Finite Group Databasebeta

← Group #13169272

Character table — Group #13169272

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212124444121212121212121212121212121212122266661212121212121212121212121212121244444121212121212121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111-1-1111111-1-111-1-1-1-1-1-1-1-11-11111-1-111-1-111111-1-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-11-1-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1111111-1-111-1-111-1-1-1-1-1-1-1111-1-111-1-1111111-11-1-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11-1-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111111111111111-1-11-1-1-1-1-1111111-1-11-1-1-1111-1-1-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-11111-1-111-11-11-1-1-111-1-11-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1111-1-1111111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111-1-1111-1-1-1-111111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-1111-1-1-1-11111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1111-1-1-1-111-1-111111-1-1111111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-1-1111111111-11111-1-1-1-111-1-1-11-11-1-1-111-1-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-111-1-1-1-1-1-1-1-111111111-111111-1-1-1-1-1-1111-1-1-1111-1-1-1-1-11-11
χ17222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-12222-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-100002222-1-1-1-122-1-1-1-12200-1-1-1-1-1-1-1-10000002000000-1-10000
χ18222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-12-200-1-111000022-2-2-1-111-2-211112-200-1-111-1-111000000-2000000110000
χ19222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1-220011-1-10000-2-22211-1-1-2-21111-220011-1-111-1-1000000-2000000110000
χ20222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-20011110000-2-2-2-2111122-1-1-1-1-2-200111111110000002000000-1-10000
χ21222222-1-1-1222222-12-1-1-22-1-12-1-1-1-12112222-1-1-1-1-2-2-2-211111111-2-200111100002222-1-1-1-122-1-1-1-1-2-2001111-1-1-1-1000000-2000000110000
χ22222222-1-1-1222222-12-1-1-22-1-12-1-1-1-121122-2-2-1-1-1-1-2-2-2-211111111-220011-1-1000022-2-2-1-111-2-21111-220011-1-1-1-1110000002000000-1-10000
χ23222222-1-1-1222222-12-1-1-22-1-12-1-1-1-1211-2-222-1-1-1-1-2-2-2-2111111112-200-1-1110000-2-22211-1-1-2-211112-200-1-11111-1-10000002000000-1-10000
χ24222222-1-1-1222222-12-1-1-22-1-12-1-1-1-1211-2-2-2-2-1-1-1-1-2-2-2-2111111112200-1-1-1-10000-2-2-2-2111122-1-1-1-12200-1-1-1-11111000000-2000000110000
χ2522222-122222-1-12-12-12-12-12-1-12-12-1-1220022-1-1-1-12-1-1-122-1-1-1-1-1-10222002222-1-100-1-100220000000-1-1200-1-100-1-1-1-1-1-10200200-1-1000-100
χ2622222-122222-1-12-12-12-12-12-1-12-12-1-1220022-1-1-1-12-1-1-122-1-1-1-1-1-102-2-20022-2-21100-1-100220000000-11-200-1-100-1-111110-200-20011000100
χ2722222-122222-1-12-12-12-12-12-1-12-12-1-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-22200-2-222-1-1001100-2-200000001-1200110011-1-1-1-10-200-20011000100
χ2822222-122222-1-12-12-12-12-12-1-12-12-1-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-200-2-2-2-211001100-2-2000000011-20011001111110200200-1-1000-100
χ2922222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-20022-1-1-1-1-2111-2-21111110-22-200-2-2221100-1-1002200000001-1-2001100-1-1-1-1110-20020011000-100
χ3022222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-20022-1-1-1-1-2111-2-21111110-2-2200-2-2-2-2-1-100-1-100220000000112001100-1-111-1-10200-200-1-1000100
χ3122222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-200-2-2-1-1-1-1-2111-2-2111111022-200222211001100-2-20000000-1-1-200-1-10011-1-1110200-200-1-1000100
χ3222222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-200-2-2-1-1-1-1-2111-2-211111102-220022-2-2-1-1001100-2-20000000-11200-1-1001111-1-10-20020011000-100
χ332222-12222-1-122-122-1-122-1-12-1-12-12-1222200-1-1-1-1-12-1-1-1-122-1-1-1-120222200-1-122-1-1002200000000-102-1-1-100-1-100-1-1-1-120020-1-10000-1000
χ342222-12222-1-122-122-1-122-1-12-1-12-12-1222200-1-1-1-1-12-1-1-1-122-1-1-1-120-2-2220011-2-2-1-1002200000000-10-21-1-100-1-1001111-200-201100001000
χ352222-12222-1-122-122-1-122-1-12-1-12-12-122-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-2022-2-200-1-1221100-2-200000000102-111001100-1-1-1-1-200-201100001000
χ362222-12222-1-122-122-1-122-1-12-1-12-12-122-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2-2-20011-2-21100-2-20000000010-2111001100111120020-1-10000-1000
χ372222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-22200-1-1-1-11-21111-2-21111-202-2-2-200-1-1-2-2-1-100220000000010211100-1-100-1-111200-20-1-100001000
χ382222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-22200-1-1-1-11-21111-2-21111-20-22-2-2001122-1-100220000000010-2-11100-1-10011-1-1-20020110000-1000
χ392222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2-2-200-1-1-1-11-21111-2-21111202-22200-1-1-2-21100-2-200000000-1021-1-1001100-1-111-20020110000-1000
χ402222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2-2-200-1-1-1-11-21111-2-2111120-22220011221100-2-200000000-10-2-1-1-100110011-1-1200-20-1-100001000
χ4122-2-2222-222-22-2-2-2-22220-2-2-2-222-2-22002i−2i2i−2i22-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i2-222-2-2000000002i−2i2i−2i0000000000000000000
χ4222-2-2222-222-22-2-2-2-22220-2-2-2-222-2-22002i−2i−2i2i22-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i-22-2-222000000002i−2i−2i2i0000000000000000000
χ4322-2-2222-222-22-2-2-2-22220-2-2-2-222-2-2200−2i2i2i−2i22-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i-22-2-22200000000−2i2i2i−2i0000000000000000000
χ4422-2-2222-222-22-2-2-2-22220-2-2-2-222-2-2200−2i2i−2i2i22-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i2-222-2-200000000−2i2i−2i2i0000000000000000000
χ4522-2-222-11-12-22-2-2-212-1-10-211-2-1-11123−32i−2i2i−2i-1-11100003−33−333−3−30000−i3i3−i3i300002i−2i2i−2i−ii−ii2-2-1-1110000−i3i3−i3i3−ii−ii00000000000003−30000
χ4622-2-222-11-12-22-2-2-212-1-10-211-2-1-11123−32i−2i−2i2i-1-11100003−33−333−3−30000−i3i3i3−i300002i−2i−2i2i−iii−i-2211-1-10000−i3i3i3−i3−iii−i0000000000000−330000
χ4722-2-222-11-12-22-2-2-212-1-10-211-2-1-11123−3−2i2i2i−2i-1-11100003−33−333−3−30000i3−i3−i3i30000−2i2i2i−2ii−i−ii-2211-1-10000i3−i3−i3i3i−i−ii0000000000000−330000
χ4822-2-222-11-12-22-2-2-212-1-10-211-2-1-11123−3−2i2i−2i2i-1-11100003−33−333−3−30000i3−i3i3−i30000−2i2i−2i2ii−ii−i2-2-1-1110000i3−i3i3−i3i−ii−i00000000000003−30000
χ4922-2-222-11-12-22-2-2-212-1-10-211-2-1-1112−332i−2i2i−2i-1-1110000−33−33−3−3330000i3−i3i3−i300002i−2i2i−2i−ii−ii2-2-1-1110000i3−i3i3−i3−ii−ii0000000000000−330000
χ5022-2-222-11-12-22-2-2-212-1-10-211-2-1-1112−332i−2i−2i2i-1-1110000−33−33−3−3330000i3−i3−i3i300002i−2i−2i2i−iii−i-2211-1-10000i3−i3−i3i3−iii−i00000000000003−30000
χ5122-2-222-11-12-22-2-2-212-1-10-211-2-1-1112−33−2i2i2i−2i-1-1110000−33−33−3−3330000−i3i3i3−i30000−2i2i2i−2ii−i−ii-2211-1-10000−i3i3i3−i3i−i−ii00000000000003−30000
χ5222-2-222-11-12-22-2-2-212-1-10-211-2-1-1112−33−2i2i−2i2i-1-1110000−33−33−3−3330000−i3i3−i3i30000−2i2i−2i2ii−ii−i2-2-1-1110000−i3i3−i3i3i−ii−i0000000000000−330000
χ5344444-2-2-2-244-2-24-2-2-2-214-2-21-2-21-21-2-2-2004411114-2-2-2-2-2111111040000-2-2000000-2-200-2-20000000-200001100110000000000000000000
χ5444444-2-2-2-244-2-24-2-2-2-214-2-21-2-21-21-2-2-200-4-411114-2-2-2-2-21111110-4000022000000220022000000020000-1-100-1-10000000000000000000
χ5544444-2-2-2-244-2-24-2-2-2-21-4-2-21-2-21-21-22200441111-422222-1-1-1-1-1-10-4000022000000-2-200-2-2000000020000-1-100110000000000000000000
χ5644444-2-2-2-244-2-24-2-2-2-21-4-2-21-2-21-21-22200-4-41111-422222-1-1-1-1-1-1040000-2-20000002200220000000-200001100-1-10000000000000000000
χ574444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-2-2-244001111-24-2-211-2-211114000-2-2000000-2-200-2-200000000-2000110011000000000000000000000
χ584444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-2-2-2-4-4001111-24-2-211-2-21111-400022000000220022000000002000-1-100-1-1000000000000000000000
χ594444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-222440011112-422-1-122-1-1-1-1-400022000000-2-200-2-2000000002000-1-10011000000000000000000000
χ604444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-222-4-40011112-422-1-122-1-1-1-14000-2-200000022002200000000-20001100-1-1000000000000000000000
χ614444-2-2444-2-2-2-2-2-241-2-241-2-21-2-2-2-214400001111-2-211-2-2-2-2111100440000-2-2-2-20000000000000000-2-2000000001111000000000000000
χ624444-2-2444-2-2-2-2-2-241-2-241-2-21-2-2-2-214400001111-2-211-2-2-2-2111100-4-40000222200000000000000002200000000-1-1-1-1000000000000000
χ634444-2-2444-2-2-2-2-2-241-2-2-41-2-21-2-2-2-21-4-40000111122-1-12222-1-1-1-1004-40000-2-2220000000000000000-220000000011-1-1000000000000000
χ644444-2-2444-2-2-2-2-2-241-2-2-41-2-21-2-2-2-21-4-40000111122-1-12222-1-1-1-100-44000022-2-200000000000000002-200000000-1-111000000000000000
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χ7044-4-44-2-22-24-4-22-422-2-21022-12-212-1-2−232300−4i4i11-1-10000−23233−333−3−3000000−2i32i30000002i−2i002i−2i000000000000i3−i300−ii0000000000000000000
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χ7444-4-4-24-22-2-224-42-42-21-202-1221-2-12-223−23−4i4i0011-1-10000−3323−23−3−33300002i3−2i30000002i−2i002i−2i000000000000−i3i300−ii000000000000000000000
χ7544-4-4-24-22-2-224-42-42-21-202-1221-2-12-2−23234i−4i0011-1-100003−3−232333−3−300002i3−2i3000000−2i2i00−2i2i000000000000−i3i300i−i000000000000000000000
χ7644-4-4-24-22-2-224-42-42-21-202-1221-2-12-2−2323−4i4i0011-1-100003−3−232333−3−30000−2i32i30000002i−2i002i−2i000000000000i3−i300−ii000000000000000000000
χ774-44-44444-4-44-44-4-4-44440444-4-4-4-4-4-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000
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χ814-44-44-244-4-442-2-42-4-24-20-24-22-42-422000000-22-2200000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ824-44-4-2444-42-2-442-4-4-2-240-2-2422-42-42000000-22-2200000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ834-44-4-2444-42-2-442-4-4-2-240-2-2422-42-42000000-22-22000000000000000000000000000000000000000000000000000000000002i3−2i300000000
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χ874-4-444-24-4-4-4-4224-24-24-202-42-2-424-22000000-222-2000000000000000000000023−23000000000000000000000000000023−23000000000000000
χ884-4-444-24-4-4-4-4224-24-24-202-42-2-424-22000000-222-20000000000000000000000−23230000000000000000000000000000−2323000000000000000
χ894-4-44-244-4-422-4-4-244-2-24022-4-22-4-242000000-222-20000000000000000000023−23000000000000000000000000000023−2300000000000000000
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χ914-4-44-2-24-4-42222-2-241-2-20-122122-2-2-10000001-1-11003-300003-33-30000000023−2323−2300000000000000000000000000−33−33000000000000000
χ924-4-44-2-24-4-42222-2-241-2-20-122122-2-2-10000001-1-11003-300003-33-300000000−2323−2323000000000000000000000000003−33−3000000000000000
χ934-4-44-2-24-4-42222-2-241-2-20-122122-2-2-10000001-1-1100-330000-33-330000000023−23−232300000000000000000000000000−333−3000000000000000
χ944-4-44-2-24-4-42222-2-241-2-20-122122-2-2-10000001-1-1100-330000-33-3300000000−232323−23000000000000000000000000003−3−33000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-48-88-44-4444-82-4-40-244-2-4-444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-4-44-444442220-2-2-2-222-2-2243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-4-44-444442220-2-2-2-222-2-22−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4-44-884-4-844-4-420-4-4244-24-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-4-444-4-884-84-42-40-42-44-24-2440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-488-84-44-444-82-4-402-4-4-24444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4-444-44-44442220222-2-2-2-2-2-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4-444-44-44442220222-2-2-2-2-2-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-444-8-8448-4-4-4-42044-2-44-2-4240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-44444-8-8-48-4-42-404-24-4-242-440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444444-4-4-42220-2-2-22-2-222-2000000-111-1006-60000-33-33000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444444-4-4-42220-2-2-22-2-222-2000000-111-100-6600003-33-3000000000000000000000000000000000000000000000000000000000

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