Finite Group Databasebeta

← Group #11721679

Character table — Group #11721679

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size11112222223333333344444444666666666666666612121212121212121212121212121212121212121212181818181818181818181818363636363636
order12223446663366666644121212121212999121212121818181818181818181212121236363636363636363636363636363636363622446666121212124412121212
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+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321−1−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−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321−1+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
χ1311111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11-11-11-1
χ1411111-1-1111111111111-1-1-111-1-1111-1-1-1-11111111111-11-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-11-11-11
χ1511111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-11-11-11
χ1611111-1-111111111111-11-1-1-1-111111-1-1-1-1111111111-11-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111111-11-11-1
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+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+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+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+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+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+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+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321−1−i32−1+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−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−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−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−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−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−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−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−1+i32−1−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
χ2522222222222222222222222222-1-1-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ26222222222222222222-2-222-2-2-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ272222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i322222222-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i32−1−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−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-11+i321−i321+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+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i32−1+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+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-11−i321+i321−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
χ3122222-2-2222222222222-2-2-222-2-2-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-12-22-2111111-1-111-1-111-1-111000000000000000000
χ3222222-2-222222222222-22-2-2-2-222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-22-2211111111-1-111-1-111-1-1000000000000000000
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−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i32-11+i321−i32−1−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−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i32-11+i321−i321+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+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i32−1+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+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i32-11−i321+i321−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
χ3722-2-22002-2-22222-2-2-2-20000000022200002-22-22-2-2-2-200000000000000000000002-2002-22-20000000000
χ3822-2-22002-2-22222-2-2-2-20000000022200002-22-22-2-2-2-20000000000000000000000-2200-22-220000000000
χ3922-2-22002-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3000000002−1−i3−1+i300002-2−1−i31+i3−1+i31−i3-21+i31−i300000000000000000000002-200−1−i31+i3−1+i31−i30000000000
χ4022-2-22002-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3000000002−1−i3−1+i300002-2−1−i31+i3−1+i31−i3-21+i31−i30000000000000000000000-22001+i3−1−i31−i3−1+i30000000000
χ4122-2-22002-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3000000002−1+i3−1−i300002-2−1+i31−i3−1−i31+i3-21−i31+i300000000000000000000002-200−1+i31−i3−1−i31+i30000000000
χ4222-2-22002-2-2−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3000000002−1+i3−1−i300002-2−1+i31−i3−1−i31+i3-21−i31+i30000000000000000000000-22001−i3−1+i31+i3−1−i30000000000
χ432-22-222-2-2-2222-2-22-22-2002-200002222-22-2-2-2-2-2-2-222200002-22-22-2000000000000000000000000000000
χ442-22-222-2-2-2222-2-22-22-2002-20000-1-1-12-22-2111111-1-1-10000-11-11-11−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000000
χ452-22-222-2-2-2222-2-22-22-2002-20000-1-1-12-22-2111111-1-1-10000-11-11-11i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000000
χ462-22-222-2-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3002-200002−1−i3−1+i3−1−i31+i3−1+i31−i3-2-21+i31+i31−i31−i32−1−i3−1+i300002-2−1−i31+i3−1+i31−i3000000000000000000000000000000
χ472-22-222-2-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3002-20000-11+i321−i32−1−i31+i3−1+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i320000-111+i32−1−i321−i32−1+i32−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i32000000000000000000
χ482-22-222-2-2-22−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3002-20000-11+i321−i32−1−i31+i3−1+i31−i311−1−i32−1−i32−1+i32−1+i32-11+i321−i320000-111+i32−1−i321−i32−1+i32i3−i3i3−i33−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i32000000000000000000
χ492-22-222-2-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3002-200002−1+i3−1−i3−1+i31−i3−1−i31+i3-2-21−i31−i31+i31+i32−1+i3−1−i300002-2−1+i31−i3−1−i31+i3000000000000000000000000000000
χ502-22-222-2-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3002-20000-11−i321+i32−1+i31−i3−1−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i320000-111−i32−1+i321+i32−1−i32−i3i3−i3i33+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i32000000000000000000
χ512-22-222-2-2-22−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3002-20000-11−i321+i32−1+i31−i3−1−i31+i311−1+i32−1+i32−1−i32−1−i32-11−i321+i320000-111−i32−1+i321+i32−1−i32i3−i3i3−i3−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i32000000000000000000
χ522-22-22-22-2-2222-2-22-22-200-220000222-22-22-2-2-2-2-2-22220000-22-22-22000000000000000000000000000000
χ532-22-22-22-2-2222-2-22-22-200-220000-1-1-1-22-22111111-1-1-100001-11-11-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.