Finite Group Databasebeta

← Group #13168349

Character table — Group #13168349

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212124444121212121212121212121212121212122266661212121212121212121212121212121244444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-111111111-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111-1-111-1-111-1-11111-1-1-1-1-1-11-11111-1-111-1-11111-11-11-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1-1-11-11-1-111-1-1-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-111-1-111-1-1111111-1-1-1-1-1-1-1111-1-111-1-1111111-1-11-11-1-111-1-1-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-1-11-11-111-1-1-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111
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
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-111-1-1111111-1-11-11111-1-1-1-111-1-1-11-1-11-1-111-1-11-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-111111-1-1-1-1-1-111-1-111-111-1-1-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1111-1-1-1-1-1-11111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111-1-111111111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-11-1-111111111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111111-1-1-1-1-1-111111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1111111-1-1-1-111-111-1-1-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111-1-11111111111-11-1-1-1-11111-1-111-11-1-11-1-111-1-11-1-11
χ17222222-1-122-122-1222-1-1222-1-1-1-1-1-12-1-12222-1-1-1-122-1-1-1-122-1-1-1-122002222-1-1-1-1-1-1-1-1000022-1-1-1-12200-1-1-1-1-1-1-1-10000200000000-1-10000
χ18222222-1-122-122-1222-1-1222-1-1-1-1-1-12-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-12-20022-2-2-1-111-1-1110000-2-211112-200-1-111-1-1110000-200000000110000
χ19222222-1-122-122-1222-1-1222-1-1-1-1-1-12-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-2200-2-22211-1-111-1-10000-2-21111-220011-1-111-1-10000-200000000110000
χ20222222-1-122-122-1222-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-2-200-2-2-2-211111111000022-1-1-1-1-2-200111111110000200000000-1-10000
χ21222222-1-122-122-1222-1-1-222-1-1-1-1-1-12112222-1-1-1-1-2-21111-2-21111-2-2002222-1-1-1-11111000022-1-1-1-1-2-200-1-1-1-111110000-200000000110000
χ22222222-1-122-122-1222-1-1-222-1-1-1-1-1-121122-2-2-1-1-1-1-2-21111-2-21111-220022-2-2-1-11111-1-10000-2-21111-2200-1-11111-1-10000200000000-1-10000
χ23222222-1-122-122-1222-1-1-222-1-1-1-1-1-1211-2-222-1-1-1-1-2-21111-2-211112-200-2-22211-1-1-1-1110000-2-211112-20011-1-1-1-1110000200000000-1-10000
χ24222222-1-122-122-1222-1-1-222-1-1-1-1-1-1211-2-2-2-2-1-1-1-1-2-21111-2-211112200-2-2-2-21111-1-1-1-1000022-1-1-1-122001111-1-1-1-10000-200000000110000
χ2522222-1222-122-122-1-12-12-1-12-12-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-1022200-1-100220022-1-1220000000-12-100-1-100-1-1-1-1-1-10020200-1-1000-100
χ2622222-1222-122-122-1-12-12-1-12-12-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-102-2-200-1-10022002211-2-20000000-1-2100-1-100-1-1111100-20-20011000100
χ2722222-1222-122-122-1-12-12-1-12-12-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-222001100-2-200-2-2-1-122000000012-100110011-1-1-1-100-20-20011000100
χ2822222-1222-122-122-1-12-12-1-12-12-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-2001100-2-200-2-211-2-200000001-210011001111110020200-1-1000-100
χ2922222-1222-122-122-1-12-1-2-1-12-12-12-1-1-2-20022-1-1-1-1-21-2-2111111110-22-200-1-1002200-2-2-1-1-2-2000000012100-1-10011-1-11100-20200-1-1000100
χ3022222-1222-122-122-1-12-1-2-1-12-12-12-1-1-2-20022-1-1-1-1-21-2-2111111110-2-2200-1-1002200-2-2112200000001-2-100-1-1001111-1-10020-20011000-100
χ3122222-1222-122-122-1-12-1-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111022-2001100-2-20022-1-1-2-20000000-121001100-1-1-1-1110020-20011000-100
χ3222222-1222-122-122-1-12-1-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-21-2-21111111102-22001100-2-2002211220000000-1-2-1001100-1-111-1-100-20200-1-1000100
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χ352222-1222-122-122-12-1-122-1-1-12-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-20221100-2-200-2-20022-1-100000010-1211001100-1-1-1-10-20-201100001000
χ362222-1222-122-122-12-1-122-1-1-12-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-21100-2-200-2-200-2-211000000101-211001100111102020-1-10000-1000
χ372222-1222-122-122-12-1-12-2-1-1-12-12-12-1-2-22200-1-1-1-11-211-2-2111111-202-2-1-1002200-2-200221100000010-1-2-1-1001100-1-111020-20110000-1000
χ382222-1222-122-122-12-1-12-2-1-1-12-12-12-1-2-22200-1-1-1-11-211-2-2111111-20-22-1-1002200-2-200-2-2-1-10000001012-1-100110011-1-10-2020-1-100001000
χ392222-1222-122-122-12-1-12-2-1-1-12-12-12-1-2-2-2-200-1-1-1-11-211-2-2111111202-21100-2-20022002211000000-10-1-21100-1-100-1-1110-2020-1-100001000
χ402222-1222-122-122-12-1-12-2-1-1-12-12-12-1-2-2-2-200-1-1-1-11-211-2-211111120-221100-2-2002200-2-2-1-1000000-10121100-1-10011-1-1020-20110000-1000
χ4122-2-2222-2222-2-2-2-2-222202-2-2-222-2-2-2002-22-222-2-200000000000000002-22-22-22-2000000002-222-2-200002-22-200000000000000000000000
χ4222-2-2222-2222-2-2-2-2-222202-2-2-222-2-2-2002-2-2222-2-200000000000000002-2-222-2-2200000000-22-2-22200002-2-2200000000000000000000000
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χ4622-2-222-1122-1-2-21-2-22-1-102-211-1-111-23−32-2-22-1-111003−33−30033−3−300002-2-22-111-13−3−330000-2211-1-10000-111-13−3−330000000000000−330000
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χ4822-2-222-1122-1-2-21-2-22-1-102-211-1-111-23−3-22-22-1-111003−33−30033−3−30000-22-221-11-1−33−3300002-2-1-11100001-11-1−33−3300000000000003−30000
χ4922-2-222-1122-1-2-21-2-22-1-102-211-1-111-2−332-22-2-1-11100−33−3300−3−33300002-22-2-11-11−33−3300002-2-1-1110000-11-11−33−330000000000000−330000
χ5022-2-222-1122-1-2-21-2-22-1-102-211-1-111-2−332-2-22-1-11100−33−3300−3−33300002-2-22-111-1−333−30000-2211-1-10000-111-1−333−300000000000003−30000
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χ5222-2-222-1122-1-2-21-2-22-1-102-211-1-111-2−33-22-22-1-11100−33−3300−3−3330000-22-221-11-13−33−300002-2-1-11100001-11-13−33−30000000000000−330000
χ5344444-2-2-24-2-24-2-24-2-2-214-2-2-21-21-21-2-2-2004411114-2-2-211-2-21111040000-2-200-2-200-2-200000000000-200001100110000000000000000000
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χ9788-8-8-4-48-8-4-4844-8442-4-402-244-4-444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-44-4-4-44444422202-2-2-222-2-2-243−430000-1-11100−2323−23230033−3−3000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-44-4-4-44444422202-2-2-222-2-2-2−43430000-1-1110023−2323−2300−3−333000000000000000000000000000000000000000000000000000000000
χ1008-88-88-4-44-844-84-48-4-4-420444-24-2-42-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-48-444-844-8-4-48-42-4044-24-242-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-2222000000-111-10000006-6-33-33000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4444444-4-4-42220-2-2-2-2-2-2222000000-111-1000000-663-33-3000000000000000000000000000000000000000000000000000000000
χ1048-8-888-4-4-4-8448-44-84-4-4204-4-424-24-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-4-44-84-4844-8-42-404-42-4-24-2440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-48844-8-4-4-8442-4-40-22-4-44444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4-4444-4-44442220-2222-2-2-2-2-2000000-11-110000000033−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-4444-4-44442220-2222-2-2-2-2-2000000-11-1100000000−333333−33000000000000000000000000000000000000000000000000000000000

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