Finite Group Databasebeta

← Group #11721480

Character table — Group #11721480

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size11112222223333333344444444666666666666666612121212121212121212121212121212121212121212181818181818181818181818363636363636
order122234466633666666441212121212129991212121218181818181818181812121212363636363636363636363636363636363636224466661212121224661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−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+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+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−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+i32-1-1-1-111-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+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+i32-1-1-1-111-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i321+i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+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−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+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−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−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+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−i32-1-1-1-111-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−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−i32-1-1-1-111-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i321−i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ1311111-1-1111111111111-111-1-1-1-1111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111
χ1411111-1-1111111111111-111-1-1-1-1111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1
χ1511111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-111-1-1
χ1611111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-11-1-111
χ1711111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-111-1-1-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ1811111-1-1111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-111-1-1-1-11−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i32−1+i321+i321−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+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1−1−i32−1+i321+i321−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+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ2111111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-111-1-1-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32
χ2211111-1-1111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-111-1-1-1-11−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i32−1−i321−i321+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−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321-1−1+i32−1−i321−i321+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−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ2522222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222-2-2-2-222-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2111111-1-1-1-1-1-1111111000000000000000000
χ272222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000000
χ282222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-2-2-222-2-2-11+i321−i32−1−i3−1−i3−1+i3−1+i3-11+i321−i32-11+i321−i32-11+i321−i321+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3211−1−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+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-11−i321+i32−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000000
χ302222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-2-2-222-2-2-11−i321+i32−1+i3−1+i3−1−i3−1−i3-11−i321+i32-11−i321+i32-11−i321+i321−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000000
χ3122222-2-2222222222222-222-2-2-2-2-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-122-2-2-1-1-1-1-1-1111111111111000000000000000000
χ3222222-2-222222222222-22-2-2-2-222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-2-222111111111111-1-1-1-1-1-1000000000000000000
χ3322222-2-2222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32-222-2-2-2-2-11+i321−i321+i31+i31−i31−i3-11+i321−i32-11+i321−i32-11+i321−i32−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−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−i321+i31+i31−i31−i3-11+i321−i32-11+i321−i32-11+i321−i321+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000000
χ3522222-2-2222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32-222-2-2-2-2-11−i321+i321−i31−i31+i31+i3-11−i321+i32-11−i321+i32-11−i321+i32−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+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+i321−i31−i31+i31+i3-11−i321+i32-11−i321+i32-11−i321+i321−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000000
χ3722-2-222i−2i-22-22222-2-2-2-200002i−2i002222i−2i2i−2i-2-2-2222-2-2-200000000002i−2i2i−2i2i−2i000000000000000000000000
χ3822-2-222i−2i-22-22222-2-2-2-200002i−2i00-1-1-12i−2i2i−2i111-1-1-11110000−i3i3−i3i3−i3i3−ii−ii−ii3−33−33−3000000000000000000
χ3922-2-222i−2i-22-22222-2-2-2-200002i−2i00-1-1-12i−2i2i−2i111-1-1-11110000i3−i3i3−i3i3−i3−ii−ii−ii−33−33−33000000000000000000
χ4022-2-222i−2i-22-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300002i−2i002−1−i3−1+i32ζ11−2ζ112ζ7−2ζ7-21+i31−i32−1−i3−1+i3-21+i31−i300000000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ4122-2-222i−2i-22-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300002i−2i00-11+i321−i322ζ11−2ζ112ζ7−2ζ71−1−i32−1+i32-11+i321−i321−1−i32−1+i320000−i3i3−3+i323−i323+i32−3−i32−ii−ζ11ζ11−ζ7ζ73−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000
χ4222-2-222i−2i-22-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300002i−2i00-11+i321−i322ζ11−2ζ112ζ7−2ζ71−1−i32−1+i32-11+i321−i321−1−i32−1+i320000i3−i33−i32−3+i32−3−i323+i32−ii−ζ11ζ11−ζ7ζ7−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000
χ4322-2-222i−2i-22-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300002i−2i002−1+i3−1−i32ζ7−2ζ72ζ11−2ζ11-21−i31+i32−1+i3−1−i3-21−i31+i300000000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ4422-2-222i−2i-22-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300002i−2i00-11−i321+i322ζ7−2ζ72ζ11−2ζ111−1+i32−1−i32-11−i321+i321−1+i32−1−i320000−i3i33+i32−3−i32−3+i323−i32−ii−ζ7ζ7−ζ11ζ113−3−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000000000000000
χ4522-2-222i−2i-22-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300002i−2i00-11−i321+i322ζ7−2ζ72ζ11−2ζ111−1+i32−1−i32-11−i321+i321−1+i32−1−i320000i3−i3−3−i323+i323−i32−3+i32−ii−ζ7ζ7−ζ11ζ11−33ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000000000000000
χ4622-2-22−2i2i-22-22222-2-2-2-20000−2i2i00222−2i2i−2i2i-2-2-2222-2-2-20000000000−2i2i−2i2i−2i2i000000000000000000000000
χ4722-2-22−2i2i-22-22222-2-2-2-20000−2i2i00-1-1-1−2i2i−2i2i111-1-1-11110000−i3i3−i3i3−i3i3i−ii−ii−i−33−33−33000000000000000000
χ4822-2-22−2i2i-22-22222-2-2-2-20000−2i2i00-1-1-1−2i2i−2i2i111-1-1-11110000i3−i3i3−i3i3−i3i−ii−ii−i3−33−33−3000000000000000000
χ4922-2-22−2i2i-22-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000−2i2i002−1−i3−1+i3−2ζ112ζ11−2ζ72ζ7-21+i31−i32−1−i3−1+i3-21+i31−i30000000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ5022-2-22−2i2i-22-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30000−2i2i00-11+i321−i32−2ζ112ζ11−2ζ72ζ71−1−i32−1+i32-11+i321−i321−1−i32−1+i320000−i3i3−3+i323−i323+i32−3−i32i−iζ11−ζ11ζ7−ζ7−33−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000000000000000
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χ562-22-22002-2-222-2-222-2-2000000002220000222-2-2-2-2-2-2000000000000000000000000−2i2i0000−2i2i−2i2i000000
χ572-22-22002-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000002−1−i3−1+i300002−1−i3−1+i3-21+i31−i3-21+i31−i30000000000000000000000002i−2i00002ζ11−2ζ112ζ7−2ζ7000000
χ582-22-22002-2-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000002−1−i3−1+i300002−1−i3−1+i3-21+i31−i3-21+i31−i3000000000000000000000000−2i2i0000−2ζ112ζ11−2ζ72ζ7000000
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χ602-22-22002-2-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000002−1+i3−1−i300002−1+i3−1−i3-21−i31+i3-21−i31+i3000000000000000000000000−2i2i0000−2ζ72ζ7−2ζ112ζ11000000
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χ622-2-22200-2-2222-2-2-2-222000000002220000-2-2-2-2-2-22220000000000000000000000-2200-22-220000000000
χ632-2-22200-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i3000000002−1−i3−1+i30000-21+i31−i3-21+i31−i32−1−i3−1+i300000000000000000000002-200−1−i31+i3−1+i31−i30000000000
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χ724-4-44400-4-44−2+2i3−2−2i32−2i32+2i32−2i32+2i3−2+2i3−2−2i300000000-21−i31+i300002−1+i3−1−i32−1+i3−1−i3-21−i31+i30000000000000000000000000000000000000000
χ736666-366-3-3-30000000066-3-3-3-3-3-300000000000000000000000000000000000000000000000000000000
χ746666-366-3-3-300000000-6-633-3-33300000000000000000000000000000000000000000000000000000000
χ756666-3-6-6-3-3-3000000006-6-3-3333300000000000000000000000000000000000000000000000000000000
χ766666-3-6-6-3-3-300000000-663333-3-300000000000000000000000000000000000000000000000000000000
χ7766-6-6-36i−6i3-330000000000−3i33i3−3i3i33−3300000000000000000000000000000000000000000000000000000000
χ7866-6-6-36i−6i3-3300000000003i3−3i3−3i3i−333300000000000000000000000000000000000000000000000000000000
χ7966-6-6-3−6i6i3-330000000000−3i33i33i−3i−333300000000000000000000000000000000000000000000000000000000
χ8066-6-6-3−6i6i3-3300000000003i3−3i33i−3i33−3300000000000000000000000000000000000000000000000000000000
χ8112-1212-12-600-666000000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-6000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.