Finite Group Databasebeta

← Group #13168201

Character table — Group #13168201

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212122244446666366612121212121212121244466666612121212121212121212121212121212224412121212121212121212121244446612121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1111111111111111-1-1111111-1-1111-1-1-11111-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111111111111111-1111111-1-111-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-11
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111111111111-11-1-111-1-1-1-1-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111-1-1-1-111111-1-1-1-1-1111111-1-1-11
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-111-1-111-1-11-11-11111-1-111-11-1-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-1-1-11-111
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-111-1-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-1-1111-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111111111111111-11-1-111-1-111-1-1-1-1-1111-1-111-1-1-1-111
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-111-1-1111111-1-111-1-11111-1-1-1-111-111-1-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11111-1-111-11-1-111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11-111-1-111-1-1111-11-11111-1-1-1-1-11-11
χ17222222-122-1-1222-12-1-122-1-122-1-1-12-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1222000000220022-1-1-1-10000002200-122-1-1-1-1-1-1-1-1-10200-1-1000000-1000
χ18222222-122-1-1222-12-1-122-1-122-1-1-12-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22000000220022-1-111000000-2-200-1-2-21-1-1-1-111110-200110000001000
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χ2522222-122-1222-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-100222-1-1-1-1-1-1-1-1-1-1220022-1-1-1-100222000-1-1-1-10000200000-1-1-1-1000000
χ2622222-122-1222-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-100-222-1-1-1-111-1-111-2-20022-1-1-1-100-2-2-200011110000-2000001111000000
χ2722222-122-1222-1-1222-1-122-1-1-12-1-1-12-1-122-1-1-1-1-2-222-2-21111-1-1-1-1222-1-1-1-1-1-1002-2-21111-1-111-1-12200-2-2111100-2-22000-1-1-1-10000-2000001111000000
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χ362222-122-1222-1222-1-12-12-12-1-1-122-1-122-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2011111100-2-20000-2-21111110000011-2000011110022000000000-1-10
χ372222-122-1222-1222-1-12-1-2-12-1-1-122-1-1-2-21111112200-2-22222-1-1-1-1-211-2-211112-20-1-1-1-1-1-100-2-200002211111100000-11-20000-1-111002-2000000000-110
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χ844-44-44-2-2-42224-22-2-4-21-202-12-221-12-2−232300−23−23232300-440000001-11-10003−333−3−30000000002-20023−232-20000000000000000-11−3300000000000000000000
χ854-44-4-2442-4-4-4-24-442-24-202-42-224-42-20000000000004i−4i0000-22-22000000000000000000004i−4i000000−2i2i−2i−2i2i2i00000000000000000000000000000000
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χ894-44-4-2-2422-4-4-2-2242-2-21022-112-22-1-2−23230033−3−300004i−4i2i3−2i32i3−2i31-11-1000−232333−3−300000−i3i3−i3i300−2i2i000000−2i2iii−i−i00000000000000000000000000000000
χ904-44-4-2-2422-4-4-2-2242-2-21022-112-22-1-2−23230033−3−30000−4i4i−2i32i3−2i32i31-11-1000−232333−3−300000i3−i3i3−i3002i−2i0000002i−2i−i−iii00000000000000000000000000000000
χ914-4-44444-4-4-44-4-44-444440-4-4-4-44-444-40000000000000000004-4-44000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-2-4-42-2-4-4424-2-24022-4-4-22-242000000000000000000-222-20000000000000000000000000023−2300000000000000000023−23000000000000000000
χ934-4-4444-2-4-42-2-4-4424-2-24022-4-4-22-242000000000000000000-222-200000000000000000000000000−2323000000000000000000−2323000000000000000000
χ944-4-444-24-42-44-42-2-444-2-20-422242-2-2-400000000000000−2i32i32i3−2i3-222-200000000000000−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ954-4-444-24-42-44-42-2-444-2-20-422242-2-2-4000000000000002i3−2i3−2i32i3-222-2000000000000002i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ964-4-44-2442-4-442-44-4-2-24-202-422-2-44-2200−2i32i3−2i32i32i3−2i30000000000-222-20−2i32i300−2i32i32i3−2i3000000000000000000000000000000000000000000000000000000000
χ974-4-44-2442-4-442-44-4-2-24-202-422-2-44-22002i3−2i32i3−2i3−2i32i30000000000-222-202i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000000000000000000000000000
χ984-4-44-24-22-42-22-442-21-2-20-122212-2-2-100−2i32i3−2i32i32i3−2i300000000001-1-110i3−i300i3−i3−i3i30000000000000000023−23000000000000000000−333i−3i0000000000000000
χ994-4-44-24-22-42-22-442-21-2-20-122212-2-2-100−2i32i3−2i32i32i3−2i300000000001-1-110i3−i300i3−i3−i3i300000000000000000−23230000000000000000003−3−3i3i0000000000000000
χ1004-4-44-24-22-42-22-442-21-2-20-122212-2-2-1002i3−2i32i3−2i3−2i32i300000000001-1-110−i3i300−i3i3i3−i30000000000000000023−23000000000000000000−33−3i3i0000000000000000
χ1014-4-44-24-22-42-22-442-21-2-20-122212-2-2-1002i3−2i32i3−2i3−2i32i300000000001-1-110−i3i300−i3i3i3−i300000000000000000−23230000000000000000003−33i−3i0000000000000000
χ1024-4-44-2-2422-4422-2-4-2-2-21022-1-1-22-21200−2i32i3i3−i3−i3i3000000−2i32i32i3−2i31-1-110−2i32i300i3−i3−i3i300000i3−i3−i3i3000000000000-333-300000000000000000000000000000000
χ1034-4-44-2-2422-4422-2-4-2-2-21022-1-1-22-21200−2i32i3i3−i3−i3i30000002i3−2i3−2i32i31-1-110−2i32i300i3−i3−i3i300000−i3i3i3−i30000000000003-3-3300000000000000000000000000000000
χ1044-4-44-2-2422-4422-2-4-2-2-21022-1-1-22-212002i3−2i3−i3i3i3−i3000000−2i32i32i3−2i31-1-1102i3−2i300−i3i3i3−i300000i3−i3−i3i30000000000003-3-3300000000000000000000000000000000
χ1054-4-44-2-2422-4422-2-4-2-2-21022-1-1-22-212002i3−2i3−i3i3i3−i30000002i3−2i3−2i32i31-1-1102i3−2i300−i3i3i3−i300000−i3i3i3−i3000000000000-333-300000000000000000000000000000000
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
χ10888-8-88-4-48-4-44-8444-8-42-40-42-444-2-24400000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-48-4-48-444-8-8442-4-402-4-44-2444-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200006i−6i6i−6i0000000000-1-11100000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-20000−6i6i−6i6i0000000000-1-111000003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1128-88-8-48-44-844-48-8-442-4-40-244-4-2-44420000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-44444-4-44-442220-2-2-22-22-2-2243−4300−23−2323230000000000-11-11000−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-44444-4-44-442220-2-2-22-22-2-22−4343002323−23−230000000000-11-1100023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1158-8-888-4-4-844-4-84-448-42-404-244-4-22-440000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4444-444-44-42220-2-2-2-22-222-200−4i34i32i3−2i3−2i32i30000000000-111-102i3−2i300−i3i3i3−i3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4444-444-44-42220-2-2-2-22-222-2004i3−4i3−2i32i32i3−2i30000000000-111-10−2i32i300i3−i3−i3i3000000000000000000000000000000000000000000000000000000000

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