1−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ181-11-1i−i11-1-1ii−i−i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-11−ii1−i32−1+i321+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ191-11-1−ii11-1-1−i−iii11-1-111-1-11-1−ii1-11-1−ii−ii−ii−ii
χ201-11-1−ii11-1-1−i−iii11-1-111-1-1-11i−i-11-11−ii−iii−ii−i
χ211-11-1−ii11-1-1−i−iii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321-1−ii−1−i321+i32−1+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ221-11-1−ii11-1-1−i−iii−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-11i−i1+i32−1−i321−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ231-11-1−ii11-1-1−i−iii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321-1−ii−1+i321−i32−1−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ241-11-1−ii11-1-1−i−iii−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-11i−i1−i32−1+i321+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ2522-2-2002-22-200002222-2-2-2-20000000000000000
χ2622-2-2002-22-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000000000000000
χ2722-2-2002-22-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30000000000000000
χ282-2-22002-2-22000022-2-2-2-2220000000000000000
χ292-2-22002-2-220000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i30000000000000000
χ302-2-22002-2-220000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i30000000000000000
χ31666666-1-1-1-1-1-1-1-1000000000000000000000000
χ326666-6-6-1-1-1-11111000000000000000000000000
χ3366-6-600-11-117−77−7000000000000000000000000
χ3466-6-600-11-11−77−77000000000000000000000000
χ356-66-66i−6i-1-111−i−iii000000000000000000000000
χ366-66-6−6i6i-1-111ii−i−i000000000000000000000000
χ376-6-6600-111-1−i7i7i7−i7000000000000000000000000
χ386-6-6600-111-1i7−i7−i7i7000000000000000000000000

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