Finite Group Databasebeta

← Group #13051574

Character table — Group #13051574

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111444444666666667777777777777777121212121212121212121212282828282828282828282828282828282828282828282828282828282828282828282828
order12222222444444714141414141414336666666666666628282828282828282828282822224444666666661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
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+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ71111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1
χ81111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111
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+i321111-1-1-1-1-1-1-1-111-1-111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+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+i321111-1-1-1-1-1-1-1-1-1-111-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−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−i321111-1-1-1-1-1-1-1-111-1-111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−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−i321111-1-1-1-1-1-1-1-1-1-111-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311111111-1-111-1-1111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ1411111111-1-111-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1
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−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+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+i32−1−i32−1−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+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+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−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−i32−1+i32−1+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−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ1911111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ2011111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
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+i32-1-1-1-1-1-1-1-111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−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+i32-1-1-1-1-1-1-1-11111-1-1-1-111111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−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
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−i32-1-1-1-1-1-1-1-111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+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−i32-1-1-1-1-1-1-1-11111-1-1-1-111111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+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
χ25222-22-2-2-2002i−2i00222-2-22-2-22222-222-22-2-22-2-2-2-200002i2i−2i−2i00000000000000000000002i−2i002i−2i000000000000
χ26222-22-2-2-2002i−2i00222-2-22-2-2−1−i3−1+i3−1−i3−1−i31+i3−1+i3−1+i31−i3−1−i31+i31+i3−1+i31−i31−i31+i31−i300002i2i−2i−2i00000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79000000000000
χ27222-22-2-2-2002i−2i00222-2-22-2-2−1+i3−1−i3−1+i3−1+i31−i3−1−i3−1−i31+i3−1+i31−i31−i3−1−i31+i31+i31−i31+i300002i2i−2i−2i00000000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83000000000000
χ28222-22-2-2-200−2i2i00222-2-22-2-22222-222-22-2-22-2-2-2-20000−2i−2i2i2i0000000000000000000000−2i2i00−2i2i000000000000
χ29222-22-2-2-200−2i2i00222-2-22-2-2−1−i3−1+i3−1−i3−1−i31+i3−1+i3−1+i31−i3−1−i31+i31+i3−1+i31−i31−i31+i31−i30000−2i−2i2i2i0000000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79000000000000
χ30222-22-2-2-200−2i2i00222-2-22-2-2−1+i3−1−i3−1+i3−1+i31−i3−1−i3−1−i31+i3−1+i31−i31−i3−1−i31+i31+i31−i31+i30000−2i−2i2i2i0000000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83000000000000
χ3122-22-22-2-22i−2i000022-22-2-22-2222-222-22-22-2-22-2-2-22i2i−2i−2i0000000000000000000000002i−2i002i−2i00000000000000
χ3222-22-22-2-22i−2i000022-22-2-22-2−1−i3−1+i3−1−i31+i3−1−i3−1+i31−i3−1+i31+i3−1−i31+i31−i3−1+i31−i31+i31−i32i2i−2i−2i0000000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ7900000000000000
χ3322-22-22-2-22i−2i000022-22-2-22-2−1+i3−1−i3−1+i31−i3−1+i3−1−i31+i3−1−i31−i3−1+i31−i31+i3−1−i31+i31−i31+i32i2i−2i−2i0000000000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ8300000000000000
χ3422-22-22-2-2−2i2i000022-22-2-22-2222-222-22-22-2-22-2-2-2−2i−2i2i2i000000000000000000000000−2i2i00−2i2i00000000000000
χ3522-22-22-2-2−2i2i000022-22-2-22-2−1−i3−1+i3−1−i31+i3−1−i3−1+i31−i3−1+i31+i3−1−i31+i31−i3−1+i31−i31+i31−i3−2i−2i2i2i000000000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900000000000000
χ3622-22-22-2-2−2i2i000022-22-2-22-2−1+i3−1−i3−1+i31−i3−1+i3−1−i31+i3−1−i31−i3−1+i31−i31+i3−1−i31+i31−i31+i3−2i−2i2i2i000000000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300000000000000
χ3722-2-2-2-22200002-222-2-22-2-22222-2-22-2-2-2-22-2-22220000000022-2-200000000000000000000000000002-22-20000
χ3822-2-2-2-22200002-222-2-22-2-22−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i31+i31+i3−1−i31−i31−i3−1+i3−1−i3−1+i30000000022-2-20000000000000000000000000000−1−i31+i3−1+i31−i30000
χ3922-2-2-2-22200002-222-2-22-2-22−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i31−i31−i3−1+i31+i31+i3−1−i3−1+i3−1−i30000000022-2-20000000000000000000000000000−1+i31−i3−1−i31+i30000
χ4022-2-2-2-2220000-2222-2-22-2-22222-2-22-2-2-2-22-2-222200000000-2-2220000000000000000000000000000-22-220000
χ4122-2-2-2-2220000-2222-2-22-2-22−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i31+i31+i3−1−i31−i31−i3−1+i3−1−i3−1+i300000000-2-22200000000000000000000000000001+i3−1−i31−i3−1+i30000
χ4222-2-2-2-2220000-2222-2-22-2-22−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i31−i31−i3−1+i31+i31+i3−1−i3−1+i3−1−i300000000-2-22200000000000000000000000000001−i3−1+i31+i3−1−i30000
χ432-222-2-22-20000002-2222-2-2-222-222-222-2-22-2-22-2-20000000000000000002i−2i0000000000000000000000002i−2i2i−2i
χ442-222-2-22-20000002-2222-2-2-222-222-222-2-22-2-22-2-2000000000000000000−2i2i000000000000000000000000−2i2i−2i2i
χ452-222-2-22-20000002-2222-2-2-2−1−i3−1+i31+i3−1−i3−1−i31−i3−1+i3−1+i31+i31+i3−1−i31−i31−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
χ462-222-2-22-20000002-2222-2-2-2−1−i3−1+i31+i3−1−i3−1−i31−i3−1+i3−1+i31+i31+i3−1−i31−i31−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
χ472-222-2-22-20000002-2222-2-2-2−1+i3−1−i31−i3−1+i3−1+i31+i3−1−i3−1−i31−i31−i3−1+i31+i31+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
χ482-222-2-22-20000002-2222-2-2-2−1+i3−1−i31−i3−1+i3−1+i31+i3−1−i3−1−i31−i31−i3−1+i31+i31+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
χ492-22-2-22-220000002-22-2-2-22222-22-2-22-2-22-2-22-2220000000000002-20000002-2002-20000000000000000000000
χ502-22-2-22-220000002-22-2-2-22222-22-2-22-2-22-2-22-222000000000000-22000000-2200-220000000000000000000000
χ512-22-2-22-220000002-22-2-2-222−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i3−1−i3−1+i30000000000002-2000000−1−i31+i300−1+i31−i30000000000000000000000
χ522-22-2-22-220000002-22-2-2-222−1−i3−1+i31+i3−1−i31+i31−i3−1+i31−i31+i3−1−i31+i31−i3−1+i31−i3−1−i3−1+i3000000000000-220000001+i3−1−i3001−i3−1+i30000000000000000000000
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χ71666-66-6-6-6006i−6i00-1-1-111-1110000000000000000−i7i7−i7i7−i−iii7−77−7000000000000000000000000000000000000
χ72666-66-6-6-6006i−6i00-1-1-111-1110000000000000000i7−i7i7−i7−i−iii−77−77000000000000000000000000000000000000
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χ7766-66-66-6-6−6i6i0000-1-11-111-110000000000000000ii−i−i−i7i7−i7i7−777−7000000000000000000000000000000000000
χ7866-66-66-6-6−6i6i0000-1-11-111-110000000000000000ii−i−ii7−i7i7−i77−7−77000000000000000000000000000000000000
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χ8166-6-6-6-6660000-66-1-111-111-100000000000000007−7−777−7−7711-1-1000000000000000000000000000000000000
χ8266-6-6-6-6660000-66-1-111-111-10000000000000000−777−7−777−711-1-1000000000000000000000000000000000000
χ8312-121212-12-1212-12000000-22-2-2-22220000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-1212-1212000000-22-2222-2-20000000000000000000000000000000000000000000000000000000000000000
χ8512-12-121212-12-1212000000-222-22-22-20000000000000000000000000000000000000000000000000000000000000000
χ8612-12-12-12121212-12000000-2222-2-2-220000000000000000000000000000000000000000000000000000000000000000

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