Finite Group Databasebeta

← Group #13169172

Character table — Group #13169172

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212124444121212123666121212121212121212244466121212121212121212121212121212121212121222666121212121212121212244446666121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-111-1-1-11111111111111111111111-1-1-1-11-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11111111111111111111-11111111-1-1-1-111-1-111111111-1-11111-1111-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-111-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-111-1-1-1-1-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-1-1-11-1-1-1-11111-1-1-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-1-1-1111111-1-1-1-111111-1-1-1-1-111-1-1-11-1-1111-1-111-1-111-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-11-111111-1-1-1-111-111-1-1-1-111-1-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111-11-1-1-1-1-11111-11-1-1-111-1-1-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1111-11-11-1-111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-11111-1-1111-1-1-1-1-111-1-11-11-11-1-111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-111111-1-111-11-1-1-111-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-11111-1-1-1-11111-1-1-1-1-1-1111111111-11-1-1-1-1-111-1-111-111-1-1-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-111111-1-111-11-1-1111-1-111-1-11-11
χ17222222-12-1-12-12222-1-122-12-1-12-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1022000-1-122-1-1-1-12222-1-1-1-1-1-1-1-12200002000-1-1-1-120000-1-1-1-10000000
χ18222222-12-1-12-12222-1-122-12-1-12-1-12-1-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-102-2000-1-122111122-2-2-1-1-1-1-1-1-1-1-2-20000-20001111-2000011110000000
χ19222222-12-1-12-12222-1-122-12-1-12-1-12-1-1-122-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-10-2200011-2-2-1-1-1-1-2-22211111111-2-200002000-1-1-1-1-2000011110000000
χ20222222-12-1-12-12222-1-122-12-1-12-1-12-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-10-2-200011-2-21111-2-2-2-211111111220000-2000111120000-1-1-1-10000000
χ21222222-12-1-12-12222-1-12-2-12-1-12-1-12-111-2-211112222-1-1-1-1-1-1-1-1-2-2-21111110-2-20001122-1-111-2-222-1-1-1-11111220000-2000-1-111-20000-1-1110000000
χ22222222-12-1-12-12222-1-12-2-12-1-12-1-12-111-2-2111122-2-2-1-1-1-1-1-1-1-1-2-2-21111110-22000112211-1-1-2-2-2-2-1-1-1-11111-2-20000200011-1-12000011-1-10000000
χ23222222-12-1-12-12222-1-12-2-12-1-12-1-12-111-2-21111-2-2221111-1-1-1-1-2-2-211111102-2000-1-1-2-2-1-11122221111-1-1-1-1-2-20000-2000-1-1112000011-1-10000000
χ24222222-12-1-12-12222-1-12-2-12-1-12-1-12-111-2-21111-2-2-2-21111-1-1-1-1-2-2-2111111022000-1-1-2-211-1-122-2-21111-1-1-1-1220000200011-1-1-20000-1-1110000000
χ2522222-12222-122-1-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-122022222-1-10000-1-100-1-1-1-1-1-1-1-100-1-1-1-102-1-1000002200000000-10-100
χ2622222-12222-122-1-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1-220-2-2-222-1-10000-1-100-1-1-1-1-1-1-1-10011110-21100000-2-20000000010100
χ2722222-12222-122-1-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-12-20222-2-211000011001111111100-1-1-1-102-1-100000-2-20000000010100
χ2822222-12222-122-1-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-20-2-2-2-2-21100001100111111110011110-211000002200000000-10-100
χ2922222-12222-122-1-122-1-1-22-12-1-1-1-1-12-2-211111122002222-1-1-1-1-211-2-211112-20-222-2-2-1-100001100-1-1-1-1111100-1-1-110-211000002-20000000010-100
χ3022222-12222-122-1-122-1-1-22-12-1-1-1-1-12-2-211111122002222-1-1-1-1-211-2-21111-2-202-2-2-2-2-1-100001100-1-1-1-1111100111-102-1-100000-2200000000-10100
χ3122222-12222-122-1-122-1-1-22-12-1-1-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-21111220-22222110000-1-1001111-1-1-1-100-1-1-110-21100000-2200000000-10100
χ3222222-12222-122-1-122-1-1-22-12-1-1-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-21111-2202-2-222110000-1-1001111-1-1-1-100111-102-1-1000002-20000000010-100
χ332222-122-12222-122-1-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-12022-1-10000222200-1-100000000002-1-12-1-1-1-1-1-1-1-1000220000-1-10-1000
χ342222-122-12222-122-1-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-202-2110000222200-1-10000000000-211-2-1111-1-1-1-1000-2-200001101000
χ352222-122-12222-122-1-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-120-22-1-10000-2-2-2-2001100000000002-1-121-1-1-11111000-2-200001101000
χ362222-122-12222-122-1-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-2110000-2-2-2-200110000000000-211-211111111000220000-1-10-1000
χ372222-122-12222-122-1-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-111111111120-2-2-1-1000022-2-200-1-100000000002-1-1-21111-1-111000-220000-1-101000
χ382222-122-12222-122-1-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-20-2211000022-2-200-1-10000000000-21121-1-1-1-1-1110002-20000110-1000
χ392222-122-12222-122-1-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111202-2-1-10000-2-222001100000000002-1-1-2-111111-1-10002-20000110-1000
χ402222-122-12222-122-1-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111-2022110000-2-22200110000000000-2112-1-1-1-111-1-1000-220000-1-101000
χ412-22-2222-22-2-2-222-2-22220-2-2222-2-2-2-2000000002i−2i2i−2i2i2i−2i−2i2-2-22000000000000000002i−2i2i−2i00002i−2i2i2i−2i−2i00002-2000000002i−2i00000002-2000000000
χ422-22-2222-22-2-2-222-2-22220-2-2222-2-2-2-2000000002i−2i−2i2i2i2i−2i−2i2-2-22000000000000000002i−2i−2i2i0000−2i2i2i2i−2i−2i0000-2200000000−2i2i0000000-22000000000
χ432-22-2222-22-2-2-222-2-22220-2-2222-2-2-2-200000000−2i2i2i−2i−2i−2i2i2i2-2-2200000000000000000−2i2i2i−2i00002i−2i−2i−2i2i2i0000-22000000002i−2i0000000-22000000000
χ442-22-2222-22-2-2-222-2-22220-2-2222-2-2-2-200000000−2i2i−2i2i−2i−2i2i2i2-2-2200000000000000000−2i2i−2i2i0000−2i2i−2i−2i2i2i00002-200000000−2i2i00000002-2000000000
χ452-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21−i3i300−i3−i3i3i32i−2i2i−2i−i−iii-111-1000−i3i3−i3−i3i3i30000003−32i−2i−ii3−3002i−2i−i−iii33−3−32-200000000−ii3−300000-11−i3i30000000
χ462-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21−i3i300−i3−i3i3i32i−2i−2i2i−i−iii-111-1000−i3i3−i3−i3i3i30000003−32i−2ii−i−3300−2i2i−i−iii33−3−3-2200000000i−i−33000001-1i3−i30000000
χ472-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21−i3i300−i3−i3i3i3−2i2i2i−2iii−i−i-111-1000−i3i3−i3−i3i3i3000000−33−2i2i−ii3−3002i−2iii−i−i−3−333-2200000000−ii3−3000001-1i3−i30000000
χ482-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21−i3i300−i3−i3i3i3−2i2i−2i2iii−i−i-111-1000−i3i3−i3−i3i3i3000000−33−2i2ii−i−3300−2i2iii−i−i−3−3332-200000000i−i−3300000-11−i3i30000000
χ492-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21i3−i300i3i3−i3−i32i−2i2i−2i−i−iii-111-1000i3−i3i3i3−i3−i3000000−332i−2i−ii−33002i−2i−i−iii−3−3332-200000000−ii−3300000-11i3−i30000000
χ502-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21i3−i300i3i3−i3−i32i−2i−2i2i−i−iii-111-1000i3−i3i3i3−i3−i3000000−332i−2ii−i3−300−2i2i−i−iii−3−333-2200000000i−i3−3000001-1−i3i30000000
χ512-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21i3−i300i3i3−i3−i3−2i2i2i−2iii−i−i-111-1000i3−i3i3i3−i3−i30000003−3−2i2i−ii−33002i−2iii−i−i33−3−3-2200000000−ii−33000001-1−i3i30000000
χ522-22-222-1-2-11-2122-2-2-1-1201-2-1-1211-21i3−i300i3i3−i3−i3−2i2i−2i2iii−i−i-111-1000i3−i3i3i3−i3−i30000003−3−2i2ii−i3−300−2i2iii−i−i33−3−32-200000000i−i3−300000-11i3−i30000000
χ5344444-2-24-2-2-2-24-2-24-21-24-2-2-21-211-2-2-2-2-2-211114400-2-2-2-211114-2-2-2-21111040000-2-2-2-20000-2-20011111111000000000000000000000000000000
χ5444444-2-24-2-2-2-24-2-24-21-24-2-2-21-211-2-2-2-2-2-21111-4-400222211114-2-2-2-211110-40000222200002200-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5544444-2-24-2-2-2-24-2-24-21-2-4-2-2-21-211-2-22222-1-1-1-14400-2-2-2-21111-42222-1-1-1-10-4000022-2-2000022001111-1-1-1-1000000000000000000000000000000
χ5644444-2-24-2-2-2-24-2-24-21-2-4-2-2-21-211-2-22222-1-1-1-1-4-40022221111-42222-1-1-1-1040000-2-2220000-2-200-1-1-1-11111000000000000000000000000000000
χ574444-24-2-2-2-24-2-244-21-2-241-21-2-2-2-2-21-2-244-2-2-2-2004400001111-2-2-21111110040000000-2-2-2-200-2-200000000000000-200011110000000000000000
χ584444-24-2-2-2-24-2-244-21-2-241-21-2-2-2-2-21-2-244-2-2-2-200-4-400001111-2-2-211111100-4000000022220022000000000000002000-1-1-1-10000000000000000
χ594444-24-2-2-2-24-2-244-21-2-2-41-21-2-2-2-2-2122-4-42222004400001111222-1-1-1-1-1-100-40000000-2-22200-2-200000000000000200011-1-10000000000000000
χ604444-24-2-2-2-24-2-244-21-2-2-41-21-2-2-2-2-2122-4-4222200-4-400001111222-1-1-1-1-1-1004000000022-2-2002200000000000000-2000-1-1110000000000000000
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χ7144-4-44-2-242-222-42-2-4-21-20-2-22-121-1220023−23−33−330000−2323−232311-1-1023−2300−33−330000000000000000003−33−3-33-33000000000000000000000000000000
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χ7444-4-4-244-2-44-4-42-442-24-20-2-22-424-4220000000000000000-2-2220000000000000−2i32i300000000000000000000000−2i32i30000000000000000000000000
χ7544-4-4-244-2-44-4-42-442-24-20-2-22-424-4220000000000000000-2-22200000000000002i3−2i3000000000000000000000002i3−2i30000000000000000000000000
χ7644-4-4-2-24-2-442-422-22-2-210-2122-1-22-120023−2323−2323−230000000011-1-10−3300−33−330000−2i32i300000000000000000000000i3−i30003i−3i00000000000000000000
χ7744-4-4-2-24-2-442-422-22-2-210-2122-1-22-120023−2323−2323−230000000011-1-10−3300−33−3300002i3−2i300000000000000000000000−i3i3000−3i3i00000000000000000000
χ7844-4-4-2-24-2-442-422-22-2-210-2122-1-22-1200−2323−2323−23230000000011-1-103−3003−33−30000−2i32i300000000000000000000000i3−i3000−3i3i00000000000000000000
χ7944-4-4-2-24-2-442-422-22-2-210-2122-1-22-1200−2323−2323−23230000000011-1-103−3003−33−300002i3−2i300000000000000000000000−i3i30003i−3i00000000000000000000
χ804-44-44-24-44-42-44-22-44-2-20-424-2-2222-4000000004i−4i004i4i−4i−4i-222-200000000000000000−2i2i00000000−2i−2i2i2i0000000000000000000000000000000000
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χ864-44-4-24424-4-4-4-24-42-24-2022-24-2-4-42200000000004i−4i0000-222-200000000000000000004i−4i0000−2i2i000000000000000000−2i2i000000000000000000
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χ954-4-444-24-4-4-4-24-42244-2-20-42-4222-2-240000000000000000-22-220000000000000000000000023−2300000023−23−2323000000000000000000000000000000
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χ974-4-444-2-2-422-2-2-4224-21-20222-12-11-2-200003i−3i−3i3i0000−2i32i32i3−2i31-11-1000003i−3i−3i3i00000000000000−232300i3−i3−i3i33−3−33000000000000000000000000000000
χ984-4-444-2-2-422-2-2-4224-21-20222-12-11-2-200003i−3i−3i3i00002i3−2i3−2i32i31-11-1000003i−3i−3i3i0000000000000023−2300−i3i3i3−i3−333−3000000000000000000000000000000
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χ1004-4-444-2-2-422-2-2-4224-21-20222-12-11-2-20000−3i3i3i−3i00002i3−2i3−2i32i31-11-100000−3i3i3i−3i00000000000000−232300−i3i3i3−i33−3−33000000000000000000000000000000
χ1014-4-44-2442-4-4442-4-4-2-24-20222-42-44-2-20000000000000000-22-220000000000000000000000000000000000000000000000000000000000−2i32i300000
χ1024-4-44-2442-4-4442-4-4-2-24-20222-42-44-2-20000000000000000-22-2200000000000000000000000000000000000000000000000000000000002i3−2i300000
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χ1098-88-8-4-4-44-4444-4-4442220-2-2222-2-2-2-2−4i34i3002i32i3−2i3−2i300000000-111-10002i3−2i3−i3−i3i3i300000000000000000000000000000000000000000000000000000000
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χ1118-8-88-48-44448-44-8-8-42-4-40-24-2444-4-4200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).