Finite Group Databasebeta

← Group #13169331

Character table — Group #13169331

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212124444441212121236661212121212121212124441212121212121212121212121212121212121212121244441212121212121212121212124444121212121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11111-1-1111111111111111111-1-11-1-1-111-1-111-1-1-1-11-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-1111-1-111-1-11111-1-111111111-1-1-1-1-1111-1-111-1-1111-1-11-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-111-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-1-1-111-1-1-1-11-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-11-1-11-1-1-1-1-1-11111-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-111-1-11-11111-1-111-1-1-11
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1111111-1-1-1-11111-11-1-111-1-1-1-111-1-1-11-1-11111-1-11-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-11111-1-11-11-111-1-111-1-1-11-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111111-1-1-1-1111-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-11-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-111-11-1-111-1-1-1-1111-11-111-1-11111-11-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111-111-1-11111-1-1-1-1-11-1-11111111-1-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1111
χ17222222-122-122-12-122-1-122-1-12-1-1-12-122-1-1-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-1202-1-100220022-1-100-1-1-1-1-1-1-1-100000-1-1200-1-100-1-1200200000000-1-100
χ18222222-122-122-12-122-1-122-1-12-1-1-12-122-1-1-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-1-20-2-1-100-2-20022-1-100-1-1-1-1-1-1-1-10000011-200110011-200-2000000001100
χ19222222-122-122-12-122-1-122-1-12-1-1-12-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-120211002200-2-211001111111100000-1-1200-1-100-1-1-200-2000000001100
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χ21222222-122-122-12-122-1-1-22-1-12-1-1-12-1-2-21111112200-2-2-2-2-2-2-1-1-1-1-2-2-211111120-2-1-100-2-200221100-1-1-1-11111000001-1200-1-10011200-2000000001-100
χ22222222-122-122-12-122-1-1-22-1-12-1-1-12-1-2-21111112200-2-2-2-2-2-2-1-1-1-1-2-2-2111111-202-1-1002200221100-1-1-1-1111100000-11-2001100-1-1-200200000000-1100
χ23222222-122-122-12-122-1-1-22-1-12-1-1-12-1-2-2111111-2-200222222-1-1-1-1-2-2-211111120-21100-2-200-2-2-1-1001111-1-1-1-1000001-1200-1-10011-200200000000-1100
χ24222222-122-122-12-122-1-1-22-1-12-1-1-12-1-2-2111111-2-200222222-1-1-1-1-2-2-2111111-20211002200-2-2-1-1001111-1-1-1-100000-11-2001100-1-1200-2000000001-100
χ2522222-122-122-12-122-12-12-12-1-12-1-1-12-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-1020222200-1-1-1-122-1-1-1-1-1-1-1-1-1-122002000-1-100-1-1000020-1-1-1-100000000
χ2622222-122-122-12-122-12-12-12-1-12-1-1-12-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-10-2022-2-20011-1-12211-1-1-1-1-1-1-1-1-2-200-20001100110000-20111100000000
χ2722222-122-122-12-122-12-12-12-1-12-1-1-12-1-122-1-1-1-1-2-222-2-21111-1-1-1-12-1-122-1-1-1-1020-2-22200-1-111-2-2-1-111111111-2-2002000-1-100-1-10000-20111100000000
χ2822222-122-122-12-122-12-12-12-1-12-1-1-12-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-10-20-2-2-2-2001111-2-211111111112200-2000110011000020-1-1-1-100000000
χ2922222-122-122-12-122-12-1-2-12-1-12-1-1-1211-2-211112222-2-21111-1-1-1-1-211-2-211110-2022220011-1-1-2-2-1-1-1-1-1-111112200-2000-1-100110000-2011-1-100000000
χ3022222-122-122-12-122-12-1-2-12-1-12-1-1-1211-2-2111122-2-2-2-21111-1-1-1-1-211-2-2111102022-2-200-1-1-1-1-2-211-1-1-1-11111-2-20020001100-1-1000020-1-11100000000
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χ3222222-122-122-12-122-12-1-2-12-1-12-1-1-1211-2-21111-2-2-2-222-1-1-1-1-1-1-1-1-211-2-21111020-2-2-2-200-1-11122111111-1-1-1-1220020001100-1-10000-2011-1-100000000
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χ342222-122-122-12222-1-1-122-1-12-1-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-200-1-111220000220000000000-2-2-1-2-21-1-111-1-1110-200000011000010
χ352222-122-122-12222-1-1-122-1-12-1-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-12-220011-1-1-2-20000-2-20000000000-2-2122-111-1-111-1-10-200000011000010
χ362222-122-122-12222-1-1-122-1-12-1-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2001111-2-20000-2-20000000000221-2-211111111102000000-1-10000-10
χ372222-122-122-12222-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-11111111112-2-200-1-111-2-20000220000000000-2-21-22-1-1-1-1-1111102000000110000-10
χ382222-122-122-12222-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-2-2200-1-1-1-1-2-200002200000000002212-21-1-11111-1-10-2000000-1-1000010
χ392222-122-122-12222-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-111111111122-2001111220000-2-2000000000022-1-22-111-1-1-1-1110-2000000-1-1000010
χ402222-122-122-12222-1-1-12-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-1111111111-2220011-1-1220000-2-20000000000-2-2-12-211111-1-1-1-102000000110000-10
χ4122-2-22222-22-2-2-22-2-22220-22-22-22-2-2-2000000002-22-200000022-2-20000000000002-22-200002-2002-222-2-200002-20000002-20000000000002-200000000
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χ4822-2-22-12212-21-2-1-2-2-12-10121-1-2-111-23−30033−3−3-22-2200−3−333-1-11103−30033−3−3000-22-2200−331-1001-111-1-1−3−3332-20000001-100−330000003−3-1100000000
χ4922-2-22-12212-21-2-1-2-2-12-10121-1-2-111-2−3300−3−3332-22-200−3−333-1-1110−3300−3−3330002-22-200−33-1100-11-1-111−3−3332-2000000-1100−33000000−33-1100000000
χ5022-2-22-12212-21-2-1-2-2-12-10121-1-2-111-2−3300−3−3332-2-2200−3−333-1-1110−3300−3−3330002-2-22003−3-11001-1-1-111−3−333-220000001-1003−30000003−31-100000000
χ5122-2-22-12212-21-2-1-2-2-12-10121-1-2-111-2−3300−3−333-222-20033−3−3-1-1110−3300−3−333000-222-200−331-100-1111-1-133−3−3-22000000-1100−330000003−31-100000000
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χ864-44-44-2-2-4-22-4222-24-2-210-22-12-2-11220023−23−33−33000000−2i32i32i3−2i31-11-100023−23−33−33000000000000000003i−3i3i−3ii3−i3−i3i300000000000000000000000000000000
χ874-44-44-2-2-4-22-4222-24-2-210-22-12-2-11220023−23−33−330000002i3−2i3−2i32i31-11-100023−23−33−3300000000000000000−3i3i−3i3i−i3i3i3−i300000000000000000000000000000000
χ884-44-44-2-2-4-22-4222-24-2-210-22-12-2-112200−23233−33−3000000−2i32i32i3−2i31-11-1000−23233−33−300000000000000000−3i3i−3i3ii3−i3−i3i300000000000000000000000000000000
χ894-44-44-2-2-4-22-4222-24-2-210-22-12-2-112200−23233−33−30000002i3−2i3−2i32i31-11-1000−23233−33−3000000000000000003i−3i3i−3i−i3i3i3−i300000000000000000000000000000000
χ904-44-4-24424-42-4-4-44-2-2-240-22-42-2-4422000000000000000000-22-22000000000000000023−2300000000000000000000000000000023−230000000000000000
χ914-44-4-24424-42-4-4-44-2-2-240-22-42-2-4422000000000000000000-22-220000000000000000−2323000000000000000000000000000000−23230000000000000000
χ924-44-4-24-22422-42-4-2-2-21-20-2-12212-22-10023−2323−2323−2300000000001-11-1000−33−33−33000000023−23000000000000000000000000003-300−330000000000000000
χ934-44-4-24-22422-42-4-2-2-21-20-2-12212-22-10023−2323−2323−2300000000001-11-1000−33−33−330000000−232300000000000000000000000000-33003−30000000000000000
χ944-44-4-24-22422-42-4-2-2-21-20-2-12212-22-100−2323−2323−232300000000001-11-10003−33−33−3000000023−2300000000000000000000000000-3300−330000000000000000
χ954-44-4-24-22422-42-4-2-2-21-20-2-12212-22-100−2323−2323−232300000000001-11-10003−33−33−30000000−2323000000000000000000000000003-3003−30000000000000000
χ964-4-4444-2-4-4244-2-42-44-2-20-42-2-42224-20000000000004i−4i4i−4i4i−4i-222-20000000000000000000000−2i2i000000−2i2i−2i2i00000000000000000000000000000000
χ974-4-4444-2-4-4244-2-42-44-2-20-42-2-42224-2000000000000−4i4i−4i4i−4i4i-222-200000000000000000000002i−2i0000002i−2i2i−2i00000000000000000000000000000000
χ984-4-444-24-42-44-242-4-4-24-202-4-22-422-240000000000004i−4i−2i2i−2i2i-222-200000000000000000000004i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ994-4-444-24-42-44-242-4-4-24-202-4-22-422-24000000000000−4i4i2i−2i2i−2i-222-20000000000000000000000−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ1004-4-444-2-2-4224-2-222-4-2-21022122-1-1-2-200003-3-3300004i−4i−2i2i−2i2i1-1-11000003-3-330000000000000−2i2i003i−3i−3i3ii−ii−i00000000000000000000000000000000
χ1014-4-444-2-2-4224-2-222-4-2-21022122-1-1-2-200003-3-330000−4i4i2i−2i2i−2i1-1-11000003-3-3300000000000002i−2i00−3i3i3i−3i−ii−ii00000000000000000000000000000000
χ1024-4-444-2-2-4224-2-222-4-2-21022122-1-1-2-20000-333-300004i−4i−2i2i−2i2i1-1-1100000-333-30000000000000−2i2i00−3i3i3i−3ii−ii−i00000000000000000000000000000000
χ1034-4-444-2-2-4224-2-222-4-2-21022122-1-1-2-20000-333-30000−4i4i2i−2i2i−2i1-1-1100000-333-300000000000002i−2i003i−3i−3i3i−ii−ii00000000000000000000000000000000
χ1044-4-44-2442-4-4-244-4-42-2-24022422-4-4-2-2000000000000000000-222-20000000000000000000000000000000000004i−4i00000000000000000000−2i2i000000
χ1054-4-44-2442-4-4-244-4-42-2-24022422-4-4-2-2000000000000000000-222-2000000000000000000000000000000000000−4i4i000000000000000000002i−2i000000
χ1068888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-422220000000000-1-1-1-1-42222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-48-4-4-8-44-84844-42-40424-4-2-444-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-4-44-4444-4442220-22-22-22-2-2-243−4300−23−2323230000000000-1-1110−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4-44-4444-4442220-22-22-22-2-2-2−4343002323−23−230000000000-1-111023−2300−3−333000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-484-4-844-848-42-4-40244-2-44-4-240000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-44-444444-4-422202-2-2-22-22-2-20043−43−2323−23230000000000-11-11000−23233−33−3000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-44-444444-4-422202-2-2-22-22-2-200−434323−2323−230000000000-11-1100023−23−33−33000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-44-84-48-4-844-42-404-2-44-244-420000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-4844-8-4-484-842-4-40-24-4-24442-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4444-4-4-44442220-2-22-2-2-2-22200006-6-660000000000-111-100000-333-3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4444-4-4-44442220-2-22-2-2-2-2220000-666-60000000000-111-1000003-3-33000000000000000000000000000000000000000000000000000000000

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