Finite Group Databasebeta

← Group #13139037

Character table — Group #13139037

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order12223446668888121212122424242424242424336666664444366612121212121212122424242424242424242424242424242422666688881212121224242424242424242244444466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-111-1-1
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-111-1-111
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χ101-1-1111-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11-1-1111-1-11-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-111-1-1ii−i−i11-1-1iiii−i−i−i−i-11−ii−ii-11-11−ii−ii-11
χ111-1-1111-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11-1-11-1-1111-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiii1-1i−i−ii-111-1i−i−ii-11
χ121-1-1111-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11-1-11-1-1111-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-1-111−i−iii-1-111−i−i−i−iiiii-11−iii−i1-1-11−iii−i1-1
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χ141-1-1111-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11-1-1111-1-11-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-111-1-1−i−iii11-1-1−i−i−i−iiiii-11i−ii−i-11-11i−ii−i-11
χ151-1-1111-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11-1-11-1-1111-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−i1-1−iii−i-111-1−iii−i-11
χ161-1-1111-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11-1-11-1-1111-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-1-111ii−i−i-1-111iiii−i−i−i−i-11i−i−ii1-1-11i−i−ii1-1
χ17222222222222222222222222222-12-1-12-120000-1-1-1-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000022220000-1-1-1-10000
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χ222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-12-120000-1-1-1-1-12-1-1-12-1-1-2-2111111-2-21111110000000000000000000000-2-222000011-1-10000
χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-122-12-10000-1-1-1-12-1-1-12-1-1-111-2-2111111-2-211110000000000000000000000000022-2-20000-1-111
χ242222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-122-12-10000-1-1-1-12-1-1-12-1-1-111-2-2111111-2-2111100000000000000000000000000-2-222000011-1-1
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.