Finite Group Databasebeta

← Group #13138786

Character table — Group #13138786

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order122234466688881212121224242424242424243366666644443666121212121212121224242424242424242424242424242424448888121212121212121224242424242424242244444466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111
χ911-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-11-1-11ii−i−i1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i1-1i−ii−i1-1
χ1011-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-11-1-11ii−i−i1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii-11−ii−ii-11
χ1111-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-11-1-11−i−iii1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii1-1−ii−ii1-1
χ1211-1-111-11-1-111-1-111-1-11111-1-1-1-111-1-11-1-11−i−iii1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1−ii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i-11i−ii−i-11
χ1311-1-111-11-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-11ii−i−i1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii1-1i−i−ii-11
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χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1222-1-1-120000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-211110000000000000000000000000022-2-200-1-11100
χ242222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1222-1-1-120000-1-1-1-1-12-1-1-12-1-111-2-2111111-2-2111100000000000000000000000000-2-2220011-1-100
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χ2922-2-222-22-2-222-2-222-2-22222-2-2-2-2-12-2-2-11120000-111-11-211-12-1-1-1-122-1-1-1-111-2-21111000000000000000000000000002i−2i2i−2i00−ii−ii00
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.