Finite Group Databasebeta

← Group #13173207

Character table — Group #13173207

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111122222244444444444444444444444444444444999918181818181836363636363636361111222222444444444444444444444444444444449999181818181818363636363636363611112222224444444444444444444444444444444499991818181818183636363636363636
order1222444444336666661212121212121212121212121212121212121212121212122222444444444444443666121212121212336666661212121212121212121212121212121212121212121212126666121212121212121212121212121236661212121212123366666612121212121212121212121212121212121212121212121266661212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ6111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ7111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-11-11-11-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-11-11-11-11111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-11-11-11-1
χ101111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-111111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-111111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-11
χ111111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−ii−i−ii−ii1111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−ii−i−ii−ii1111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−ii−i−ii−ii
χ121111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−ii−iii−ii−i1111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−ii−iii−ii−i1111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−ii−iii−ii−i
χ131111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-11
χ141111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-1
χ151111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ161111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
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χ1822-2-200002i−2i2222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i-22-220000−2i2i0000000022-2-200002i−2i2222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i-22-220000−2i2i0000000022-2-200002i−2i2222-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i-22-220000−2i2i00000000
χ1922-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2-22-20000−2i2i0000000022-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2-22-20000−2i2i0000000022-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i2-22-20000−2i2i00000000
χ2022-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i-22-2200002i−2i0000000022-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i-22-2200002i−2i0000000022-2-20000−2i2i2222-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i-22-2200002i−2i00000000
χ212-22-2002-20022-2-222-2-2000000002222-2-2-2-20000000022-2-2002-200000000002-22-2002-20022-2-222-2-2000000002222-2-2-2-20000000022-2-2002-200000000002-22-2002-20022-2-222-2-2000000002222-2-2-2-20000000022-2-2002-20000000000
χ222-22-2002-20022-2-222-2-2000000002222-2-2-2-200000000-2-22200-2200000000002-22-2002-20022-2-222-2-2000000002222-2-2-2-200000000-2-22200-2200000000002-22-2002-20022-2-222-2-2000000002222-2-2-2-200000000-2-22200-220000000000
χ232-22-200-220022-2-222-2-200000000-2-2-2-222220000000022-2-200-2200000000002-22-200-220022-2-222-2-200000000-2-2-2-222220000000022-2-200-2200000000002-22-200-220022-2-222-2-200000000-2-2-2-222220000000022-2-200-220000000000
χ242-22-200-220022-2-222-2-200000000-2-2-2-2222200000000-2-222002-200000000002-22-200-220022-2-222-2-200000000-2-2-2-2222200000000-2-222002-200000000002-22-200-220022-2-222-2-200000000-2-2-2-2222200000000-2-222002-20000000000
χ252-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000002-2-222i−2i0000000000002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000002-2-222i−2i0000000000002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000000002-2-222i−2i000000000000
χ262-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000-222-2−2i2i0000000000002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000-222-2−2i2i0000000000002-2-222i−2i000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000-222-2−2i2i000000000000
χ272-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000002-2-22−2i2i0000000000002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000002-2-22−2i2i0000000000002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000002-2-22−2i2i000000000000
χ282-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000-222-22i−2i0000000000002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000-222-22i−2i0000000000002-2-22−2i2i000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000-222-22i−2i000000000000
χ2944444444441-21-21-21-211-2-211-2-211-2-211-2-211-2-211-2-200000000000000000044444444441-21-21-21-211-2-211-2-211-2-211-2-211-2-211-2-200000000000000000044444444441-21-21-21-211-2-211-2-211-2-211-2-211-2-211-2-2000000000000000000
χ304444444444-21-21-21-21-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000004444444444-21-21-21-21-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000004444444444-21-21-21-21-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000
χ31444444-4-4-4-41-21-21-21-211-2-211-2-2-1-122-1-122-1-122-1-122000000000000000000444444-4-4-4-41-21-21-21-211-2-211-2-2-1-122-1-122-1-122-1-122000000000000000000444444-4-4-4-41-21-21-21-211-2-211-2-2-1-122-1-122-1-122-1-122000000000000000000
χ32444444-4-4-4-4-21-21-21-21-2-211-2-21122-1-122-1-122-1-122-1-1000000000000000000444444-4-4-4-4-21-21-21-21-2-211-2-21122-1-122-1-122-1-122-1-1000000000000000000444444-4-4-4-4-21-21-21-21-2-211-2-21122-1-122-1-122-1-122-1-1000000000000000000
χ334444-4-444-4-41-21-21-21-2-1-122-1-12211-2-211-2-2-1-122-1-1220000000000000000004444-4-444-4-41-21-21-21-2-1-122-1-12211-2-211-2-2-1-122-1-1220000000000000000004444-4-444-4-41-21-21-21-2-1-122-1-12211-2-211-2-2-1-122-1-122000000000000000000
χ344444-4-444-4-4-21-21-21-2122-1-122-1-1-2-211-2-21122-1-122-1-10000000000000000004444-4-444-4-4-21-21-21-2122-1-122-1-1-2-211-2-21122-1-122-1-10000000000000000004444-4-444-4-4-21-21-21-2122-1-122-1-1-2-211-2-21122-1-122-1-1000000000000000000
χ354444-4-4-4-4441-21-21-21-2-1-122-1-122-1-122-1-12211-2-211-2-20000000000000000004444-4-4-4-4441-21-21-21-2-1-122-1-122-1-122-1-12211-2-211-2-20000000000000000004444-4-4-4-4441-21-21-21-2-1-122-1-122-1-122-1-12211-2-211-2-2000000000000000000
χ364444-4-4-4-444-21-21-21-2122-1-122-1-122-1-122-1-1-2-211-2-2110000000000000000004444-4-4-4-444-21-21-21-2122-1-122-1-122-1-122-1-1-2-211-2-2110000000000000000004444-4-4-4-444-21-21-21-2122-1-122-1-122-1-122-1-1-2-211-2-211000000000000000000
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χ1301111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-11−1−i32−1−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−i321+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+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i32−1+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+i321−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−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ1311111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−ii−i−ii−ii−1−i32−1−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−i321+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+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11−1+i32−1+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+i321−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−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7
χ1321111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111−ii−iii−ii−i−1−i32−1−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−i321+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+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11−1+i32−1+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+i321−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−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.