Finite Group Databasebeta

← Group #13167997

Character table — Group #13167997

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212222236661212121212121212121212124444666666661212121212121212226666666612121212121212121212121244444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1111111111111-1-11111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111111-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-11-11111-1-11111-11-11-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-111-1-1-1-1-1-1-1-11-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-111111111111111111111-11-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111-1111-1-1111111-1-11-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-1-11-11-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-111-1-11111111111-1-11-1-1-1-1-111-1-1-11-1-11-1-111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1111111111111-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-11111-1-1111-1-1111111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-11-11-1-111-1-1111-1-11111-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111-11-111-1-111-1-11-1-11111-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111111-1-1111111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1111-1111111-1-1-1-111-1-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-111111-1-111-11-1-11-1-111-1-1-11-11
χ17222222-122-1-1-122222-1-1222-1-1-1-1-1-12-1-12222-1-1-1-122-1-1-1-122-1-1-1-100222222-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-12200-1-1-1-1000020000-1-100000000
χ18222222-122-1-1-122222-1-1222-1-1-1-1-1-12-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-1002-222-2-2-1-111-1-1110000-2-21111-1-1112-200-1-1110000-200001100000000
χ19222222-122-1-1-122222-1-1222-1-1-1-1-1-12-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-100-22-2-22211-1-111-1-10000-2-2111111-1-1-220011-1-10000-200001100000000
χ20222222-122-1-1-122222-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-100-2-2-2-2-2-211111111000022-1-1-1-11111-2-2001111000020000-1-100000000
χ21222222-122-1-1-122222-1-1-222-1-1-1-1-1-12112222-1-1-1-1-2-21111-2-2111100-2-22222-1-1-1-11111000022-1-1-1-1-1-1-1-1-2-20011110000-200001100000000
χ22222222-122-1-1-122222-1-1-222-1-1-1-1-1-121122-2-2-1-1-1-1-2-21111-2-2111100-2222-2-2-1-11111-1-10000-2-21111-1-111-220011-1-1000020000-1-100000000
χ23222222-122-1-1-122222-1-1-222-1-1-1-1-1-1211-2-222-1-1-1-1-2-21111-2-21111002-2-2-22211-1-1-1-1110000-2-2111111-1-12-200-1-111000020000-1-100000000
χ24222222-122-1-1-122222-1-1-222-1-1-1-1-1-1211-2-2-2-2-1-1-1-1-2-21111-2-211110022-2-2-2-21111-1-1-1-1000022-1-1-1-111112200-1-1-1-10000-200001100000000
χ2522222-122-12222-12-1-12-12-1-12-12-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1220200-1-10022002222-1-100000000-1-10-1-1200-1-1-1-1-1-1002020000-1-10-100
χ2622222-122-12222-12-1-12-12-1-12-12-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20200-1-100220022-2-21100000000-1-10-11-200-1-1111100-20-20000110100
χ2722222-122-12222-12-1-12-12-1-12-12-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1220-2001100-2-200-2-222-1-1000000001101-120011-1-1-1-100-20-20000110100
χ2822222-122-12222-12-1-12-12-1-12-12-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-2001100-2-200-2-2-2-2110000000011011-200111111002020000-1-10-100
χ2922222-122-12222-12-1-12-1-2-1-12-12-12-1-1-2-20022-1-1-1-1-21-2-2111111112-20-200-1-1002200-2-2221100000000-1-101-1-20011-1-11100-2020000110-100
χ3022222-122-12222-12-1-12-1-2-1-12-12-12-1-1-2-20022-1-1-1-1-21-2-211111111-220-200-1-1002200-2-2-2-2-1-100000000-1-10112001111-1-10020-20000-1-10100
χ3122222-122-12222-12-1-12-1-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-21-2-2111111112-202001100-2-20022221100000000110-1-1-200-1-1-1-1110020-20000-1-10100
χ3222222-122-12222-12-1-12-1-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111-2202001100-2-20022-2-2-1-100000000110-11200-1-111-1-100-2020000110-100
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χ352222-122-12222-12-12-1-122-1-1-12-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-122-201100-2-200-2-200-1-1220000001100102-11100-1-1-1-10-20-200011001000
χ362222-122-12222-12-12-1-122-1-1-12-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-2-201100-2-200-2-20011-2-2000000110010-21110011110202000-1-100-1000
χ372222-122-12222-12-12-1-12-2-1-1-12-12-12-1-2-22200-1-1-1-11-211-2-21111112-2-20-1-1002200-2-200-1-1-2-2000000-1-10010211100-1-111020-2000-1-1001000
χ382222-122-12222-12-12-1-12-2-1-1-12-12-12-1-2-22200-1-1-1-11-211-2-2111111-22-20-1-1002200-2-2001122000000-1-10010-2-1110011-1-10-2020001100-1000
χ392222-122-12222-12-12-1-12-2-1-1-12-12-12-1-2-2-2-200-1-1-1-11-211-2-21111112-2201100-2-2002200-1-1-2-20000001100-1021-1-100-1-1110-2020001100-1000
χ402222-122-12222-12-12-1-12-2-1-1-12-12-12-1-2-2-2-200-1-1-1-11-211-2-2111111-22201100-2-200220011220000001100-10-2-1-1-10011-1-1020-2000-1-1001000
χ4122-2-2222222-2-2-2-2-2-222202-222-2-2-2-2-2002-22-222-2-200000000000000002-22-22-22-2000000002-222-2-22-22-2000000000000000000000000000
χ4222-2-2222222-2-2-2-2-2-222202-222-2-2-2-2-2002-2-2222-2-200000000000000002-2-222-2-2200000000-22-2-2222-2-22000000000000000000000000000
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χ4422-2-2222222-2-2-2-2-2-222202-222-2-2-2-2-200-22-2222-2-20000000000000000-22-22-22-22000000002-222-2-2-22-22000000000000000000000000000
χ4522-2-222-122-111-2-2-2-22-1-102-2-1-11111-23−32-22-2-1-111003−33−30033−3−300002-22-2-11-113−33−300002-2-1-111-11-1100003−33−30000000003−300000000
χ4622-2-222-122-111-2-2-2-22-1-102-2-1-11111-23−32-2-22-1-111003−33−30033−3−300002-2-22-111-13−3−330000-2211-1-1-111-100003−3−33000000000−3300000000
χ4722-2-222-122-111-2-2-2-22-1-102-2-1-11111-23−3-222-2-1-111003−33−30033−3−30000-222-21-1-11−333−30000-2211-1-11-1-110000−333−3000000000−3300000000
χ4822-2-222-122-111-2-2-2-22-1-102-2-1-11111-23−3-22-22-1-111003−33−30033−3−30000-22-221-11-1−33−3300002-2-1-1111-11-10000−33−330000000003−300000000
χ4922-2-222-122-111-2-2-2-22-1-102-2-1-11111-2−332-22-2-1-11100−33−3300−3−33300002-22-2-11-11−33−3300002-2-1-111-11-110000−33−33000000000−3300000000
χ5022-2-222-122-111-2-2-2-22-1-102-2-1-11111-2−332-2-22-1-11100−33−3300−3−33300002-2-22-111-1−333−30000-2211-1-1-111-10000−333−30000000003−300000000
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χ5344444-2-24-2-2-2-24-24-2-2-214-2-2-21-21-21-2-2-2004411114-2-2-211-2-21111000400-2-200-2-200-2-2000000000000110-20000110000000000000000000
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χ9788-8-8-4-48-4-48-8-844442-4-402-2-4-44444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-4-4-4-444444422202-222-2-2-2-2-243−430000-1-11100−2323−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4-4-444444422202-222-2-2-2-2-2−43430000-1-1110023−2323−2300−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-4-8444-4-848-4-4-420444-2-424-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-44-844-44-8-48-42-4044-242-4-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-44444-444-4-42220-2-2-2-222-2-22000000-111-10000006-6-33-33000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-44444-444-4-42220-2-2-2-222-2-22000000-111-1000000-663-33-3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-4-844-448-4-84-4-4204-44-24-2-4240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-84-44-484-8-42-404-4-24-242-440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-88-8-4-4442-4-40-224444-4-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-44-4-4442220-22-2-2-2-222-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-44-4-4442220-22-2-2-2-222-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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