Finite Group Databasebeta

← Group #13051576

Character table — Group #13051576

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111444444666666667777777777777777121212121212121212121212282828282828282828282828282828282828282828282828282828282828282828282828
order122222224444447141414141414143366666666666666282828282828282828282828224444446666121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ41111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32111111111111-1-1-1-1-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ51111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ61111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32111111111111-1-1-1-1-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ71111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1
χ81111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-11111
χ91111111111-1-1-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-11111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32
χ101111111111-1-1-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1-1-1-1-111111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ111111111111-1-1-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-11111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ121111111111-1-1-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1-1-1-1-111111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311111111-1-111-1-1111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1411111111-1-111-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ1511111111-1-111-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-111-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1611111111-1-111-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-1-1-11111-1-11+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ1711111111-1-111-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-111-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1811111111-1-111-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-1-1-11111-1-11−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ1911111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ2011111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111
χ2111111111-1-1-1-11111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1111111-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ2211111111-1-1-1-11111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-11111-1-111-1-1111+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ2311111111-1-1-1-11111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1111111-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ2411111111-1-1-1-11111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-11111-1-111-1-1111−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ25222-2-2-2-222i−2i0000222-2-22-2-2222222-2-2-2-2-2-2-2-2222i2i−2i−2i000000000000000000002i−2i002i−2i000000000000000000
χ26222-2-2-2-222i−2i0000222-2-22-2-2−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31+i31+i31+i31−i31−i31−i31−i3−1−i3−1+i32i2i−2i−2i000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79000000000000000000
χ27222-2-2-2-222i−2i0000222-2-22-2-2−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31−i31−i31−i31+i31+i31+i31+i3−1+i3−1−i32i2i−2i−2i000000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83000000000000000000
χ28222-2-2-2-22−2i2i0000222-2-22-2-2222222-2-2-2-2-2-2-2-222−2i−2i2i2i00000000000000000000−2i2i00−2i2i000000000000000000
χ29222-2-2-2-22−2i2i0000222-2-22-2-2−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31+i31+i31+i31−i31−i31−i31−i3−1−i3−1+i3−2i−2i2i2i00000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79000000000000000000
χ30222-2-2-2-22−2i2i0000222-2-22-2-2−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31−i31−i31−i31+i31+i31+i31+i3−1+i3−1−i3−2i−2i2i2i00000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83000000000000000000
χ3122-222-2-2-200000022-2-2-2-222222-22-222-2-222-2-2-2-200000000000000002i−2i00000000000000002i−2i002i−2i00000000
χ3222-222-2-2-200000022-2-2-2-222222-22-222-2-222-2-2-2-20000000000000000−2i2i0000000000000000−2i2i00−2i2i00000000
χ3322-222-2-2-200000022-2-2-2-222−1−i3−1+i3−1−i31+i3−1+i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i31+i31−i300000000000000002i−2i00000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ7900000000
χ3422-222-2-2-200000022-2-2-2-222−1−i3−1+i3−1−i31+i3−1+i31−i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i31+i31−i30000000000000000−2i2i0000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900000000
χ3522-222-2-2-200000022-2-2-2-222−1+i3−1−i3−1+i31−i3−1−i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i31−i31+i300000000000000002i−2i00000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ8300000000
χ3622-222-2-2-200000022-2-2-2-222−1+i3−1−i3−1+i31−i3−1−i31+i3−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i31−i31+i30000000000000000−2i2i0000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300000000
χ3722-2-2-222-200000022-222-2-2-2222-22-2-2-222-2-222-2-20000000000000000002i−2i0000000000000000000000002i−2i2i−2i
χ3822-2-2-222-200000022-222-2-2-2222-22-2-2-222-2-222-2-2000000000000000000−2i2i000000000000000000000000−2i2i−2i2i
χ3922-2-2-222-200000022-222-2-2-2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i31+i31−i30000000000000000002i−2i0000000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79
χ4022-2-2-222-200000022-222-2-2-2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i31+i31−i3000000000000000000−2i2i000000000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79
χ4122-2-2-222-200000022-222-2-2-2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i31−i31+i30000000000000000002i−2i0000000000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83
χ4222-2-2-222-200000022-222-2-2-2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31−i3−1+i3−1+i31+i31+i3−1−i3−1−i31−i31+i3000000000000000000−2i2i000000000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83
χ432-222-22-2-2002i−2i002-222-2-22-222-22-222-22-22-22-2-2-200002i2i−2i−2i0000000000000000002i−2i002i−2i0000000000000000
χ442-222-22-2-2002i−2i002-222-2-22-2−1−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i31+i31−i300002i2i−2i−2i0000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ790000000000000000
χ452-222-22-2-2002i−2i002-222-2-22-2−1+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i31−i31+i300002i2i−2i−2i0000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ830000000000000000
χ462-222-22-2-200−2i2i002-222-2-22-222-22-222-22-22-22-2-2-20000−2i−2i2i2i000000000000000000−2i2i00−2i2i0000000000000000
χ472-222-22-2-200−2i2i002-222-2-22-2−1−i3−1+i31+i3−1−i31−i3−1+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i31+i31−i30000−2i−2i2i2i000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ790000000000000000
χ482-222-22-2-200−2i2i002-222-2-22-2−1+i3−1−i31−i3−1+i31+i3−1−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i31−i31+i30000−2i−2i2i2i000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ830000000000000000
χ492-22-22-22-200002i−2i2-22-22-2-2222-22-22-22-22-22-22-2-2000000002i2i−2i−2i00000000000000000000000000002i−2i2i−2i0000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.