Finite Group Databasebeta

← Group #13144345

Character table — Group #13144345

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164
size11111111111122222244444466666666666666661212121212121212121212121212121212121212121212121818181818181818181818183636363636361111111111112222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636
order122233666666441212121244121212123333666666666666121212121212121212121212121212121212121212121212888824242424242424244412121212222266666666441212121244121212126666666666666666121212121212121212121212121212121212121212121212888824242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511-1-11111-1-1-1-1-11-1-111i−iii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-1-11-1-111i−iii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1i−iii−i−i
χ611-1-11111-1-1-1-1-11-1-111i−iii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−ii−i−iii11-1-11111-1-1-1-1-11-1-111i−iii−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-11111−ii−i−iii
χ711-1-11111-1-1-1-1-11-1-111−ii−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-1-11-1-111−ii−i−iii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1−ii−i−iii
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χ10222222222222222222222222-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000222222222222222222222222-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ11222222222222222222222222-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000222222222222222222222222-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ12222222222222222222222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000222222222222222222222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ13222222222222222222-2-2-2-2-2-22-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000222222222222222222-2-2-2-2-2-22-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000000000000000
χ14222222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000000000222222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-21111000000000000000000
χ15222222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-211000000000000000000222222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-211000000000000000000
χ16222222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000222222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2000000000000000000
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χ19222222222222-2-2-2-2-2-20000002-1-1-12-1-1-12-1-1-12-1-1-1-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000222222222222-2-2-2-2-2-20000002-1-1-12-1-1-12-1-1-12-1-1-1-2111-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000
χ20222222222222-2-2-2-2-2-2000000-12-1-1-12-1-1-12-1-1-12-1-11-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000222222222222-2-2-2-2-2-2000000-12-1-1-12-1-1-12-1-1-12-1-11-2111-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000
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χ22222222222222-2-2-2-2-2-2000000-1-12-1-1-12-1-1-12-1-1-12-111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000222222222222-2-2-2-2-2-2000000-1-12-1-1-12-1-1-12-1-1-12-111-2111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000
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χ2622-2-22222-2-2-2-22-222-2-20000002222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000022-2-22222-2-2-2-22-222-2-20000002222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000000000
χ2722-2-22222-2-2-2-22-222-2-20000002-1-1-1-21112-1-1-1-2111-21112-1-1-1003−33−33−300−33−33−3300000000000000000022-2-22222-2-2-2-22-222-2-20000002-1-1-1-21112-1-1-1-2111-21112-1-1-1003−33−33−300−33−33−33000000000000000000
χ2822-2-22222-2-2-2-22-222-2-20000002-1-1-1-21112-1-1-1-2111-21112-1-1-100−33−33−33003−33−33−300000000000000000022-2-22222-2-2-2-22-222-2-20000002-1-1-1-21112-1-1-1-2111-21112-1-1-100−33−33−33003−33−33−3000000000000000000
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χ3022-2-22222-2-2-2-22-222-2-2000000-12-1-11-211-12-1-11-2111-211-12-1-1−3300−333−33−3003−3−3300000000000000000022-2-22222-2-2-2-22-222-2-2000000-12-1-11-211-12-1-11-2111-211-12-1-1−3300−333−33−3003−3−33000000000000000000
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χ3422-2-22222-2-2-2-22-222-2-2000000-1-1-12111-2-1-1-12111-2111-2-1-1-12−33−333−3003−33−3−330000000000000000000022-2-22222-2-2-2-22-222-2-2000000-1-1-12111-2-1-1-12111-2111-2-1-1-12−33−333−3003−33−3−3300000000000000000000
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χ3622-2-22222-2-2-2-2-22-2-2222i−2i2i2i−2i−2i-12-1-11-211-12-1-11-211-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii00000000000000000022-2-22222-2-2-2-2-22-2-2222i−2i2i2i−2i−2i-12-1-11-211-12-1-11-211-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.