Finite Group Databasebeta

← Group #11721469

Character table — Group #11721469

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size11112222223333333344444444666666666666666612121212121212121212121212121212121212121212181818181818181818181818363636363636
order1222344666336666664412121212121233366666666612121212121212121212121212121212121212121212121212122244666612121212226666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−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+i3211−1−i32−1−i32−1+i32−1+i32
χ61111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32
χ71111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32
χ81111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32
χ91111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+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−i3211−1+i32−1+i32−1−i32−1−i32
χ101111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32
χ111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32
χ121111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311111-1-1111111111111-1-1-111-1-1111111111111-1-1-1-11-11-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11-11-11-1
χ1411111-1-1111111111111-1-1-111-1-1111111111111-1-1-1-11-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-11-11-11
χ1511111-1-111111111111-11-1-1-1-111111111111111-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-11-11-11
χ1611111-1-111111111111-11-1-1-1-111111111111111-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111111-11-11-1
χ1711111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ1811111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-111-1-11−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i32−1−i321+i32−1+i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ1911111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ2011111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1111−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321+i321−i321−i321+i32−1−i321−i32−1+i32-1-11+i321+i321−i321−i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ2111111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ2211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-111-1-11−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i32−1+i321−i32−1−i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ2311111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ2411111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1111−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321−i321+i321+i321−i32−1+i321+i32−1−i32-1-11−i321−i321+i321+i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ2522222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ272222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322222222-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32000000000000000000
χ282222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-222-2-2-2-2-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000000000
χ292222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322222222-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32000000000000000000
χ302222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-222-2-2-2-2-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i3-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000000000
χ3122222-2-2222222222222-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2111111-1-111-1-111-1-111000000000000000000
χ3222222-2-222222222222-22-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-2211111111-1-111-1-111-1-1000000000000000000
χ3322222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-2-2-222-2-2-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i321+i31+i31−i31−i3−1−i31+i3−1+i31−i311−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32000000000000000000
χ3422222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-22-2-2-2-222-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i321+i31+i31−i31−i31+i3−1−i31−i3−1+i311−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32000000000000000000
χ3522222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-2-2-222-2-2-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i321−i31−i31+i31+i3−1+i31−i3−1−i31+i311−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32000000000000000000
χ3622222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-22-2-2-2-222-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i321−i31−i31+i31+i31−i3−1+i31+i3−1−i311−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32000000000000000000
χ3722-2-22002-2-22222-2-2-2-200000000222222-2-2-2-2-2-200000000000000000000000000002i−2i00002i−2i2i−2i000000
χ3822-2-22002-2-22222-2-2-2-200000000222222-2-2-2-2-2-20000000000000000000000000000−2i2i0000−2i2i−2i2i000000
χ3922-2-22002-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000002−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i300000000000000000000000000002i−2i00002ζ11−2ζ112ζ7−2ζ7000000
χ4022-2-22002-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3000000002−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i30000000000000000000000000000−2i2i0000−2ζ112ζ11−2ζ72ζ7000000
χ4122-2-22002-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000002−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i300000000000000000000000000002i−2i00002ζ7−2ζ72ζ11−2ζ11000000
χ4222-2-22002-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3000000002−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i30000000000000000000000000000−2i2i0000−2ζ72ζ7−2ζ112ζ11000000
χ432-22-2200-2-2222-2-222-2-200000000222-2-2-2-2-2-2222000000000000000000000000002-2002-22-20000000000
χ442-22-2200-2-2222-2-222-2-200000000222-2-2-2-2-2-222200000000000000000000000000-2200-22-220000000000
χ452-22-2200-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000002−1−i3−1+i3-21+i31−i3-21+i31−i32−1−i3−1+i3000000000000000000000000002-200−1−i31+i3−1+i31−i30000000000
χ462-22-2200-2-22−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000002−1−i3−1+i3-21+i31−i3-21+i31−i32−1−i3−1+i300000000000000000000000000-22001+i3−1−i31−i3−1+i30000000000
χ472-22-2200-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000002−1+i3−1−i3-21−i31+i3-21−i31+i32−1+i3−1−i3000000000000000000000000002-200−1+i31−i3−1−i31+i30000000000
χ482-22-2200-2-22−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000002−1+i3−1−i3-21−i31+i3-21−i31+i32−1+i3−1−i300000000000000000000000000-22001−i3−1+i31+i3−1−i30000000000
χ492-2-2222-2-22-222-2-2-2-222002-20000222-2-2-2222-2-2-22-22-200002-22-22-2000000000000000000000000000000
χ502-2-2222-2-22-222-2-2-2-222002-20000-1-1-1111-1-1-11112-22-20000-11-11-113−33−33−33−33−33−3000000000000000000
χ512-2-2222-2-22-222-2-2-2-222002-20000-1-1-1111-1-1-11112-22-20000-11-11-11−33−33−33−33−33−33000000000000000000
χ522-2-2222-2-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3002-200002−1−i3−1+i3-21+i31−i32−1−i3−1+i3-21+i31−i3−1−i31+i3−1+i31−i300002-2−1−i31+i3−1+i31−i3000000000000000000000000000000
χ532-2-2222-2-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3002-20000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32−1−i31+i3−1+i31−i30000-111+i32−1−i321−i32−1+i323−33−32ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000
χ542-2-2222-2-22-2−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3002-20000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32−1−i31+i3−1+i31−i30000-111+i32−1−i321−i32−1+i32−33−33−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.