Finite Group Databasebeta

← Group #13168247

Character table — Group #13168247

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order122233366666666633346666666661212121212121212224444121212123666121212121212121212444666612121212121212121212121212121212121244446612121212121212121212244412121212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-11111111111-1-111-11-1-111-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-11-1-11-1-1-1-1-1-11111-11
χ51111111111111111111111111111111111111-1-1111111111111111111111-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11-111-1-111111-1-11-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-11111-1-11-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1-11-1111-1-1-1-111-111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1111-1-1-111-1-111-1-11-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1111-1-1-111-1-1-1-11-111
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-111111-1-1-1-1-1-1-111-1-111-1-1111111-11-1-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-11111111-1-1-1-111-1-11111-1-1-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111-1-1-111-1-1111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-11111111-1-11-1-1-111-1-111111-1-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111-11-1111-1-1-1-1-1-1-1111
χ17222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-10022222222-1-1-1-1222-1-1-1-1-1-102200000022-1-1-1-122-1-1-1-1-1-1-1-1000000-102-100-1-1-1-1200200000000-1-100
χ18222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-10022222222-1-1-1-1222-1-1-1-1-1-10-2-200000022-1-1-1-1-2-2-1-1-1-1-1-1-1-100000010-21001111-200-2000000001100
χ19222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-100-2-2-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1022000000-2-211112211111111000000-102-100-1-1-1-1-200-2000000001100
χ20222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-100-2-2-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-10-2-2000000-2-21111-2-21111111100000010-21001111200200000000-1-100
χ21222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-211110022-2-2-2-2-2-2-1-1-1-1-2-2-211111102-200000022-1-111-2-2-1-1-1-11111000000102-100-1-111-2002000000001-100
χ22222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-211110022-2-2-2-2-2-2-1-1-1-1-2-2-21111110-2200000022-1-11122-1-1-1-11111000000-10-210011-1-1200-200000000-1100
χ23222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-2111100-2-2222222-1-1-1-1-2-2-211111102-2000000-2-211-1-1-2-21111-1-1-1-1000000102-100-1-111200-200000000-1100
χ24222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-2111100-2-2222222-1-1-1-1-2-2-21111110-22000000-2-211-1-1221111-1-1-1-1000000-10-210011-1-1-2002000000001-100
χ2522222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-120022-1-1-1-1-1-1222200-1-1-1-1-1-1-1-12200-1-10200-1-100000020-1-1-1-100000000
χ2622222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-122-2-2-2-21111-1-1-1-12-1-122-1-1-1-120022-1-1-1-111-2-2-2-20011111111-2-200-1-10200-1-1000000-20111100000000
χ2722222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-200-2-21111-1-1222200-1-1-1-1-1-1-1-1-2-200110-20011000000-20111100000000
χ2822222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-200-2-2111111-2-2-2-200111111112200110-2001100000020-1-1-1-100000000
χ2922222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-21111112222-2-21111-1-1-1-1-211-2-21111-20022-1-111-1-122-2-200-1-1-1-111112200-1-10-20011000000-20-1-11100000000
χ3022222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-211111122-2-222-1-1-1-1-1-1-1-1-211-2-21111-20022-1-11111-2-222001111-1-1-1-1-2-200-1-10-200110000002011-1-100000000
χ3122222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-2111111-2-222-2-21111-1-1-1-1-211-2-21111200-2-211-1-1-1-122-2-200-1-1-1-11111-2-200110200-1-10000002011-1-100000000
χ3222222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-2111111-2-2-2-222-1-1-1-1-1-1-1-1-211-2-21111200-2-211-1-111-2-222001111-1-1-1-12200110200-1-1000000-20-1-11100000000
χ332222-122-12-122222-1-12-12-1-12-1-122-1-1222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-12222000000-1-1000000000022-1-12-1-12-1-1-1-1-1-102000000-1-10000-10
χ342222-122-12-122222-1-12-12-1-12-1-122-1-1222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-1-12222000000110000000000-2-2-1-1-2-11-2-1-111110-200000011000010
χ352222-122-12-122222-1-12-12-1-12-1-122-1-122222222-2-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-22211-2-2-2-2000000-1-10000000000-2-21121-1211-1-1-1-10-200000011000010
χ362222-122-12-122222-1-12-12-1-12-1-122-1-122222222-2-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211-2-2-2-20000001100000000002211-211-211111102000000-1-10000-10
χ372222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-22200000000-1-1-1-1111111111-22-2-1-122-2-2000000110000000000-2-2-1-1-21-1211-1-11102000000110000-10
χ382222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-22200000000-1-1-1-1111111111-2-22-1-122-2-2000000-1-1000000000022-1-1211-21111-1-10-2000000-1-1000010
χ392222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-2-2-200000000-1-1-1-111111111122-211-2-2220000001100000000002211-2-1-12-1-1-1-1110-2000000-1-1000010
χ402222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-2-2-200000000-1-1-1-11111111112-2211-2-222000000-1-10000000000-2-2112-11-2-1-111-1-102000000110000-10
χ412-22-2222-22-2-2-22-2-222220-2-222-2-2-2-220000000000002i−2i2i2i−2i−2i2-2-2200000000000000000000002i−2i0000002i2i−2i−2i002-2000000000000000000002-22i−2i0000
χ422-22-2222-22-2-2-22-2-222220-2-222-2-2-2-220000000000002i−2i2i2i−2i−2i2-2-2200000000000000000000002i−2i0000002i2i−2i−2i00-2200000000000000000000-22−2i2i0000
χ432-22-2222-22-2-2-22-2-222220-2-222-2-2-2-22000000000000−2i2i−2i−2i2i2i2-2-220000000000000000000000−2i2i000000−2i−2i2i2i002-2000000000000000000002-2−2i2i0000
χ442-22-2222-22-2-2-22-2-222220-2-222-2-2-2-22000000000000−2i2i−2i−2i2i2i2-2-220000000000000000000000−2i2i000000−2i−2i2i2i00-2200000000000000000000-222i−2i0000
χ452-2-222222-2-2-2-2-222-2222022-2-2-22-2-2-2000000002-22i−2i00000022-2-20000000000002-22-2002i−2i2i−2i00002i2i−2i−2i00002i−2i002-2000000000000002i−2i0000000000
χ462-2-222222-2-2-2-2-222-2222022-2-2-22-2-2-2000000002-2−2i2i00000022-2-20000000000002-22-200−2i2i−2i2i0000−2i−2i2i2i0000−2i2i002-200000000000000−2i2i0000000000
χ472-2-222222-2-2-2-2-222-2222022-2-2-22-2-2-200000000-222i−2i00000022-2-2000000000000-22-22002i−2i2i−2i00002i2i−2i−2i0000−2i2i00-2200000000000000−2i2i0000000000
χ482-2-222222-2-2-2-2-222-2222022-2-2-22-2-2-200000000-22−2i2i00000022-2-2000000000000-22-2200−2i2i−2i2i0000−2i−2i2i2i00002i−2i00-22000000000000002i−2i0000000000
χ492-2-222-122-2-21-21-12-22-1-102-111-2-111-2003−333−3−32-22i−2i00−i3i3−i3i3-1-11103−30033−3−30002-2-113−3−ii2i−2i0000−i−iii−i3i3−i3i32i−2i00-1100003−300000000−ii−i3i300000000
χ502-2-222-122-2-21-21-12-22-1-102-111-2-111-2003−333−3−32-2−2i2i00i3−i3i3−i3-1-11103−30033−3−30002-2-113−3i−i−2i2i0000ii−i−ii3−i3i3−i3−2i2i00-1100003−300000000i−ii3−i300000000
χ512-2-222-122-2-21-21-12-22-1-102-111-2-111-2003−333−3−3-222i−2i00−i3i3−i3i3-1-11103−30033−3−3000-221-1−33−ii2i−2i0000−i−iii−i3i3−i3i3−2i2i001-10000−3300000000i−ii3−i300000000
χ522-2-222-122-2-21-21-12-22-1-102-111-2-111-2003−333−3−3-22−2i2i00i3−i3i3−i3-1-11103−30033−3−3000-221-1−33i−i−2i2i0000ii−i−ii3−i3i3−i32i−2i001-10000−3300000000−ii−i3i300000000
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χ552-2-222-122-2-21-21-12-22-1-102-111-2-111-200−33−3−333-222i−2i00i3−i3i3−i3-1-1110−3300−3−333000-221-13−3−ii2i−2i0000−i−iiii3−i3i3−i3−2i2i001-100003−300000000i−i−i3i300000000
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χ5744444-2-24-24-2-2-2-2-24-21-24-2-21-2-211-2-2-2-2-2-21111004444-2-2-2-211114-2-2-2-21111000000000-2-2-2-2-2-2001111111100000000000000000000000000000000
χ5844444-2-24-24-2-2-2-2-24-21-24-2-21-2-211-2-2-2-2-2-2111100-4-4-4-4222211114-2-2-2-2111100000000022222200-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5944444-2-24-24-2-2-2-2-24-21-2-4-2-21-2-211-2-22222-1-1-1-10044-4-422221111-42222-1-1-1-1000000000-2-2-2-222001111-1-1-1-100000000000000000000000000000000
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χ914-44-44-2-2-4-2-422-2224-21-20221-22-1-12-20000-333-30000−4i4i2i2i−2i−2i1-1-1100000-333-300000000000002i−2i003i−3i−3i3i−i−iii00000000000000000000000000000000
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χ934-44-4-244242-4-44-4-4-2-24-20224-22-4-42-2000000000000000000-222-2000000000000000000000000000000000000-44000000000000000000002-2000000
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χ964-4-444-2-242-4222-2-2-4-21-20-2-2-1221-1220023−23−3−333004i−4i00−2i32i3−2i32i311-1-1023−2300−3−333000000000−2i2i−2i2i0000ii−i−ii3−i3i3−i300000000000000000000000000000000
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χ984-4-444-2-242-4222-2-2-4-21-20-2-2-1221-12200−232333−3−3004i−4i002i3−2i32i3−2i311-1-10−23230033−3−3000000000−2i2i−2i2i0000ii−i−i−i3i3−i3i300000000000000000000000000000000
χ994-4-444-2-242-4222-2-2-4-21-20-2-2-1221-12200−232333−3−300−4i4i00−2i32i3−2i32i311-1-10−23230033−3−30000000002i−2i2i−2i0000−i−iiii3−i3i3−i300000000000000000000000000000000
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χ1054-4-44-2-24-2-422-42-242-2-210-212-12-22-1200−2323−23−232323-440000000011-1-103−30033−3−30002-22-223−2300000000000000000000-110000−3300000000000000000000
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χ10988-8-8-4-4-444-4-4-444442220-2-2-2-22-222-243−4300−2323−23230000000000-11-11000−23233−33−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-444-4-4-444442220-2-2-2-22-222-2−43430023−2323−230000000000-11-1100023−23−33−33000000000000000000000000000000000000000000000000000000000
χ1118-88-8-48-44-44-848-84-42-4-40-24-4-4-244420000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-484844-8-44-8-4-4-4204-2-42444-2-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
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χ1148-88-8-4-4-44-4444-444-42220-2-222-2-2-2-220000-666-60000000000-111-1000003-3-33000000000000000000000000000000000000000000000000000000000
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χ1168-8-88-4-4-4-444444-4-44222022-2-2-22-2-2-20043−43−23−2323230000000000-1-1110−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-444444-4-44222022-2-2-22-2-2-200−43432323−23−230000000000-1-111023−2300−3−333000000000000000000000000000000000000000000000000000000000

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