Finite Group Databasebeta

← Group #13168529

Character table — Group #13168529

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order12223336666666663334666666666121212121212121244444412121212366612121212121212121224466121212121212121212121212121212121212121244446661212121212121212122244661212121244612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1111111111111-1-1111-1-1-111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11111111111111111111-111-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1111-1-11
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-111-1-1-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111111-1-1-111-1-11111-1-1-11
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11-11111-1-11-11-11111-1-111-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1111-1-1-1-1-1-11-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1111-11-1-1-111-1-1-111-1-1-1-1-111-1-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-1-1-111-1-1-11-1-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-11111-1-1-1-1-11-1-11111-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-11-1111-1-111-111-1-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-111-1111-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1-1-1-1111-11-11111-1-1-1-1-11-11
χ17222222-12222-1-1-1222-1-12-1-1-12-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-122222000000-1-1-1-122000000000022-1-1-1-122-1-1-1-1-1-1020000-1-10000-1000
χ18222222-12222-1-1-1222-1-12-1-1-12-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-12-2-222000000-1-111220000000000-2-2-1-1-11-2-2-1-111110-200001100001000
χ19222222-12222-1-1-1222-1-12-1-1-12-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-222-2-200000011-1-1-2-20000000000-2-2111-12211-1-1-1-10-200001100001000
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χ21222222-12222-1-1-1222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-22-2-2-2000000-1-1-1-12200000000002211112-2-1-1-1-1110-20000-1-100001000
χ22222222-12222-1-1-1222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-2-22-2-2000000-1-111220000000000-2-2111-1-22-1-111-1-1020000110000-1000
χ23222222-12222-1-1-1222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-111111111122-22200000011-1-1-2-20000000000-2-2-1-1-112-211-1-111020000110000-1000
χ24222222-12222-1-1-1222-1-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-11111111112-22220000001111-2-2000000000022-1-1-1-1-221111-1-10-20000-1-100001000
χ2522222-12-122-1222-12-12-1222-1-1-1-1-1-12-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-1200-1-12222-1-12200-1-1-1-1-1-1-1-1-1-122002-1-1000-1-100002000-1-100-1-1000000
χ2622222-12-122-1222-12-12-1222-1-1-1-1-1-12-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-200112222-1-1-2-20011-1-1-1-1-1-1-1-1-2-200-211000110000-2000110011000000
χ2722222-12-122-1222-12-12-1222-1-1-1-1-1-12-1-122-1-1-1-1-2-222-2-21111-1-1-1-12-1-122-1-1-1-1200-1-1-2-2-2-2112200-1-111111111-2-2002-1-1000-1-10000-2000110011000000
χ2822222-12-122-1222-12-12-1222-1-1-1-1-1-12-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-20011-2-2-2-211-2-20011111111112200-2110001100002000-1-100-1-1000000
χ2922222-12-122-1222-12-12-1-222-1-1-1-1-1-1211-2-211112222-2-2-1-1-1-1-1-1-1-1-211-2-21111-2001122-2-2112200-1-1-1-1-1-11111-2-200-211000-1-100002000-1-10011000000
χ3022222-12-122-1222-12-12-1-222-1-1-1-1-1-1211-2-2111122-2-2-2-2-1-1-1-1-1-1-1-1-211-2-21111200-1-122-2-211-2-20011-1-1-1-1111122002-1-1000110000-20001100-1-1000000
χ3122222-12-122-1222-12-12-1-222-1-1-1-1-1-1211-2-21111-2-222221111-1-1-1-1-211-2-21111-20011-2-222-1-12200-1-11111-1-1-1-12200-211000-1-10000-20001100-1-1000000
χ3222222-12-122-1222-12-12-1-222-1-1-1-1-1-1211-2-21111-2-2-2-2221111-1-1-1-1-211-2-21111200-1-1-2-222-1-1-2-200111111-1-1-1-1-2-2002-1-10001100002000-1-10011000000
χ332222-1222-1-122222-1-1-122-1-12-12-1-12-122-1-1-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-102200-1-1-1-122002200-1-1-1-1-1-1-1-100000002-1-100-1-1-1-10022000000000-1-10
χ342222-1222-1-122222-1-1-122-1-12-12-1-12-122-1-1-1-1-1-12200222222-1-1-1-1222-1-1-1-1-1-10-2-200-1-1-1-12200-2-200-1-1-1-1-1-1-1-10000000-21100111100-2-2000000000110
χ352222-1222-1-122222-1-1-122-1-12-12-1-12-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-1022001111-2-20022001111111100000002-1-100-1-1-1-100-2-2000000000110
χ362222-1222-1-122222-1-1-122-1-12-12-1-12-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-10-2-2001111-2-200-2-200111111110000000-2110011110022000000000-1-10
χ372222-1222-1-122222-1-1-12-2-1-12-12-1-12-1-2-21111112200-2-22222-1-1-1-1-2-2-211111102-200-1-111-2-2002200-1-1-1-111110000000-2-1100-1-111002-2000000000-110
χ382222-1222-1-122222-1-1-12-2-1-12-12-1-12-1-2-21111112200-2-22222-1-1-1-1-2-2-21111110-2200-1-111-2-200-2-200-1-1-1-11111000000021-10011-1-100-220000000001-10
χ392222-1222-1-122222-1-1-12-2-1-12-12-1-12-1-2-2111111-2-20022-2-2-2-2-1-1-1-1-2-2-211111102-20011-1-1220022001111-1-1-1-10000000-2-1100-1-11100-220000000001-10
χ402222-1222-1-122222-1-1-12-2-1-12-12-1-12-1-2-2111111-2-20022-2-2-2-2-1-1-1-1-2-2-21111110-220011-1-12200-2-2001111-1-1-1-1000000021-10011-1-1002-2000000000-110
χ4122-2-2222-22-2-22-2-22-222202-2-2-2-22-22-2000000002-2000022-2-222-2-2000000000000002-2000000000022-2-20000002i−2i0000000000000000002i−2i002i−2i0000
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χ492-2-222-121-22-1-2-221-2-12-10-22-1111-11-23−30033−3−3002i−2i2-23−33−3-11-1103−30033−3−3000−i3i3002-2-112i−2i00−ii3−33−3-1-1112i−2i000−i3i3000−ii00000000−i3i300−ii000000
χ502-2-222-121-22-1-2-221-2-12-10-22-1111-11-23−30033−3−3002i−2i-22−33−33-11-1103−30033−3−3000−i3i300-221-12i−2i00−ii−33−3311-1-1−2i2i000−i3i3000−ii00000000i3−i300i−i000000
χ512-2-222-121-22-1-2-221-2-12-10-22-1111-11-23−30033−3−300−2i2i2-23−33−3-11-1103−30033−3−3000i3−i3002-2-11−2i2i00i−i3−33−3-1-111−2i2i000i3−i3000i−i00000000i3−i300i−i000000
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χ904-44-4-2-24-2222-44-42-21-2-202221-2-1-12-200−2i32i3i3−i3−i3i300000023−23−23231-1-11000−2i32i3i3−i3−i3i300000000000000000−333−33i−3i−3i3i00000000000000000000000000000000
χ914-44-4-2-24-2222-44-42-21-2-202221-2-1-12-200−2i32i3i3−i3−i3i3000000−232323−231-1-11000−2i32i3i3−i3−i3i3000000000000000003−3−33−3i3i3i−3i00000000000000000000000000000000
χ924-44-4-2-24-2222-44-42-21-2-202221-2-1-12-2002i3−2i3−i3i3i3−i300000023−23−23231-1-110002i3−2i3−i3i3i3−i300000000000000000−333−3−3i3i3i−3i00000000000000000000000000000000
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χ944-4-4444-2-4-44422-2-4-44-2-202-2-2-42-442200000000004i−4i000000-22-2200000000000000000000−2i2i004i−4i000000000000000000−2i2i00000000000000000000
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χ984-4-444-2-22-44-222-22-4-2-2102-212-12-2-12−232300−23−232323004i−4i0000001-11-103−30033−3−30002i3−2i3000000−2i2i00−2i2i0000000000000−i3i3000i−i00000000000000000000
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χ1004-4-44-244-42-24-4-44-42-2-2402-242-42-2-420000000000004-40000-22-220000000000000000-224-40000000000-2-22200000000000000000000000000000000
χ1014-4-44-244-42-24-4-44-42-2-2402-242-42-2-42000000000000-440000-22-2200000000000000002-2-44000000000022-2-200000000000000000000000000000000
χ1024-4-44-2-2422-2-2-4-44221-2-202-2-2-12-112223−2300−3−33300004-423−2323−231-11-1023−2300−3−3330000000-22-22000000−33−3311-1-100000000000000000000000000000000
χ1034-4-44-2-2422-2-2-4-44221-2-202-2-2-12-112223−2300−3−3330000-44−2323−23231-11-1023−2300−3−33300000002-22-20000003−33−3-1-11100000000000000000000000000000000
χ1044-4-44-2-2422-2-2-4-44221-2-202-2-2-12-1122−23230033−3−300004-4−2323−23231-11-10−23230033−3−30000000-22-220000003−33−311-1-100000000000000000000000000000000
χ1054-4-44-2-2422-2-2-4-44221-2-202-2-2-12-1122−23230033−3−30000-4423−2323−231-11-10−23230033−3−300000002-22-2000000−33−33-1-11100000000000000000000000000000000
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
χ10888-8-88-4-448-84-444-4-8-4-420-44-24-2-442400000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-48-4-8-44-8-44484-42-402-2444-44-4-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-44-444-444-4422202-2-2-2-22-22-200006i−6i6i−6i0000000000-1-11100000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-44-444-444-4422202-2-2-2-22-22-20000−6i6i−6i6i0000000000-1-111000003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1128-88-88-4-4-4-8-844-4448-4-42044-2-4244-2-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4-44444-444-42220-2-2-222-2-2-2200−4i34i32i3−2i3−2i32i30000000000-111-10002i3−2i3−i3i3i3−i3000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-4-44444-444-42220-2-2-222-2-2-22004i3−4i3−2i32i32i3−2i30000000000-111-1000−2i32i3i3−i3−i3i3000000000000000000000000000000000000000000000000000000000
χ1158-8-88-48-4-84-4844-4-84-42-40-22-4444-44-20000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-444-4-444-4442220-222-2-2-22-2-243−4300−23−2323230000000000-11-110−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-444-4-444-4442220-222-2-2-22-2-2−4343002323−23−230000000000-11-11023−2300−3−333000000000000000000000000000000000000000000000000000000000

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