Finite Group Databasebeta

← Group #13159024

Character table — Group #13159024

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204
size11222222222222244444444444444444444121212121212121212181818181818108112222222222222444444444444444444441212121212121212121818181818181081122222222222224444444444444444444412121212121212121218181818181810811222222222222244444444444444444444121212121212121212181818181818108
order12333334666661212333366661212121212121212121212124121212121212121288242424244441212121212412121212121212121212121212121212121212121212121212121241212121212121212882424242442266666466666121266666666121212121212121212121212412121212121212128824242424444121212121241212121212121212121212121212121212121212121212121212124121212121212121288242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11
χ52222222-222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222222-222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222222-222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222222-222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000
χ6222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10
χ7222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110222222-12-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110
χ8222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000033−3−30222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000033−3−30222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000033−3−30222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000033−3−30
χ9222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000−3−3330222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000−3−3330222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000−3−3330222222-1-2-1222211-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000−3−3330
χ10222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-10000000222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-10000000222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-10000000222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1222-1-1-1-1-1-10000000
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χ12222-1-1-12-222-1-1-1-2-22-1-1-12-1-1-1-2111-2-2111111000−i3−i3−i3i3i3i30000000222-1-1-12-222-1-1-1-2-22-1-1-12-1-1-1-2111-2-2111111000−i3−i3−i3i3i3i30000000222-1-1-12-222-1-1-1-2-22-1-1-12-1-1-1-2111-2-2111111000−i3−i3−i3i3i3i30000000222-1-1-12-222-1-1-1-2-22-1-1-12-1-1-1-2111-2-2111111000−i3−i3−i3i3i3i30000000
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χ1722-12-1-12-22-12-1-1-2-2-12-1-1-12-1-11-21111-2-211110i3−i30i3−i30i3−i3000000022-12-1-12-22-12-1-1-2-2-12-1-1-12-1-11-21111-2-211110i3−i30i3−i30i3−i3000000022-12-1-12-22-12-1-1-2-2-12-1-1-12-1-11-21111-2-211110i3−i30i3−i30i3−i3000000022-12-1-12-22-12-1-1-2-2-12-1-1-12-1-11-21111-2-211110i3−i30i3−i30i3−i30000000
χ1822-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-12-1-1-12-1-1-12000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-12-1-1-12-1-1-12000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-12-1-1-12-1-1-12000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-12-1-1-12-1-1-120000000
χ1922-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-2111-2111-2000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-2111-2111-2000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-2111-2111-2000000022-1-12-1222-1-12-122-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-2111-2111-20000000
χ2022-1-12-12-22-1-12-1-2-2-1-12-1-1-12-111-211111-2-2110−i3i3i30−i3−i3i30000000022-1-12-12-22-1-12-1-2-2-1-12-1-1-12-111-211111-2-2110−i3i3i30−i3−i3i30000000022-1-12-12-22-1-12-1-2-2-1-12-1-1-12-111-211111-2-2110−i3i3i30−i3−i3i30000000022-1-12-12-22-1-12-1-2-2-1-12-1-1-12-111-211111-2-2110−i3i3i30−i3−i3i300000000
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χ2222-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-1222-1-1-1-12-12-1000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-1222-1-1-1-12-12-1000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-1222-1-1-1-12-12-1000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-1222-1-1-1-12-12-10000000
χ2322-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-21111-21-21000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-21111-21-21000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-21111-21-21000000022-1-1-12222-1-1-1222-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-21111-21-210000000
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χ282-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−30000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2302-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−30000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2302-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−30000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2302-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−30000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230
χ292-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−3000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2302-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−3000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2302-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−3000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2302-22222-101-2-2-2-23−3-1-1-1-1111100003−33−33−33−3000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230
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χ3544-24-2-2-2-4-2-24-2-2221-2111-2112-422-1-122-1-1-1-1000000000000000044-24-2-2-2-4-2-24-2-2221-2111-2112-422-1-122-1-1-1-1000000000000000044-24-2-2-2-4-2-24-2-2221-2111-2112-422-1-122-1-1-1-1000000000000000044-24-2-2-2-4-2-24-2-2221-2111-2112-422-1-122-1-1-1-10000000000000000
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χ3744-2-24-2-2-4-2-2-24-22211-2111-2122-42-1-1-1-122-1-1000000000000000044-2-24-2-2-4-2-2-24-22211-2111-2122-42-1-1-1-122-1-1000000000000000044-2-24-2-2-4-2-2-24-22211-2111-2122-42-1-1-1-122-1-1000000000000000044-2-24-2-2-4-2-2-24-22211-2111-2122-42-1-1-1-122-1-10000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.