Finite Group Databasebeta

← Group #13168329

Character table — Group #13168329

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212122444661212121212121212121212121212224444441212121266612121212121212121212121212446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-1111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111111-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-11-1-111-1-11-111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1111-111-1-111-1-11111-11-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111111-1-111-1-11-1-1-11111-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1111-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111111-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-11111111111-1-11111111-11-111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1111111-1-11111-1-1-11-11-1-1111111-1-1-1-11111-1-1-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11-1-1-1-11111-1-1-1111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111-1-1-1-1-111-1-1111-1-1-11111-11-11
χ17222222-1-12-122222-1-1-122-1-12-12-12-1-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-10222002222220000-1-1-1-1220000000000000-12-1-1-100-1-1-1-1-1-120-1-100000-100
χ18222222-1-12-122222-1-1-122-1-12-12-12-1-1222200-1-1-1-1-1222-1-1-1-1-1-1-1-102-2-20022-2-2220000-1-111-2-20000000000000-1-21-1-100-1-11111-201100000100
χ19222222-1-12-122222-1-1-122-1-12-12-12-1-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-10-22200-2-222-2-2000011-1-1-2-2000000000000012-1110011-1-1-1-1-201100000100
χ20222222-1-12-122222-1-1-122-1-12-12-12-1-122-2-200-1-1-1-1-1222-1-1-1-1-1-1-1-10-2-2-200-2-2-2-2-2-2000011112200000000000001-21110011111120-1-100000-100
χ21222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-22200-1-1-1-11-2-2-2111111110-22-200-2-222220000-1-111-2-200000000000001-2-1-1-10011-1-111201100000-100
χ22222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-22200-1-1-1-11-2-2-2111111110-2-2200-2-2-2-2220000-1-1-1-1220000000000000121-1-1001111-1-1-20-1-100000100
χ23222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-2-2-200-1-1-1-11-2-2-211111111022-2002222-2-200001111220000000000000-1-2-11100-1-1-1-111-20-1-100000100
χ24222222-1-12-122222-1-1-12-2-1-12-12-12-1-1-2-2-2-200-1-1-1-11-2-2-21111111102-220022-2-2-2-2000011-1-1-2-20000000000000-1211100-1-111-1-1201100000-100
χ2522222-12222-1-122-122-1-122-1-1-1-12-12-1220022-1-1-1-12-1-1-1-1-122-1-1-1-120222200-1-10022-1-10022002200000000-1-1-10-1200-1-100-1-1-1-10200-1-100-1000
χ2622222-12222-1-122-122-1-122-1-1-1-12-12-1220022-1-1-1-12-1-1-1-1-122-1-1-1-120-2-22200110022-1-100-2-200-2-200000000-1-1-101-200-1-10011110-20011001000
χ2722222-12222-1-122-122-1-122-1-1-1-12-12-12200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2022-2-200-1-100-2-211002200-2-2000000001110-12001100-1-1-1-10-20011001000
χ2822222-12222-1-122-122-1-122-1-1-1-12-12-12200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-2-2-2001100-2-21100-2-200220000000011101-200110011110200-1-100-1000
χ2922222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-20022-1-1-1-1-211111-2-21111-202-2-2-200-1-10022-1-100-2-200220000000011101200-1-100-1-1110-200-1-1001000
χ3022222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-20022-1-1-1-1-211111-2-21111-20-22-2-200110022-1-1002200-2-2000000001110-1-200-1-10011-1-102001100-1000
χ3122222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-200-2-2-1-1-1-1-211111-2-21111202-22200-1-100-2-21100-2-200-2-200000000-1-1-1012001100-1-11102001100-1000
χ3222222-12222-1-122-122-1-1-22-1-1-1-12-12-1-2-200-2-2-1-1-1-1-211111-2-2111120-2222001100-2-2110022002200000000-1-1-10-1-200110011-1-10-200-1-1001000
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χ342222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1-220011-1-100-1-111-2-222000000-2-2-2-21111-211200-1-111-1-10000000000110000
χ352222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-12-200-1-1110011-1-122-2-2000000-2-2-2-211112-1-1-20011-1-1110000000000110000
χ362222-1222-1222-1-122-12-12-12-12-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-2-2001111001111-2-2-2-20000002222-1-1-1-1-211-2001111110000000000-1-10000
χ372222-1222-1222-1-122-12-1-2-12-12-1-1-1-12112222-1-1-1-1-2-211-2-2111111-2-200111100-1-1-1-12222000000-2-2221111-211-200-1-1-1-1110000000000-1-10000
χ382222-1222-1222-1-122-12-1-2-12-12-1-1-1-121122-2-2-1-1-1-1-2-211-2-21111112-200-1-11100-1-111-2-22200000022-2-2-1-1-1-12-1-1-200-1-111110000000000110000
χ392222-1222-1222-1-122-12-1-2-12-12-1-1-1-1211-2-222-1-1-1-1-2-211-2-2111111-220011-1-10011-1-122-2-200000022-2-2-1-1-1-1-21120011-1-1-1-10000000000110000
χ402222-1222-1222-1-122-12-1-2-12-12-1-1-1-1211-2-2-2-2-1-1-1-1-2-211-2-21111112200-1-1-1-1001111-2-2-2-2000000-2-22211112-1-12001111-1-10000000000-1-10000
χ412-22-2222-2-2-22-22-2-222220-2-22-2-22-2-22002-22i−2i22-2-200000000000000000000002-22i−2i2i−2i2-2000000002i−2i00000000002-22i−2i0000000000002i−2i0000
χ422-22-2222-2-2-22-22-2-222220-2-22-2-22-2-22002-2−2i2i22-2-200000000000000000000002-2−2i2i−2i2i2-200000000−2i2i00000000002-2−2i2i000000000000−2i2i0000
χ432-22-2222-2-2-22-22-2-222220-2-22-2-22-2-2200-222i−2i22-2-20000000000000000000000-222i−2i2i−2i-2200000000−2i2i0000000000-222i−2i000000000000−2i2i0000
χ442-22-2222-2-2-22-22-2-222220-2-22-2-22-2-2200-22−2i2i22-2-20000000000000000000000-22−2i2i−2i2i-22000000002i−2i0000000000-22−2i2i0000000000002i−2i0000
χ452-22-2-122-21-22-2-11-22-12-101-2-1-21-11123−32-22i−2i-1-111003−3003−333−3−30000−i3i33−300-11−ii2i−2i2-2000000002i−2i−i3−i3i3i30−i3i3000-11−ii3−30000000000−ii0000
χ462-22-2-122-21-22-2-11-22-12-101-2-1-21-11123−32-2−2i2i-1-111003−3003−333−3−30000i3−i33−300-11i−i−2i2i2-200000000−2i2ii3i3−i3−i30i3−i3000-11i−i3−30000000000i−i0000
χ472-22-2-122-21-22-2-11-22-12-101-2-1-21-11123−3-222i−2i-1-111003−3003−333−3−30000−i3i3−33001-1−ii2i−2i-2200000000−2i2ii3i3−i3−i30−i3i30001-1−ii−330000000000i−i0000
χ482-22-2-122-21-22-2-11-22-12-101-2-1-21-11123−3-22−2i2i-1-111003−3003−333−3−30000i3−i3−33001-1i−i−2i2i-22000000002i−2i−i3−i3i3i30i3−i30001-1i−i−330000000000−ii0000
χ492-22-2-122-21-22-2-11-22-12-101-2-1-21-1112−332-22i−2i-1-11100−3300−33−3−3330000i3−i3−3300-11−ii2i−2i2-2000000002i−2ii3i3−i3−i30i3−i3000-11−ii−330000000000−ii0000
χ502-22-2-122-21-22-2-11-22-12-101-2-1-21-1112−332-2−2i2i-1-11100−3300−33−3−3330000−i3i3−3300-11i−i−2i2i2-200000000−2i2i−i3−i3i3i30−i3i3000-11i−i−330000000000i−i0000
χ512-22-2-122-21-22-2-11-22-12-101-2-1-21-1112−33-222i−2i-1-11100−3300−33−3−3330000i3−i33−3001-1−ii2i−2i-2200000000−2i2i−i3−i3i3i30i3−i30001-1−ii3−30000000000i−i0000
χ522-22-2-122-21-22-2-11-22-12-101-2-1-21-1112−33-22−2i2i-1-11100−3300−33−3−3330000−i3i33−3001-1i−i−2i2i-22000000002i−2ii3i3−i3−i30−i3i30001-1i−i3−30000000000−ii0000
χ532-2-222222-2-2-2-2-222-2222022-2-2-2-22-2-20000002-22-2000000000000000000000000000000002-22i−2i2i−2i002i−2i2i−2i0000000000000000002-22i−2i000000
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χ5944444-2-2-24-2-2-244-2-2-21-2-4-21-21-2-2-2-21-4-4000011112222-1-122-1-1-1-1004-40000-2-2000000002200000000000000002-200000011-1-1000000000000
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χ894-44-4-2-24-42-4-22-2224-2-2102212-1-2-12-223−2300−4i4i11-1-100−330023−23−3−33300002i3−2i30000002i−2i2i−2i00000000000000000−i3i300000−ii000000000000000000
χ904-44-4-2-24-42-4-22-2224-2-2102212-1-2-12-2−2323004i−4i11-1-1003−300−232333−3−300002i3−2i3000000−2i2i−2i2i00000000000000000−i3i300000i−i000000000000000000
χ914-44-4-2-24-42-4-22-2224-2-2102212-1-2-12-2−232300−4i4i11-1-1003−300−232333−3−30000−2i32i30000002i−2i2i−2i00000000000000000i3−i300000−ii000000000000000000
χ924-4-4444-2-2-42-4-4-4442-2-240-2-2-42-42422000000-22-22000000000000000000000000000000004-40000000000000000000000000000-2200000000
χ934-4-4444-2-2-42-4-4-4442-2-240-2-2-42-42422000000-22-2200000000000000000000000000000000-4400000000000000000000000000002-200000000
χ944-4-444-244-4-422-44-2-44-2-204-2222-4-2-42000000-22-2200000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000
χ954-4-444-244-4-422-44-2-44-2-204-2222-4-2-42000000-22-220000000000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000
χ964-4-44-24442-4-4-42-24-4-24-20-242-422-22-4000000-22-220000000000000000000000000000000000004i−4i00−2i2i−2i2i0000000000000000000000000000
χ974-4-44-24442-4-4-42-24-4-24-20-242-422-22-4000000-22-22000000000000000000000000000000000000−4i4i002i−2i2i−2i0000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-44-4-4-8844-842-4-40-244-4-4-24240000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-48-8-484-4444-8-4-42044-2-424-2-440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-4-44-444442220-2-2-222-2-22-2000000-111-100006-600-33-33000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-4-44-444442220-2-2-222-2-22-2000000-111-10000-66003-33-3000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-44-84-448-84-4-42-404-2-4-24-444200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444-44-444-42220-2-22-2-22-2-2243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444-44-444-42220-2-22-2-22-2-22−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-4-8444-88-44-42-40-424-244-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-444-8-84-4842-4-402-4444-2-4-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4884-8444-4-4-8-4-420-4-4-24-242440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444444-4-44222022-2-2-2-22-2-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444444-4-44222022-2-2-2-22-2-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000000

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