Finite Group Databasebeta

← Group #13168184

Character table — Group #13168184

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612122244366612121212121212121212121244446666121212121212121212121212441212121266121212121212121212121212121222444661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-111111111-1-11111-1-11111111111-1-1111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-111111111-1-111-1-1-1-111-1-1-1-1-1-1111-11111-1-1-1-11111-11-11-1-1-1-1-1111-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111111111-1-11-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-11-11-1-1-1-1-1111-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111111-1-111111111-1-1-11-1-1-1-11111-1-1-111-1-1-1-111-1-11-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111111111111-1-11-1-1-1-1-111-1-111-1-1-111-1-1-1-111-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-11-1-111-1-111-1-111-1-1111-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-111-1-1-111-1-1-1-1111-111-1111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-11-111-1111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1111-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-111111-1-111-1-1-1-1-111-1-1-1-111-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-1-1-1-1-1-111111111-1-1111-11111-1-1-1-111-111-1-1-1-111-1-11-1-11
χ17222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1220022-1-1-1-1-1-10022-1-10022-1-1-1-1-1-12200-1-1-1-1-1-1000020000-1-100000000
χ18222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-12-20022-1-1-1-11100-2-21100-2-21111-1-12-200-1-111110000-200001100000000
χ19222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1-2200-2-21111-1-10022-1-100-2-2111111-220011-1-1-1-10000-200001100000000
χ20222222-122-1-1222-122-1-122-1-12-1-1-1-12-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-211111100-2-2110022-1-1-1-111-2-200111111000020000-1-100000000
χ21222222-122-1-1222-122-1-1-22-1-12-1-1-1-12112222-1-1-1-1-2-2-2-211111111-2-20022-1-111110022-1-10022-1-1-1-1-1-1-2-2001111-1-10000-200001100000000
χ22222222-122-1-1222-122-1-1-22-1-12-1-1-1-121122-2-2-1-1-1-1-2-2-2-211111111-220022-1-111-1-100-2-21100-2-21111-1-1-220011-1-111000020000-1-100000000
χ23222222-122-1-1222-122-1-1-22-1-12-1-1-1-1211-2-222-1-1-1-1-2-2-2-2111111112-200-2-211-1-1110022-1-100-2-21111112-200-1-111-1-1000020000-1-100000000
χ24222222-122-1-1222-122-1-1-22-1-12-1-1-1-1211-2-2-2-2-1-1-1-1-2-2-2-2111111112200-2-211-1-1-1-100-2-2110022-1-1-1-1112200-1-1-1-1110000-200001100000000
χ2522222-12-1-1222222-1-12-12-12-1-1-12-12-1222200-1-1-1-1-12-1-1-1-122-1-1-1-12022-1-1222200220000-1-1000000-1-1-102-1-1-10000-1-1-1-1020200000-1-1-1000
χ2622222-12-1-1222222-1-12-12-12-1-1-12-12-1222200-1-1-1-1-12-1-1-1-122-1-1-1-120-2-2-1-1222200-2-2000011000000-1-1-10-21-1-1000011110-20-200000111000
χ2722222-12-1-1222222-1-12-12-12-1-1-12-12-122-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-202211-2-2-2-200220000-1-100000011102-1110000-1-1-1-10-20-200000111000
χ2822222-12-1-1222222-1-12-12-12-1-1-12-12-122-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-211-2-2-2-200-2-20000110000001110-211100001111020200000-1-1-1000
χ2922222-12-1-1222222-1-12-1-2-12-1-1-12-12-1-2-22200-1-1-1-11-21111-2-21111-202-2-1-122-2-20022000011000000-1-110-2-1110000-1-111020-20000011-1000
χ3022222-12-1-1222222-1-12-1-2-12-1-1-12-12-1-2-22200-1-1-1-11-21111-2-21111-20-22-1-122-2-200-2-20000-1-1000000-1-1102111000011-1-10-20200000-1-11000
χ3122222-12-1-1222222-1-12-1-2-12-1-1-12-12-1-2-2-2-200-1-1-1-11-21111-2-21111202-211-2-222002200001100000011-10-2-1-1-10000-1-1110-20200000-1-11000
χ3222222-12-1-1222222-1-12-1-2-12-1-1-12-12-1-2-2-2-200-1-1-1-11-21111-2-2111120-2211-2-22200-2-20000-1-100000011-1021-1-1000011-1-1020-20000011-1000
χ332222-1222222-1-1-122-1-122-1-12-12-12-1-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1022200000022-1-1-1-12222000000000-1-1200-1-1-1-1-1-1-1-10020200-1-1000-100
χ342222-1222222-1-1-122-1-122-1-12-12-12-1-1220022-1-1-1-12-1-1-122-1-1-1-1-1-102-2-20000002211-1-122-2-2000000000-11-200-1-1-1-1111100-20-20011000100
χ352222-1222222-1-1-122-1-122-1-12-12-12-1-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-222000000-2-2-1-111-2-2220000000001-12001111-1-1-1-100-20-20011000100
χ362222-1222222-1-1-122-1-122-1-12-12-12-1-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-2000000-2-21111-2-2-2-200000000011-200111111110020200-1-1000-100
χ372222-1222222-1-1-122-1-12-2-1-12-12-12-1-1-2-20022-1-1-1-1-2111-2-21111110-22-2000000-2-2-1-1-1-122-2-20000000001120011-1-1-1-1110020-200-1-1000100
χ382222-1222222-1-1-122-1-12-2-1-12-12-12-1-1-2-20022-1-1-1-1-2111-2-21111110-2-22000000-2-211-1-122220000000001-1-20011-1-111-1-100-2020011000-100
χ392222-1222222-1-1-122-1-12-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-2111-2-2111111022-200000022-1-111-2-2-2-2000000000-11200-1-111-1-11100-2020011000-100
χ402222-1222222-1-1-122-1-12-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-2111-2-211111102-22000000221111-2-222000000000-1-1-200-1-11111-1-10020-200-1-1000100
χ412-22-2222-2-22-22-2-2-222220-2-22-2-22-2-22002-22i−2i22-2-200000000000000002-22-20000002i−2i2i−2i002i−2i2i2i−2i−2i2-2000000002i−2i0000000000000000000
χ422-22-2222-2-22-22-2-2-222220-2-22-2-22-2-22002-2−2i2i22-2-200000000000000002-22-2000000−2i2i−2i2i00−2i2i−2i−2i2i2i2-200000000−2i2i0000000000000000000
χ432-22-2222-2-22-22-2-2-222220-2-22-2-22-2-2200-222i−2i22-2-20000000000000000-22-220000002i−2i2i−2i00−2i2i−2i−2i2i2i-22000000002i−2i0000000000000000000
χ442-22-2222-2-22-22-2-2-222220-2-22-2-22-2-2200-22−2i2i22-2-20000000000000000-22-22000000−2i2i−2i2i002i−2i2i2i−2i−2i-2200000000−2i2i0000000000000000000
χ452-22-222-1-2-2-112-2-2122-1-10-21-1-21-11123−32-22i−2i-1-11100003−33−333−3−300002-2-113−3−i3i3002i−2i−ii002i−2i−i−iii-1100003−3−i3i3−ii000000000−i3i300000000
χ462-22-222-1-2-2-112-2-2122-1-10-21-1-21-11123−32-2−2i2i-1-11100003−33−333−3−300002-2-113−3i3−i300−2i2ii−i00−2i2iii−i−i-1100003−3i3−i3i−i000000000i3−i300000000
χ472-22-222-1-2-2-112-2-2122-1-10-21-1-21-11123−3-222i−2i-1-11100003−33−333−3−30000-221-1−33−i3i3002i−2i−ii00−2i2iii−i−i1-10000−33−i3i3−ii000000000i3−i300000000
χ482-22-222-1-2-2-112-2-2122-1-10-21-1-21-11123−3-22−2i2i-1-11100003−33−333−3−30000-221-1−33i3−i300−2i2ii−i002i−2i−i−iii1-10000−33i3−i3i−i000000000−i3i300000000
χ492-22-222-1-2-2-112-2-2122-1-10-21-1-21-1112−332-22i−2i-1-1110000−33−33−3−33300002-2-11−33i3−i3002i−2i−ii002i−2i−i−iii-110000−33i3−i3−ii000000000i3−i300000000
χ502-22-222-1-2-2-112-2-2122-1-10-21-1-21-1112−332-2−2i2i-1-1110000−33−33−3−33300002-2-11−33−i3i300−2i2ii−i00−2i2iii−i−i-110000−33−i3i3i−i000000000−i3i300000000
χ512-22-222-1-2-2-112-2-2122-1-10-21-1-21-1112−33-222i−2i-1-1110000−33−33−3−3330000-221-13−3i3−i3002i−2i−ii00−2i2iii−i−i1-100003−3i3−i3−ii000000000−i3i300000000
χ522-22-222-1-2-2-112-2-2122-1-10-21-1-21-1112−33-22−2i2i-1-1110000−33−33−3−3330000-221-13−3−i3i300−2i2ii−i002i−2i−i−iii1-100003−3−i3i3i−i000000000i3−i300000000
χ5344444-2-2-2-2-2-2444-2-2-2-214-2-21-21-21-2-2-2-244001111-24-2-211-2-211114000-2-2-2-2-2-2000000000000000011-20001100000000000000000000000
χ5444444-2-2-2-2-2-2444-2-2-2-214-2-21-21-21-2-2-2-2-4-4001111-24-2-211-2-21111-40002222220000000000000000-1-12000-1-100000000000000000000000
χ5544444-2-2-2-2-2-2444-2-2-2-21-4-2-21-21-21-2-222440011112-422-1-122-1-1-1-1-4000-2-2-2-2220000000000000000112000-1-100000000000000000000000
χ5644444-2-2-2-2-2-2444-2-2-2-21-4-2-21-21-21-2-222-4-40011112-422-1-122-1-1-1-140002222-2-20000000000000000-1-1-20001100000000000000000000000
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χ604444-24-244-2-2-2-2-2-24-21-2-4-21-2-2-21-21-22200-4-41111-422222-1-1-1-1-1-10400000000-2-200222200000000000-2000011-1-10000000000000000000
χ614444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-2-214400001111-2-211-2-2-2-21111004400000000-2-20000-2-20000000000-2-20000001111000000000000000
χ624444-2-24-2-244-2-2-24-21-2-241-2-21-2-2-2-214400001111-2-211-2-2-2-2111100-4-40000000022000022000000000022000000-1-1-1-1000000000000000
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χ644444-2-24-2-244-2-2-24-21-2-2-41-2-21-2-2-2-21-4-40000111122-1-12222-1-1-1-100-4400000000220000-2-20000000000-22000000-1-111000000000000000
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χ814-44-4-24-2-4-4-22-22224-21-202-1-22212-1-223−2300−4i4i11-1-1000023−23−33−3−33300000000002i3−2i3002i−2i2i−2i0000000000000000−i3i3−ii0000000000000000000
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χ834-44-4-24-2-4-4-22-22224-21-202-1-22212-1-2−232300−4i4i11-1-10000−23233−333−3−30000000000−2i32i3002i−2i2i−2i0000000000000000i3−i3−ii0000000000000000000
χ844-4-444444-4-4-4-4-444-44440-4-4-444-4-44-40000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
χ854-4-4444-24-422-4-44-2-44-2-20-4224-222-2-4000000-222-20000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ864-4-4444-24-422-4-44-2-44-2-20-4224-222-2-4000000-222-200000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
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χ914-4-44-2-24-22-4-422-2421-2-20-1221-222-2-10000001-1-11003-300003-33-300000000000023−23000023−23000000000000000000−33−33000000000000000
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χ934-4-44-2-24-22-4-422-2421-2-20-1221-222-2-10000001-1-1100-330000-33-3300000000000023−230000−2323000000000000000000−333−3000000000000000
χ944-4-44-2-24-22-4-422-2421-2-20-1221-222-2-10000001-1-1100-330000-33-33000000000000−2323000023−230000000000000000003−3−33000000000000000
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
χ9788-8-88-4-44-44-4-88-844-4-420-4-4-24-242440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-884-44-444-8-42-40-42444-2-4-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-484-4-884-44-842-4-402-44-244-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-44-44-44-4444222022-2-2-2-22-2-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-44-44-4444222022-2-2-2-22-2-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-48448-8-444-8-42-4-40-24-4-24-444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-444-44-4444-42220-2-22-2-22-2-2243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444-44-4444-42220-2-22-2-22-2-22−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000
χ1058-8-888-4-4-4444-8-88-44-4-42044-2-424-2-440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-48-48-84444-4-4-8-42-404-24-4-4-24240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-444444-4-442220-2-2-222-2-22-2000000-111-1006-60000-33-33000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-444444-4-442220-2-2-222-2-22-2000000-111-100-6600003-33-3000000000000000000000000000000000000000000000000000000000

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