Finite Group Databasebeta

← Group #10702270

Character table — Group #10702270

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222222222222366666666666666644444444666666661212121212121212121212121212121244444444121212121212121212121212121212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ121-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ131-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ141-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ151-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161-1-1111-1-111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-2-2-22-2-2-2-22-22-2-22222-2-2-2-222-2-220000000022-2-222-2-2000000000000000000000000000000000000000000002-22-200000000
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χ2422222222-2-222-2-22-2-2-2-222-2-22222-2-2-2-222-2-2200000000-2-222-2-2220000000000000000000000000000000000000000-22-22000000000000
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χ32222-2-22-2-22-22-22222-2-2-2-222222-2-222-2-2-2-2-2-22-2-222-2-2222-22-22-22-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000
χ33222-2-22-2-22-22-22222-2-2-2-2-1-1-1-1-111-1-1111111-122-2-222-2-2-11-11-11-11-1-111-1-111-1-111-1-111000000003−33−33−33−33−33−33−33−30000000000000000
χ34222-2-22-2-22-22-22222-2-2-2-2-1-1-1-1-111-1-1111111-122-2-222-2-2-11-11-11-11-1-111-1-111-1-111-1-11100000000−33−33−33−33−33−33−33−330000000000000000
χ35222-2-22-2-22-22-22222-2-2-2-2-1-1-1-1-111-1-1111111-1-2-222-2-222-11-11-11-1111-1-111-1-111-1-111-1-1000000003−33−33−33−3−33−33−33−330000000000000000
χ36222-2-22-2-22-22-22222-2-2-2-2-1-1-1-1-111-1-1111111-1-2-222-2-222-11-11-11-1111-1-111-1-111-1-111-1-100000000−33−33−33−333−33−33−33−30000000000000000
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χ38222-2-22-2-22-2-22-22-2-222-222-2-222-2-2-2-222-2-2222000000002-2-222-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ39222-2-22-2-2-222-2-2-22-2222-22-2-222-2-2-2-222-2-222200000000-222-2-222-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ40222-2-22-2-2-222-2-2-22-2222-22-2-222-2-2-2-222-2-222200000000-222-2-222-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ41222-2-22-2-2-22-222-2-22-2-22222222-2-222-2-2-2-2-2-2200000000-22-22-22-22000000000000000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ42222-2-22-2-2-22-222-2-22-2-22222222-2-222-2-2-2-2-2-2200000000-22-22-22-2200000000000000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ43222-2-22-2-2-22-222-2-22-2-222-1-1-1-1-111-1-1111111-1000000001-11-11-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300002i−2i2i−2i3−3−333−3−33−iii−i−iii−i0000000000000000
χ44222-2-22-2-2-22-222-2-22-2-222-1-1-1-1-111-1-1111111-1000000001-11-11-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000−2i2i−2i2i−333−3−333−3i−i−iii−i−ii0000000000000000
χ45222-2-22-2-2-22-222-2-22-2-222-1-1-1-1-111-1-1111111-1000000001-11-11-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300002i−2i2i−2i−333−3−333−3−iii−i−iii−i0000000000000000
χ46222-2-22-2-2-22-222-2-22-2-222-1-1-1-1-111-1-1111111-1000000001-11-11-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000−2i2i−2i2i3−3−333−3−33i−i−iii−i−ii0000000000000000
χ472-2-2222-2-222222-2-2-2-22-2-2-1-1-111111111-1-1-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ482-2-2222-2-222222-2-2-2-22-2-2-1-1-111111111-1-1-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ492-2-2222-2-222222-2-2-2-22-2-2-1-1-111111111-1-1-1-1-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ502-2-2222-2-222222-2-2-2-22-2-2-1-1-111111111-1-1-1-1-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ522-2-2222-2-222-2-2-2-2222-2-222-2-2-2-2-2-2222222-2-220000000022-2-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i00000000
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χ542-2-2222-2-2-2-222-22-222-22-22-2-2-2-2-2-2222222-2-2200000000-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ552-2-2222-2-2-2-2-2-2222-2-2222222-2-2-2-2-2-2-2-22222200000000-2-2-2-2222200000000000000002-2-22000022-2-2-2-222000000000000000000000000
χ562-2-2222-2-2-2-2-2-2222-2-2222222-2-2-2-2-2-2-2-22222200000000-2-2-2-222220000000000000000-222-20000-2-22222-2-2000000000000000000000000
χ572-2-2222-2-2-2-2-2-2222-2-2222-1-1-111111111-1-1-1-1-1000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
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χ602-2-2222-2-2-2-2-2-2222-2-2222-1-1-111111111-1-1-1-1-1000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-2000011-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ612-2-2-2-22222-22-22-2-2-22-222222-2-222-2-222-2-2-2-2222-2-2-2-2222-22-2-22-2222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ622-2-2-2-22222-22-22-2-2-22-222222-2-222-2-222-2-2-2-22-2-22222-2-22-22-2-22-22-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ632-2-2-2-22222-22-22-2-2-22-222-1-1-111-1-111-1-11111-122-2-2-2-222-11-111-11-1-1-111-1-11111-1-111-1-1000000003−33−3−33−333−33−3−33−330000000000000000
χ642-2-2-2-22222-22-22-2-2-22-222-1-1-111-1-111-1-11111-122-2-2-2-222-11-111-11-1-1-111-1-11111-1-111-1-100000000−33−333−33−3−33−333−33−30000000000000000
χ652-2-2-2-22222-22-22-2-2-22-222-1-1-111-1-111-1-11111-1-2-22222-2-2-11-111-11-111-1-111-1-1-1-111-1-111000000003−33−3−33−33−33−333−33−30000000000000000
χ662-2-2-2-22222-22-22-2-2-22-222-1-1-111-1-111-1-11111-1-2-22222-2-2-11-111-11-111-1-111-1-1-1-111-1-11100000000−33−333−33−33−33−3−33−330000000000000000
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χ742-2-2-2-2222-22-22222-22-2-2-2-1-1-111-1-111-1-11111-1000000001-11-1-11-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−2i2i2i−2i−333−33−3−33i−i−ii−iii−i0000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.