Finite Group Databasebeta

← Group #13168574

Character table — Group #13168574

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212124444441212121236661212121212121212124441212121212121212121212121212121212121212121222441212121212121212121212122444661212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111111-1-11111111111111111-1-1111-1-1-111-1-111-1-1-1-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111111-111-1-111-1-11111-1-111111111-1-1-1-1-1111-1-111-1-111-111-1-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-111-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1111-1-11
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111111-1-1-111-1-1-1-1-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-111-1-1-1-1-1-1-111-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-1-11-1-1111111-1-1-11
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-11111-1-11-111-1-1-1-111-1-111-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1-1-1-11111-11-1111-1-11111-1-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-111111-1-1-1-1-1-11-11111-1-111-11-1-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1111-11-111-1-1-1-11111-1-1-1-111-1-1-1-11-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-111-1-1-1-1-1-11111-1-111-11-11-1-11111-1-111-1-1-1-111-1-1111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111111111-1-111-1-1-1-1-1-111111111-1-11-1-1-1-1-11111-1-11-11111-1-1-1-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-111111-1-1-1-1-11-1111-1-111-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-1-1-1111-111-1-1-1-1111111-1-1
χ17222222-122-1-1-122222-1-12-1-1222-1-1-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-122200-1-1-1-122000022000000002200-1-122-1-1-1-1-1-1-1-12000-1-1000000-1000
χ18222222-122-1-1-122222-1-12-1-1222-1-1-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2200-1-1112200002200000000-2-200-11-2-2-1-111-1-111-2000110000001000
χ19222222-122-1-1-122222-1-12-1-1222-1-1-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-122-20011-1-1-2-20000-2-200000000-2-2001-12211-1-111-1-1-2000110000001000
χ20222222-122-1-1-122222-1-12-1-1222-1-1-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2001111-2-20000-2-200000000220011-2-2111111112000-1-1000000-1000
χ21222222-122-1-1-122222-1-1-2-1-1222-1-1-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-11111111112-2-200-1-111220000-2-200000000-2-2001-1-2211-1-1-1-111200011000000-1000
χ22222222-122-1-1-122222-1-1-2-1-1222-1-1-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-22-200-1-1-1-1220000-2-2000000002200112-21111-1-1-1-1-2000-1-10000001000
χ23222222-122-1-1-122222-1-1-2-1-1222-1-1-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-11111111112-22001111-2-2000022000000002200-1-1-22-1-1-1-11111-2000-1-10000001000
χ24222222-122-1-1-122222-1-1-2-1-1222-1-1-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-1111111111-2220011-1-1-2-200002200000000-2-200-112-2-1-11111-1-1200011000000-1000
χ2522222-122-12222-12-1-12-122-1-1-1-12-12-122-1-1-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-1220-1-1002200-1-12200-1-1-1-1-1-1-1-1000002-1-100-1-100-1-10220000000000-1-10
χ2622222-122-12222-12-1-12-122-1-1-1-12-12-122-1-1-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-1-2-20-1-100-2-200-1-12200-1-1-1-1-1-1-1-100000-211001100110-2-20000000000110
χ2722222-122-12222-12-1-12-122-1-1-1-12-12-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-12201100220011-2-20011111111000002-1-100-1-100-1-10-2-20000000000110
χ2822222-122-12222-12-1-12-122-1-1-1-12-12-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-2-201100-2-20011-2-2001111111100000-211001100110220000000000-1-10
χ2922222-122-12222-12-1-12-1-22-1-1-1-12-12-1-2-21111112200-2-22222-1-1-1-1-2-2-21111112-201100-2-200-1-1-2-200-1-1-1-111110000021-100-1-100110-220000000000-110
χ3022222-122-12222-12-1-12-1-22-1-1-1-12-12-1-2-21111112200-2-22222-1-1-1-1-2-2-2111111-22011002200-1-1-2-200-1-1-1-1111100000-2-11001100-1-102-200000000001-10
χ3122222-122-12222-12-1-12-1-22-1-1-1-12-12-1-2-2111111-2-20022-2-2-2-2-1-1-1-1-2-2-21111112-20-1-100-2-2001122001111-1-1-1-10000021-100-1-1001102-200000000001-10
χ3222222-122-12222-12-1-12-1-22-1-1-1-12-12-1-2-2111111-2-20022-2-2-2-2-1-1-1-1-2-2-2111111-220-1-10022001122001111-1-1-1-100000-2-11001100-1-10-220000000000-110
χ332222-122-12222-12-12-1-122-12-1-1-1-12-12-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-1002222200-1-122-1-1-1-1-1-1-1-1-1-1-1-100222000-1-100-1-100000200-1-1-1-1000000
χ342222-122-12222-12-12-1-122-12-1-1-1-12-12-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-100-222-2-2001122-1-111-1-1-1-1-1-1-1-100-2-2-200011001100000-2001111000000
χ352222-122-12222-12-12-1-122-12-1-1-1-12-12-1-122-1-1-1-1-2-222-2-21111-1-1-1-12-1-122-1-1-1-1002-2-22200-1-1-2-211-1-11111111100-2-22000-1-100-1-100000-2001111000000
χ362222-122-12222-12-12-1-122-12-1-1-1-12-12-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-100-2-2-2-2-20011-2-21111111111110022-200011001100000200-1-1-1-1000000
χ372222-122-12222-12-12-1-12-2-12-1-1-1-12-1211-2-211112222-2-2-1-1-1-1-1-1-1-1-211-2-2111100-2-2-22200-1-1221111-1-1-1-1111100-2-2-20001100-1-10000020011-1-1000000
χ382222-122-12222-12-12-1-12-2-12-1-1-1-12-1211-2-2111122-2-2-2-2-1-1-1-1-1-1-1-1-211-2-21111002-2-2-2-200112211-1-1-1-1-1-1111100222000-1-1001100000-200-1-111000000
χ392222-122-12222-12-12-1-12-2-12-1-1-1-12-1211-2-21111-2-222221111-1-1-1-1-211-2-2111100-2222200-1-1-2-2-1-1111111-1-1-1-10022-20001100-1-100000-200-1-111000000
χ402222-122-12222-12-12-1-12-2-12-1-1-1-12-1211-2-21111-2-2-2-2221111-1-1-1-1-211-2-2111100222-2-20011-2-2-1-1-1-11111-1-1-1-100-2-22000-1-100110000020011-1-1000000
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χ432-22-2222-2-2-2-2222-2-22220-2-22-2-2-2-22200000000−2i2i0000−2i−2i2i2i2-2-2200000000000000000000−2i2i0000−2i−2i2i2i00002-20000000000000000002-20000−2i2i0000
χ442-22-2222-2-2-2-2222-2-22220-2-22-2-2-2-22200000000−2i2i0000−2i−2i2i2i2-2-2200000000000000000000−2i2i0000−2i−2i2i2i0000-22000000000000000000-2200002i−2i0000
χ452-2-22222-222-2-2-2-22-22220-22-22-22-2-2-200000000002i−2i2-2000022-2-20000000000002-22i−2i002i−2i002-200000022-2-2002i−2i000000002i−2i000000002i−2i00000000
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χ472-2-22222-222-2-2-2-22-22220-22-22-22-2-2-20000000000−2i2i2-2000022-2-20000000000002-2−2i2i00−2i2i002-200000022-2-200−2i2i00000000−2i2i00000000−2i2i00000000
χ482-2-22222-222-2-2-2-22-22220-22-22-22-2-2-20000000000−2i2i-22000022-2-2000000000000-22−2i2i00−2i2i00-22000000-2-222002i−2i00000000−2i2i000000002i−2i00000000
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χ502-2-22-122122-2-21-2-1-2-1-120121-11-1-21-23−30033−3−3002i−2i-22−33−33-1-11103−30033−3−3000-222i−2i00−ii001-1−i3i3−33−3311-1-100−2i2i0000−i3i300−ii00000000i−ii3−i3000000
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χ552-2-22-122122-2-21-2-1-2-1-120121-11-1-21-2−3300−3−33300−2i2i2-2−33−33-1-1110−3300−3−3330002-2−2i2i00i−i00-11−i3i3−33−33-1-11100−2i2i0000−i3i300i−i00000000i−i−i3i3000000
χ562-2-22-122122-2-21-2-1-2-1-120121-11-1-21-2−3300−3−33300−2i2i-223−33−3-1-1110−3300−3−333000-22−2i2i00i−i001-1−i3i33−33−311-1-1002i−2i0000−i3i300i−i00000000−iii3−i3000000
χ5744444-2-24-2-2-2-24-24-2-2-214-21-2-2-2-21-2144-2-2-2-2-2-200000000001111-2-2-21111114400000-2-2000000000000000000000-2-2-2001100110000000000000000
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χ884-44-4-2442-4-4-44-242-4-2-2402-4-2222-4-24000000004i−4i0000−2i−2i2i2i-222-2000000000000000000004i−4i0000−2i−2i2i2i000000000000000000000000000000000000
χ894-44-4-2442-4-4-44-242-4-2-2402-4-2222-4-2400000000−4i4i00002i2i−2i−2i-222-200000000000000000000−4i4i00002i2i−2i−2i000000000000000000000000000000000000
χ904-44-4-2-2422-4-44-2-2221-2-20221-1-122-2-200003-3-334i−4i0000−2i−2i2i2i1-1-11000003-3-3300000000000−2i2i0000ii−i−i3i−3i−3i3i00000000000000000000000000000000
χ914-44-4-2-2422-4-44-2-2221-2-20221-1-122-2-200003-3-33−4i4i00002i2i−2i−2i1-1-11000003-3-33000000000002i−2i0000−i−iii−3i3i3i−3i00000000000000000000000000000000
χ924-44-4-2-2422-4-44-2-2221-2-20221-1-122-2-20000-333-34i−4i0000−2i−2i2i2i1-1-1100000-333-300000000000−2i2i0000ii−i−i−3i3i3i−3i00000000000000000000000000000000
χ934-44-4-2-2422-4-44-2-2221-2-20221-1-122-2-20000-333-3−4i4i00002i2i−2i−2i1-1-1100000-333-3000000000002i−2i0000−i−iii3i−3i−3i3i00000000000000000000000000000000
χ944-4-4444-2-44-222-4-44-44-2-202-2-44-4-222200000000004i−4i000000-2-22200000000000000−2i2i004i−4i00000000000000000000000000−2i2i000000000000000000
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χ964-4-444-24-4-24-4-4-4242-24-20-4-22-2242-420000000000004-40000-2-222000000000000-22000000004-4000000-2-22200000000000000000000000000000000
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χ984-4-44-24-224-2222-4-2-4-21-20-1-22-2212-1223−23002323−23−23004i−4i00000011-1-10−3300−3−33300000−2i2i00−2i2i0000−2i32i30000000000000000i3−i300i−i000000000000000000
χ994-4-44-24-224-2222-4-2-4-21-20-1-22-2212-1223−23002323−23−2300−4i4i00000011-1-10−3300−3−333000002i−2i002i−2i00002i3−2i30000000000000000−i3i300−ii000000000000000000
χ1004-4-44-24-224-2222-4-2-4-21-20-1-22-2212-12−232300−23−232323004i−4i00000011-1-103−30033−3−300000−2i2i00−2i2i00002i3−2i30000000000000000−i3i300i−i000000000000000000
χ1014-4-44-24-224-2222-4-2-4-21-20-1-22-2212-12−232300−23−23232300−4i4i00000011-1-103−30033−3−3000002i−2i002i−2i0000−2i32i30000000000000000i3−i300−ii000000000000000000
χ1024-4-44-2-242-24-4-422-221-2-202-2-11-1-222223−2300−3−33300004-423−2323−2311-1-1023−2300−3−333000-2200000000-2200−33−3311-1-100000000000000000000000000000000
χ1034-4-44-2-242-24-4-422-221-2-202-2-11-1-222223−2300−3−3330000-44−2323−232311-1-1023−2300−3−3330002-2000000002-2003−33−3-1-11100000000000000000000000000000000
χ1044-4-44-2-242-24-4-422-221-2-202-2-11-1-2222−23230033−3−300004-4−2323−232311-1-10−23230033−3−3000-2200000000-22003−33−311-1-100000000000000000000000000000000
χ1054-4-44-2-242-24-4-422-221-2-202-2-11-1-2222−23230033−3−30000-4423−2323−2311-1-10−23230033−3−30002-2000000002-200−33−33-1-11100000000000000000000000000000000
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
χ10888-8-8-48-4-4-84-444-848-42-402444-4-2-4-240000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-4-444-44444-422202-2-2-22-22-2-20043−43−2323−23230000000000-11-11000−23233−33−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4-444-44444-422202-2-2-22-22-2-200−434323−2323−230000000000-11-1100023−23−33−33000000000000000000000000000000000000000000000000000000000
χ1118-88-88-4-4-8444-48-4-84-4-4204-2-4444-2-420000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-48-44-844-4-484-8-42-40-24-444-242-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-44444-4-4-4442220-2-22-2-2-2-22200006-6-660000000000-111-100000-333-3000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-44444-4-4-4442220-2-22-2-2-2-2220000-666-60000000000-111-1000003-3-33000000000000000000000000000000000000000000000000000000000
χ1158-8-888-4-4-8-4-444-8484-4-420424-44-4-24-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-44-4-44444-442220-22-22-22-2-2-243−4300−23−2323230000000000-1-1110−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-44-4-44444-442220-22-22-22-2-2-2−4343002323−23−230000000000-1-111023−2300−3−333000000000000000000000000000000000000000000000000000000000

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