Finite Group Databasebeta

← Group #66544

Character table — Group #66544

Order 336.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38
size111122666666667777777714141414141414141414141414141414
order12442471414142828282833661212121266888812122424242424242424
χ111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111−1−i32−1+i32−1−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
χ411111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ511111111111111−1+i32−1−i32−1+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
χ611111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ71111-1-11-1-1111-1-111111111-1-111-1-1-1-111-1-111-1-1
χ81111-1-11-1-1111-1-111111111-1-1-1-111-1-1-1-111-1-111
χ91111-1-11-1-1111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i3211-1-11+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111-1-11-1-1111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32-1-1111+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111-1-11-1-1111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i3211-1-11−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111-1-11-1-1111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32-1-1111−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ1311-1-11-11111-1-1-1-11111-1-1-1-111i−ii−i-1-1i−ii−ii−ii−i
χ1411-1-11-11111-1-1-1-11111-1-1-1-111−ii−ii-1-1−ii−ii−ii−ii
χ1511-1-11-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32i−ii−i1+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ1611-1-11-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−ii−ii1+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ1711-1-11-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32i−ii−i1−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ1811-1-11-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−ii−ii1−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ1911-1-1-111-1-11-1-1111111-1-1-1-1-1-1i−i−ii11i−i−iii−i−ii
χ2011-1-1-111-1-11-1-1111111-1-1-1-1-1-1−iii−i11−iii−i−iii−i
χ2111-1-1-111-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32i−i−ii−1−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ2211-1-1-111-1-11-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−iii−i−1−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ2311-1-1-111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32i−i−ii−1+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ2411-1-1-111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−iii−i−1+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ252-22i−2i00200-22i−2i0022-2-22i−2i2i−2i0000000000000000
χ262-22i−2i00200-22i−2i00−1−i3−1+i31+i31−i32ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ790000000000000000
χ272-22i−2i00200-22i−2i00−1+i3−1−i31−i31+i32ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ830000000000000000
χ282-2−2i2i00200-2−2i2i0022-2-2−2i2i−2i2i0000000000000000
χ292-2−2i2i00200-2−2i2i00−1−i3−1+i31+i31−i3−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790000000000000000
χ302-2−2i2i00200-2−2i2i00−1+i3−1−i31−i31+i3−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830000000000000000
χ31666666-1-1-1-1-1-1-1-1000000000000000000000000
χ326666-6-6-111-1-1-111000000000000000000000000
χ3366-6-66-6-1-1-1-11111000000000000000000000000
χ3466-6-6-66-111-111-1-1000000000000000000000000
χ356-66i−6i00-1−i7i71−ii7−7000000000000000000000000
χ366-66i−6i00-1i7−i71−ii−77000000000000000000000000
χ376-6−6i6i00-1−i7i71i−i−77000000000000000000000000
χ386-6−6i6i00-1i7−i71i−i7−7000000000000000000000000

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