Finite Group Databasebeta

← Group #13168421

Character table — Group #13168421

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666333466666666612121212121212124444121212123666121212121212121212224466666666661212121212121212121212124466612121212121212121224444661212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-11-1-11111111111111111111111-1-1-1-11-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-111-1-11-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-111-11-1-11-1-1-1-1-1-111-111
χ51111111111111111111111111111111111111-1-11111111111111111111111-11111111111-1-1-1-111-1-11111-1-11111-11-1-111-1-1-11-1-11-1-1-1-1-1-111-1-1-1
χ61111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-11-1-1-1-11111-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-11111111111111-1-1-111-1-1-1-1-111-1-1-1-111111-1-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-11-111111-1-1-1-1-111-1-111-1-1-111-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-1111-1-1-111-1-1-1-11-11-1111-1-111-11-1-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-111111-1-111-11-111-1-1-1-11-111-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111-11-1-1-1-1-11111-11-111-1-1-1-11-11-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1111-1-111111-11-1111-1-111-11-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111111111111-1-111-1-1-1-1-1-1-1-111111-11-1-1-1-1-111-1-1-111-1-111-1-1-1111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1111-1-11111-111-1-1-1-111111-1-1-11
χ17222222-122-12-12-122-12-12-12-1-12-12-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-120020022-1-1-1-1-1-1-1-1-1-12222-1-1-1-122000020-1-100-1-120000-1-1-1-10000000
χ18222222-122-12-12-122-12-12-12-1-12-12-1-1-1-122-1-1-1-122-2-21111-1-1-1-1222-1-1-1-1-1-1-200200-2-2111111-1-1-1-1-2-2221111-2-2000020-1-100-1-1-2000011110000000
χ19222222-122-12-12-122-12-12-12-1-12-12-1-1-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1200-20022-1-1-1-1-1-1111122-2-2-1-1-1-1-2-20000-20110011-2000011110000000
χ20222222-122-12-12-122-12-12-12-1-12-12-1-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-1-200-200-2-21111111111-2-2-2-21111220000-2011001120000-1-1-1-10000000
χ21222222-122-12-12-122-12-1-2-12-1-12-12-1-111-2-211112222-1-1-1-1-1-1-1-1-2-2-2111111-200-200-2-2111111-1-1112222-1-1-1-1220000-20-1-10011-2000011-1-10000000
χ22222222-122-12-12-122-12-1-2-12-1-12-12-1-111-2-2111122-2-21111-1-1-1-1-2-2-2111111200-20022-1-1-1-1-1-1-1-111-2-2221111-2-20000-20-1-1001120000-1-1110000000
χ23222222-122-12-12-122-12-1-2-12-1-12-12-1-111-2-21111-2-222-1-1-1-1-1-1-1-1-2-2-2111111-200200-2-211111111-1-122-2-2-1-1-1-1-2-20000201100-1-120000-1-1110000000
χ24222222-122-12-12-122-12-1-2-12-1-12-12-1-111-2-21111-2-2-2-21111-1-1-1-1-2-2-211111120020022-1-1-1-1-1-111-1-1-2-2-2-21111220000201100-1-1-2000011-1-10000000
χ2522222-122-1222-12-122-1-122-1-1-1-12-12-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-1222022-1-122-1-1-1-10000-1-100-1-1-1-100-1-1-1-10200-1-10002002000000-1-1000
χ2622222-122-1222-12-122-1-122-1-1-1-12-12-122-1-1-1-1-1-100222222-1-1-1-12-1-122-1-1-1-12-2-20-2-2-1-122-1-1-1-10000-1-100-1-1-1-10011110-20011000-200-200000011000
χ2722222-122-1222-12-122-1-122-1-1-1-12-12-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-22202211-2-2111100001100111100-1-1-1-10200-1-1000-200-200000011000
χ2822222-122-1222-12-122-1-122-1-1-1-12-12-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2-20-2-211-2-211110000110011110011110-200110002002000000-1-1000
χ2922222-122-1222-12-122-1-1-22-1-1-1-12-12-1-2-211111100222222-1-1-1-1-211-2-21111-22-202211-2-211110000-1-100-1-1-1-100-1-1-110-20011000200-2000000-11000
χ3022222-122-1222-12-122-1-1-22-1-1-1-12-12-1-2-211111100222222-1-1-1-1-211-2-21111-2-220-2-211-2-211110000-1-100-1-1-1-100111-10200-1-1000-20020000001-1000
χ3122222-122-1222-12-122-1-1-22-1-1-1-12-12-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-2111122-2022-1-122-1-1-1-100001100111100-1-1-110-20011000-20020000001-1000
χ3222222-122-1222-12-122-1-1-22-1-1-1-12-12-1-2-211111100-2-2-2-2-2-2-1-1-1-1-211-2-211112-220-2-2-1-122-1-1-1-100001100111100111-10200-1-1000200-2000000-11000
χ332222-122-122-12222-1-1-122-1-122-1-1-1-122222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10222-1-100000000222200-1-10000002-1-12-1-1-1-1-1-1-1-1002200000-1-100-100
χ342222-122-122-12222-1-1-122-1-122-1-1-1-122222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-221100000000222200-1-1000000-211-2-11-1-111-1-100-2-2000001100100
χ352222-122-122-12222-1-1-122-1-122-1-1-1-1222222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1022-2-1-100000000-2-2-2-200110000002-1-121-111-1-11100-2-2000001100100
χ362222-122-122-12222-1-1-122-1-122-1-1-1-1222222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-21100000000-2-2-2-20011000000-211-211111111002200000-1-100-100
χ372222-122-122-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-222000000-1-1-1-111111111102-2-2-1-10000000022-2-200-1-10000002-1-1-211-1-11111002-200000-1-100100
χ382222-122-122-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-222000000-1-1-1-11111111110-22-2110000000022-2-200-1-1000000-21121-1-1-1-1-11100-22000001100-100
χ392222-122-122-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-2-2-2000000-1-1-1-111111111102-22-1-100000000-2-22200110000002-1-1-2-111111-1-100-22000001100-100
χ402222-122-122-12222-1-1-12-2-1-122-1-1-1-12-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111110-2221100000000-2-2220011000000-2112-1-111-1-1-1-1002-200000-1-100100
χ412-22-2222-222-2-2-2-2-222220-2-22-2-222-2-2000000002-22i−2i2i2i−2i−2i22-2-2000000000000000000000002-2002i−2i2-22i2i−2i−2i2i−2i0000002-2000000000002i−2i0000000
χ422-22-2222-222-2-2-2-2-222220-2-22-2-222-2-2000000002-2−2i2i−2i−2i2i2i22-2-2000000000000000000000002-200−2i2i2-2−2i−2i2i2i−2i2i0000002-200000000000−2i2i0000000
χ432-22-2222-222-2-2-2-2-222220-2-22-2-222-2-200000000-222i−2i2i2i−2i−2i22-2-200000000000000000000000-22002i−2i-222i2i−2i−2i−2i2i000000-2200000000000−2i2i0000000
χ442-22-2222-222-2-2-2-2-222220-2-22-2-222-2-200000000-22−2i2i−2i−2i2i2i22-2-200000000000000000000000-2200−2i2i-22−2i−2i2i2i2i−2i000000-22000000000002i−2i0000000
χ452-22-222-1-22-1-21-21-22-12-101-2-11-2-12113−30033−3−32-22i−2i−i−iii-1-1110003−333−3−300000000−i3i3−i3−i3i3i3-113−32i−2i2-2−i−iii2i−2i000000-11003−300000−i3i3−ii0000000
χ462-22-222-1-22-1-21-21-22-12-101-2-11-2-12113−30033−3−32-2−2i2iii−i−i-1-1110003−333−3−300000000i3−i3i3i3−i3−i3-113−3−2i2i2-2ii−i−i−2i2i000000-11003−300000i3−i3i−i0000000
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χ482-22-222-1-22-1-21-21-22-12-101-2-11-2-12113−30033−3−3-22−2i2iii−i−i-1-1110003−333−3−300000000i3−i3i3i3−i3−i31-1−33−2i2i-22ii−i−i2i−2i0000001-100−3300000−i3i3−ii0000000
χ492-22-222-1-22-1-21-21-22-12-101-2-11-2-1211−3300−3−3332-22i−2i−i−iii-1-111000−33−3−33300000000i3−i3i3i3−i3−i3-11−332i−2i2-2−i−iii2i−2i000000-1100−3300000i3−i3−ii0000000
χ502-22-222-1-22-1-21-21-22-12-101-2-11-2-1211−3300−3−3332-2−2i2iii−i−i-1-111000−33−3−33300000000−i3i3−i3−i3i3i3-11−33−2i2i2-2ii−i−i−2i2i000000-1100−3300000−i3i3i−i0000000
χ512-22-222-1-22-1-21-21-22-12-101-2-11-2-1211−3300−3−333-222i−2i−i−iii-1-111000−33−3−33300000000i3−i3i3i3−i3−i31-13−32i−2i-22−i−iii−2i2i0000001-1003−300000−i3i3i−i0000000
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χ5344444-2-24-2-24-2-2-2-24-2-214-2-211-2-2-2-21-2-2-2-211110044-2-2-2-211114-2-2-2-21111400000-2-2-2-211110000-2-2001111000000000000000000000000000000
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χ5544444-2-24-2-24-2-2-2-24-2-21-4-2-211-2-2-2-212222-1-1-1-10044-2-2-2-21111-42222-1-1-1-1-4000002222-1-1-1-10000-2-2001111000000000000000000000000000000
χ5644444-2-24-2-24-2-2-2-24-2-21-4-2-211-2-2-2-212222-1-1-1-100-4-422221111-42222-1-1-1-1400000-2-2-2-2111100002200-1-1-1-1000000000000000000000000000000
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χ844-44-44-2-2-4-2-2-422224-2-210221-12-2-22-1−23230033−3−3004i−4i−2i−2i2i2i11-1-1000−232333−3−3000000002i3−2i3−i3−i3i3i30000−2i2i00ii−i−i000000000000000000000000000000
χ854-44-44-2-2-4-2-2-422224-2-210221-12-2-22-1−23230033−3−300−4i4i2i2i−2i−2i11-1-1000−232333−3−300000000−2i32i3i3i3−i3−i300002i−2i00−i−iii000000000000000000000000000000
χ864-44-4-2442442-4-4-4-4-2-2-240224-42-2-22-4000000004-4000000-2-222000000000000000000000004-40000-22000000000000-2200000000000000000000
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χ884-44-4-24-224-222-42-4-21-2-20-12-2221-2-1223−23002323−23−234-400000011-1-1000−33−3−33300000000000000-2223−2300-220000000000001-100−330000000000000000
χ894-44-4-24-224-222-42-4-21-2-20-12-2221-2-1223−23002323−23−23-4400000011-1-1000−33−3−333000000000000002-2−2323002-2000000000000-11003−30000000000000000
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χ954-4-444-24-42-4442-4-2-44-2-20-4222-2-424-20000000000000000-222-2000000000000000−2i32i300−2i32i32i3−2i3000000000000000000000000000000000000000000
χ964-4-444-24-42-4442-4-2-44-2-20-4222-2-424-20000000000000000-222-20000000000000002i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ974-4-444-2-2-4224-222-2-4-2-21022-1-1-222-2100003-3-330000−2i32i32i3−2i31-1-11000003-3-33000000−2i32i300i3−i3−i3i300000000i3−i3−i3i3000000000000000000000000000000
χ984-4-444-2-2-4224-222-2-4-2-21022-1-1-222-2100003-3-3300002i3−2i3−2i32i31-1-11000003-3-330000002i3−2i300−i3i3i3−i300000000−i3i3i3−i3000000000000000000000000000000
χ994-4-444-2-2-4224-222-2-4-2-21022-1-1-222-210000-333-30000−2i32i32i3−2i31-1-1100000-333-30000002i3−2i300−i3i3i3−i300000000i3−i3−i3i3000000000000000000000000000000
χ1004-4-444-2-2-4224-222-2-4-2-21022-1-1-222-210000-333-300002i3−2i3−2i32i31-1-1100000-333-3000000−2i32i300i3−i3−i3i300000000−i3i3i3−i3000000000000000000000000000000
χ1014-4-44-2442-4-4-24-4-442-2-24022-4-4-222-240000000000000000-222-2000000000000000000000000000000000000000000000000000000000023−2300000
χ1024-4-44-2442-4-4-24-4-442-2-24022-4-4-222-240000000000000000-222-20000000000000000000000000000000000000000000000000000000000−232300000
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χ10588-8-8-48-4-4-84448-4-842-4-402-44-44-24-2400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44444-4-444222022-22-2-2-2-2-20043−43−2323−232300000000-11-110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-44444-4-444222022-22-2-2-2-2-200−434323−2323−2300000000-11-11023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-484-484-84-84-4-42-404-2-44-2-4244000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-44-4-444444-42220-2-22-2-222-2-243−4300−23−23232300000000-1-111000−232333−3−300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4-444444-42220-2-22-2-222-2-2−4343002323−23−2300000000-1-11100023−23−3−33300000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-44-84-4-4-84842-4-40-2444-4-242-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4844-8-484-8-44-42-404-24424-2-4-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4-444-442220-2-2-2-22-2-22200006-6-6600000000-111-100000-333-300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4-444-442220-2-2-2-22-2-2220000-666-600000000-111-1000003-3-3300000000000000000000000000000000000000000000000000000000

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