Finite Group Databasebeta

← Group #13169289

Character table — Group #13169289

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order12223334466666666633366666666612121212121212121212441212121236661212121212121212244446612121212121212121212121212121212444444666121212121212121212121244412121212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-11111111-11-1-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-11-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-11-1111-1-111111-11-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-11-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-11-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-1-1-11-11-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1111-1-11111-1-1-11111-1-1-1-111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-111-1-1-1-1-1-1111111-1-1-1-11111-1-1111-1-11-11-1-111-1-1-1-11-1-11111-1-1111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-11-1-1-1-1-11111-1-1-111-1-111-1-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-111111-1-1-11111-1-1-1-111-1-11-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-111-11-111-1-1111-1-111-1-111-1-111-11-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-1111111-1-1-1-1-1-1-1-1111111-1-111111-1-11-11-1-111-1-11-1-111-1-111-1-1-1-1-111
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-1-1-111-11111-1-1-1-111111-1-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-111111-1-111-1-1-111-1-11111-11-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-1111111-1-1-1-1-1-111111111-1-1-1-1-111-11-111-1-111-1-11-1-11111-1-1-1-11-11
χ17222222-12222-1-122-1222-1-12-1-1-12-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122200-1-122-1-1-1-122-1-1-1-1-1-1-1-10022222-1-102000-1-10000000-1-1-1-1000000000
χ18222222-12222-1-122-1222-1-12-1-1-12-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-22-2001122-1-11122-1-1-1-1-1-1-1-100-2-2-2-2-2110-20001100000001111000000000
χ19222222-12222-1-122-1222-1-12-1-1-12-1-1-1222-1-122-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-12-2200-1-1-2-211-1-1-2-21111111100-2-2-2-22-1-102000-1-100000001111000000000
χ20222222-12222-1-122-1222-1-12-1-1-12-1-1-1222-1-122-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-1-2-2-20011-2-21111-2-211111111002222-2110-2000110000000-1-1-1-1000000000
χ21222222-1-2-222-1-122-1222-1-12-1-1-12-1-1-12-2-211-2-2111122-1-1-1-1-1-1-1-111-2-211112-2-200-1-1-2-2111122-1-1-1-111110022-2-22-1-10-200011000000011-1-1000000000
χ22222222-1-2-222-1-122-1222-1-12-1-1-12-1-1-12-2-211-2-2111122-1-1-1-1-1-1-1-111-2-21111-2-220011-2-211-1-122-1-1-1-1111100-2-222-21102000-1-10000000-1-111000000000
χ23222222-1-2-222-1-122-1222-1-12-1-1-12-1-1-12-2-211-2-21111-2-21111-1-1-1-111-2-2111122-200-1-122-1-111-2-21111-1-1-1-100-2-2222-1-10-2000110000000-1-111000000000
χ24222222-1-2-222-1-122-1222-1-12-1-1-12-1-1-12-2-211-2-21111-2-21111-1-1-1-111-2-21111-222001122-1-1-1-1-2-21111-1-1-1-10022-2-2-21102000-1-1000000011-1-1000000000
χ2522222-12222-122-1-1222-12-1-1-12-1-122-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-120222220000220000000000220000-1-1-1-1-1-122-1-1-1-1-1-10200000-1-1-1-100000
χ2622222-12222-122-1-1222-12-1-1-12-1-122-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1202-2-2220000220000000000-2-20000-1-1-11-11-2-2-1-111110-200000111100000
χ2722222-12222-122-1-1222-12-1-1-12-1-122-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-20-222-2-20000-2-20000000000-2-20000111-11-12211-1-1-1-10-200000111100000
χ2822222-12222-122-1-1222-12-1-1-12-1-122-1-1-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2-2-20000-2-20000000000220000111111-2-21111110200000-1-1-1-100000
χ2922222-12-2-22-122-1-1222-12-1-1-12-1-122-1-111-2-2-2-2-2-2-2-2000000-1-1-1-11111111120-22-2220000-2-20000000000220000-1-1-111-1-2211-1-1110-200000-1-11100000
χ3022222-12-2-22-122-1-1222-12-1-1-12-1-122-1-111-2-2-2-2-2-2-2-2000000-1-1-1-11111111120-2-22220000-2-20000000000-2-20000-1-1-1-1112-21111-1-1020000011-1-100000
χ3122222-12-2-22-122-1-1222-12-1-1-12-1-122-1-111-2-2-2-2-2-2-2-2000000-1-1-1-111111111-2022-2-2-20000220000000000-2-200001111-1-1-22-1-1-1-111020000011-1-100000
χ3222222-12-2-22-122-1-1222-12-1-1-12-1-122-1-111-2-2-2-2-2-2-2-2000000-1-1-1-111111111-202-22-2-20000220000000000220000111-1-112-2-1-111-1-10-200000-1-11100000
χ332222-12222-1222222-1-1-1-12-12-12-1-1-12-12222-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-10202200-1-12200-1-1-1-1-1-1-1-1-1-1000000000202-1-100-1-1-1-12020000000000-1-10
χ342222-12222-1222222-1-1-1-12-12-12-1-1-12-12222-1-1-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1020-2-200-1-12200-1-1-1-1-1-1-1-1-1-1000000000-20-211001111-20-20000000000110
χ352222-12222-1222222-1-1-1-12-12-12-1-1-12-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-10-20220011-2-2001111111111000000000202-1-100-1-1-1-1-20-20000000000110
χ362222-12222-1222222-1-1-1-12-12-12-1-1-12-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-10-20-2-20011-2-2001111111111000000000-20-2110011112020000000000-1-10
χ372222-122-2-2-1222222-1-1-1-12-12-12-1-1-12-1-2-2-2-2111111222222-1-1-1-1-2-21111110-202-20011-2-200-1-1-1-1-1-11111000000000-2021-100-1-111-2020000000000-110
χ382222-122-2-2-1222222-1-1-1-12-12-12-1-1-12-1-2-2-2-2111111222222-1-1-1-1-2-21111110-20-220011-2-200-1-1-1-1-1-1111100000000020-2-110011-1-120-200000000001-10
χ392222-122-2-2-1222222-1-1-1-12-12-12-1-1-12-1-2-2-2-2111111-2-2-2-2-2-2-1-1-1-1-2-21111110202-200-1-12200111111-1-1-1-1000000000-2021-100-1-11120-200000000001-10
χ402222-122-2-2-1222222-1-1-1-12-12-12-1-1-12-1-2-2-2-2111111-2-2-2-2-2-2-1-1-1-1-2-2111111020-2200-1-12200111111-1-1-1-100000000020-2-110011-1-1-2020000000000-110
χ412-22-22222i−2i-2-2-2-22-22-22222-22-2-222-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i00000000000000000000000002-22i−2i000000000000000002i−2i2-2000000000
χ422-22-22222i−2i-2-2-2-22-22-22222-22-2-222-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i0000000000000000000000000-22−2i2i00000000000000000−2i2i-22000000000
χ432-22-2222−2i2i-2-2-2-22-22-22222-22-2-222-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000002-2−2i2i00000000000000000−2i2i2-2000000000
χ442-22-2222−2i2i-2-2-2-22-22-22222-22-2-222-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i0000000000000000000000000-222i−2i000000000000000002i−2i-22000000000
χ452-22-222-12i−2i-2-2112-2-1-222-1-1-2-1112-111-22i−2i−ii2i−2i−i−iii00−i3−i3i3i3-1-111−ii2i−2i−i−iii00000−i3i3003−33−300−i3−i3i3i333−3−3002-22i−2i0−i3i3000003−30000000−ii-11000000000
χ462-22-222-12i−2i-2-2112-2-1-222-1-1-2-1112-111-22i−2i−ii2i−2i−i−iii00−i3−i3i3i3-1-111−ii2i−2i−i−iii00000i3−i3003−3−3300−i3−i3i3i333−3−300-22−2i2i0i3−i300000−330000000i−i1-1000000000
χ472-22-222-12i−2i-2-2112-2-1-222-1-1-2-1112-111-22i−2i−ii2i−2i−i−iii00i3i3−i3−i3-1-111−ii2i−2i−i−iii00000−i3i300−333−300i3i3−i3−i3−3−33300-22−2i2i0−i3i3000003−30000000i−i1-1000000000
χ482-22-222-12i−2i-2-2112-2-1-222-1-1-2-1112-111-22i−2i−ii2i−2i−i−iii00i3i3−i3−i3-1-111−ii2i−2i−i−iii00000i3−i300−33−3300i3i3−i3−i3−3−333002-22i−2i0i3−i300000−330000000−ii-11000000000
χ492-22-222-1−2i2i-2-2112-2-1-222-1-1-2-1112-111-2−2i2ii−i−2i2iii−i−i00−i3−i3i3i3-1-111i−i−2i2iii−i−i00000−i3i300−33−3300−i3−i3i3i3−3−333002-2−2i2i0−i3i300000−330000000i−i-11000000000
χ502-22-222-1−2i2i-2-2112-2-1-222-1-1-2-1112-111-2−2i2ii−i−2i2iii−i−i00−i3−i3i3i3-1-111i−i−2i2iii−i−i00000i3−i300−333−300−i3−i3i3i3−3−33300-222i−2i0i3−i3000003−30000000−ii1-1000000000
χ512-22-222-1−2i2i-2-2112-2-1-222-1-1-2-1112-111-2−2i2ii−i−2i2iii−i−i00i3i3−i3−i3-1-111i−i−2i2iii−i−i00000−i3i3003−3−3300i3i3−i3−i333−3−300-222i−2i0−i3i300000−330000000−ii1-1000000000
χ522-22-222-1−2i2i-2-2112-2-1-222-1-1-2-1112-111-2−2i2ii−i−2i2iii−i−i00i3i3−i3−i3-1-111i−i−2i2iii−i−i00000i3−i3003−33−300i3i3−i3−i333−3−3002-2−2i2i0i3−i3000003−30000000i−i-11000000000
χ532-2-2222200-22-22-2-2-22-2222-2-222-2-2-2-2200000000002i−2i2i−2i2i−2i2-2-220000000000000000000002i−2i2i−2i2i−2i00002i−2i00000000000000000000000002i−2i002-2000
χ542-2-2222200-22-22-2-2-22-2222-2-222-2-2-2-2200000000002i−2i2i−2i2i−2i2-2-220000000000000000000002i−2i2i−2i2i−2i0000−2i2i0000000000000000000000000−2i2i00-22000
χ552-2-2222200-22-22-2-2-22-2222-2-222-2-2-2-220000000000−2i2i−2i2i−2i2i2-2-22000000000000000000000−2i2i−2i2i−2i2i00002i−2i00000000000000000000000002i−2i00-22000
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χ5944444-2-2-4-44-2-2-2-2-2-244-2-21-21-21-2-2-21-22222-4-422220000001111-1-122-1-1-1-140-400-2-20000220000000000000000-21102000-1-100000000000000000000
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χ654444-2-2444-2-244-2-24-2-21-2-21-2-2-21-2-2-21-2-244-2-2-2-2-2-20000001111-2-211111100044000000000000000000000000000-20-2-2-20011110000000000000000
χ664444-2-2444-2-244-2-24-2-21-2-21-2-2-21-2-2-21-2-244-2-2-2-2-2-20000001111-2-2111111000-4-40000000000000000000000000002022200-1-1-1-10000000000000000
χ674444-2-24-4-4-2-244-2-24-2-21-2-21-2-2-21-2-2-2122-4-4222222000000111122-1-1-1-1-1-10004-400000000000000000000000000020-22-20011-1-10000000000000000
χ684444-2-24-4-4-2-244-2-24-2-21-2-21-2-2-21-2-2-2122-4-4222222000000111122-1-1-1-1-1-1000-44000000000000000000000000000-202-2200-1-1110000000000000000
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χ7244-4-44-2400424-42-2-4-4-4-24-2-22-422-44-220000000000000000-22-2200000000000000000000000000000000000000000000000000000000000023−2300000
χ7344-4-44-2400424-42-2-4-4-4-24-2-22-422-44-220000000000000000-22-22000000000000000000000000000000000000000000000000000000000000−232300000
χ7444-4-4-24400-2-44-4-44-422-2-24-2-42-422-2420000000000000000-22-22000000000000000−2i32i30000000000−2i32i3−2i32i3000000000000000000000000000000000000
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χ7744-4-4-24-200-2-4-22-44222-21-2-22-122-11-220000003i−3i3i−3i00−232323−231-11-100003i−3i3i−3i00000002i3−2i30000003−3−33−i3i3−i3i3000000000000000000000000000000000000
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χ904-44-4-24-2−4i4i2-4224-4-22-2-21-22-2-12-21-122−4i4i2i−2i2i−2i−i−iii00−2i3−2i32i32i311-1-12i−2i2i−2i−i−iii000000000−23230000i3i3−i3−i333−3−3000000000000000000000000000000000000
χ914-44-4-24-2−4i4i2-4224-4-22-2-21-22-2-12-21-122−4i4i2i−2i2i−2i−i−iii002i32i3−2i3−2i311-1-12i−2i2i−2i−i−iii00000000023−230000−i3−i3i3i3−3−333000000000000000000000000000000000000
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χ944-44-4-2-24−4i4i22-4-4-2242-21-2-2-1-2221-222-12i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii0000000000000000000000000000000000000003-3−3i3i0000000000000000
χ954-44-4-2-24−4i4i22-4-4-2242-21-2-2-1-2221-222-12i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii000000000000000000000000000000000000000-333i−3i0000000000000000
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χ984-4-444-2400-4-2-4422-44-4-24-2224-22-4-42-20000000000000000-222-200000000000000000000000000000004i−4i0000000000000000000000000−2i2i0000000
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χ1004-4-44-2440024-44-4-4-4-22-2-242-4-24222-4-200000000004i−4i4i−4i4i−4i-222-2000000000000000000000−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ1014-4-44-2440024-44-4-4-4-22-2-242-4-24222-4-20000000000−4i4i−4i4i−4i4i-222-20000000000000000000002i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ1024-4-44-24-200242-2-4-42-22-21-2221-22-1-12-20000003-3-334i−4i−2i2i−2i2i1-1-1100003-3-330000000000000−2i2ii−ii−i3i−3i−3i3i000000000000000000000000000000000000
χ1034-4-44-24-200242-2-4-42-22-21-2221-22-1-12-20000003-3-33−4i4i2i−2i2i−2i1-1-1100003-3-3300000000000002i−2i−ii−ii−3i3i3i−3i000000000000000000000000000000000000
χ1044-4-44-24-200242-2-4-42-22-21-2221-22-1-12-2000000-333-34i−4i−2i2i−2i2i1-1-110000-333-30000000000000−2i2ii−ii−i−3i3i3i−3i000000000000000000000000000000000000
χ1054-4-44-24-200242-2-4-42-22-21-2221-22-1-12-2000000-333-3−4i4i2i−2i2i−2i1-1-110000-333-300000000000002i−2i−ii−ii3i−3i−3i3i000000000000000000000000000000000000
χ1068888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-42222000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-2000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10888-8-88-4-40084-444-44-8-8-4-42-4-24-244-42400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4800-448-84-4-8442-4-42444-24-4-4-200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-400-44-444-44442222-2-2-2-2-222-20000006i−6i6i−6i000000-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-44-444-44442222-2-2-2-2-222-2000000−6i6i−6i6i000000-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-48i−8i4444-44-44-4222-22-2-222-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i000000-1-1112i−2i2i−2i−i−iii00000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4−8i8i4444-44-44-4222-22-2-222-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i000000-1-111−2i2i−2i2iii−i−i00000000000000000000000000000000000000000000000000000000000
χ1148-8-888-4-400-8-44-44448-8-4-424-2-42444-2-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-48004-4-8844-8-442-4-4-24-4-4-2444200000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4004-44-4444-44222-2-222-2-2-2-220000006-6-66000000-111-10000-333-300000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4004-44-4444-44222-2-222-2-2-2-22000000-666-6000000-111-100003-3-3300000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).