Finite Group Databasebeta

← Group #98821

Character table — Group #98821

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444448888888888888888444444444444444444448888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ171-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ζ−ζζ3−ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ181-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−ζζ−ζ3ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ191-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111ii−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ζ−ζζ3−ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ201-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111ii−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−ζζ−ζ3ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ211-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ζ−ζζ3−ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3−ζ3ζ3−ζζ
χ221-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ
χ231-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ζ−ζζ3−ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ
χ241-1-1111-1-111-1-1111-1-1-1-1iiii−i−i−i−i1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−ζζ−ζ3ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3−ζ3ζ3−ζζ
χ251-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3
χ261-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−ζ3ζ3−ζζζ−ζζ3−ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3
χ271-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3
χ281-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−ζ3ζ3−ζζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3
χ291-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ζ3−ζ3ζ−ζζ−ζζ3−ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ301-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−ζ3ζ3−ζζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ311-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−iiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ζ3−ζ3ζ−ζζ−ζζ3−ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ321-1-1111-1-111-1-1111-1-1-1-1−i−i−i−iiiii1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−iiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−ζ3ζ3−ζζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ33222222222222-2-2-2-2-2-2-222222222-2000000000000000022-2-222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000
χ34222222222222-2-2-2-2-2-2-222222222-20000000000000000-2-222-2-222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-222-2-22222-2-222-2-2220000000000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-222-2-222222222-2-222-2-20000000000000000000000000000000000000000
χ3722222222-2-2-2-222-222-2-222-2-222-2-2-20000000000000000000000002-22-2000000002i2i−2i−2i2i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3822222222-2-2-2-222-222-2-222-2-222-2-2-20000000000000000000000002-22-200000000−2i−2i2i2i−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3922222222-2-2-2-222-222-2-2-2-222-2-222-2000000000000000000000000-22-22000000002i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
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χ4122222222-2-2-2-2-2-22-2-22222-2-222-2-222222-2-2-2-22222-2-2-2-200000000-22-22000000000000000022-2-222-2-2000000000000000000000000
χ4222222222-2-2-2-2-2-22-2-22222-2-222-2-22-2-2-2-22222-2-2-2-2222200000000-22-220000000000000000-2-222-2-222000000000000000000000000
χ4322222222-2-2-2-2-2-22-2-222-2-222-2-22222222-2-2-2-22222-2-2-2-2000000002-22-20000000000000000-2-222-2-222000000000000000000000000
χ4422222222-2-2-2-2-2-22-2-222-2-222-2-2222-2-2-2-22222-2-2-2-22222000000002-22-2000000000000000022-2-222-2-2000000000000000000000000
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χ4822-22-2-22-22-22-200000002-22-22-22-20−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i000000−2i2i00−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ4922-22-2-22-22-22-20000000-22-22-22-220i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i000000−2i2i00−2i2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
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χ6022-22-2-22-2-22-220000000-222-2-222-20−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200-220000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ612-222-2-2-222-2-2200000002i−2i2i−2i−2i2i−2i2i022−2−222−2−2−2−222−2−222002i−2i00−2i2i000000-22002-2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ622-222-2-2-222-2-2200000002i−2i2i−2i−2i2i−2i2i022−2−222−2−2−2−222−2−22200−2i2i002i−2i0000002-200-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ632-222-2-2-222-2-2200000002i−2i2i−2i−2i2i−2i2i0−2−222−2−22222−2−222−2−2002i−2i00−2i2i000000-22002-2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ642-222-2-2-222-2-2200000002i−2i2i−2i−2i2i−2i2i0−2−222−2−22222−2−222−2−200−2i2i002i−2i0000002-200-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ652-222-2-2-222-2-220000000−2i2i−2i2i2i−2i2i−2i022−2−222−2−2−2−222−2−222002i−2i00−2i2i0000002-200-22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ662-222-2-2-222-2-220000000−2i2i−2i2i2i−2i2i−2i022−2−222−2−2−2−222−2−22200−2i2i002i−2i000000-22002-2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ672-222-2-2-222-2-220000000−2i2i−2i2i2i−2i2i−2i0−2−222−2−22222−2−222−2−2002i−2i00−2i2i0000002-200-22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
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χ1044-4-4-44-444000000-4004-4000000004-44-4400004-44-40000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.