Finite Group Databasebeta

← Group #13156675

Character table — Group #13156675

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212124488121212121212121212121212121212122424242424242424242424242424242441212121212121212882424242444121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
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χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2200-2-22222-2-2-2-2-2-2222200000000000000000000000000000000000000
χ11222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-100000000000000002-1-122-1-1-1-100000020-1-1000
χ12222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-211-2-21111000000-2011000
χ13222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-211111111111100000000000000002-1-122-1-1-1-1000000-2011000
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χ3922-2-22-12-22-22-1211-2-2-211-1-1-12-111-2-12-111-22-22-1-111-1-1-211-111-1-2211-1-100003−3−33000033−3−3−3−3333−3−33000033−3−3−3−333000000000-221-11-10000000
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χ4122-2-22-12-22-22-1211-2-2-211-1-1-12-111-2-12-111-22-22-1-111-1-1-211-111-1-2211-1-10000−333−30000−3−33333−3−33−3−33000033−3−3−3−3330000000002-2-11-110000000
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χ954-4-444-2-200-4-4222-2-22423−23−2323-2-212-2222-1-11-2000−2323−333−3023−231-11-100−333−3000000000023−23−333−3-333-300000000000000000000000000000000000000
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χ1068888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-2-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000000000
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χ10888-8-8-4-4-4-884-4-4-44444444-4-4222-2-2-2222-2-2-2-44-422-2-2224-2-2-111-1-2211-1-10000000000000000000000000000000000000000000000000000000000
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χ1148-8-88-4-4-40044444-4-44-4−434343−43222-22-2-2-2-2-222000−232323−23−2323023−23-11-1100−333−30000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.