Finite Group Databasebeta

← Group #13168213

Character table — Group #13168213

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order12223336666666663334666666666121222444436661212121212121212121212124446666121212121212121212121212444412121212661212121212121212121212121212244466121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111111111111111111-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-111-1-1-1-1-111-1-11-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-111111111-1-1111111-1-11111111111-111-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-111
χ51111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1111111111-1-1111-1-1-1-1-1-1-11-1
χ61111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-11-1-11-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-111-1-1-1-1-111111-11
χ81111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11111-1-111111111-1-11-1-1-111-1-111-1-1-11-11-1-1-1-11111-11-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-11-1-1-1-111-1-111-1-111-1-111-1-11111-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-111-1-111-1-1-1-1111-11-111-1-1-1-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-111-1-1111111-1-1-11-1-111-1-11111-1-11-11-111-1-1-1-1111-1-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-111-1-111-1-1-1-1111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1111-1-111-1-111-11-11-1-1-1-111-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111111111-1-1-1
χ17222222-12-12-1222-12-1-122-1-1-122-12-1-122002222-1-1-1-1-1222-1-1-1-1-1-1-1-1202000022-1-1-1-10022220000000000-10-1200-1-1-1-1-1-1-1-12002-1-10000000-10
χ18222222-12-12-1222-12-1-122-1-1-122-12-1-1220022-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-120-20000-2-2-1-11100-2-2220000000000-1012001111-1-1-1-1-200-211000000010
χ19222222-12-12-1222-12-1-122-1-1-122-12-1-12200-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-1-20200002211-1-10022-2-2000000000010-1-200-1-1-1-11111-200-211000000010
χ20222222-12-12-1222-12-1-122-1-1-122-12-1-12200-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-20-20000-2-2111100-2-2-2-20000000000101-200111111112002-1-10000000-10
χ21222222-12-12-1222-12-1-12-2-1-1-122-12-1-1-2-2002222-1-1-1-11-2-2-211111111-20-2000022-1-1-1-100-2-2220000000000101-20011-1-1-1-111200-2-1-1000000010
χ22222222-12-12-1222-12-1-12-2-1-1-122-12-1-1-2-20022-2-2-1-1-1-11-2-2-211111111-2020000-2-2-1-111002222000000000010-1-200-1-111-1-111-2002110000000-10
χ23222222-12-12-1222-12-1-12-2-1-1-122-12-1-1-2-200-2-222-1-1-1-11-2-2-21111111120-200002211-1-100-2-2-2-20000000000-10120011-1-111-1-1-2002110000000-10
χ24222222-12-12-1222-12-1-12-2-1-1-122-12-1-1-2-200-2-2-2-2-1-1-1-11-2-2-2111111112020000-2-211110022-2-20000000000-10-1200-1-11111-1-1200-2-1-1000000010
χ2522222-1222-122-1-1222-1-1222-1-1-1-1-1-12-1-1220022-1-1-1-122-1-1-1-122-1-1-1-102222-1-1-1-10022-1-1-1-1002222-1-1-1-1-1-10220-1-1-1-1-1-10000000000-1-10000000
χ2622222-1222-122-1-1222-1-1222-1-1-1-1-1-12-1-12200-2-2-1-1-1-122-1-1-1-122-1-1-1-102-222-1-11100-2-2-1-11100-2-2-2-21111-1-102-20-1-111110000000000110000000
χ2722222-1222-122-1-1222-1-1222-1-1-1-1-1-12-1-1-2-20022-1-1-1-122-1-1-1-122-1-1-1-10-22-2-211-1-1002211-1-100-2-2-2-21111110-22011-1-1-1-10000000000110000000
χ2822222-1222-122-1-1222-1-1222-1-1-1-1-1-12-1-1-2-200-2-2-1-1-1-122-1-1-1-122-1-1-1-10-2-2-2-2111100-2-21111002222-1-1-1-1110-2-201111110000000000-1-10000000
χ2922222-1222-122-1-1222-1-1-222-1-1-1-1-1-1211220022-1-1-1-1-2-21111-2-211110-2-222-1-1-1-1002211110022-2-21111-1-10-2-201111-1-10000000000-1-10000000
χ3022222-1222-122-1-1222-1-1-222-1-1-1-1-1-12112200-2-2-1-1-1-1-2-21111-2-211110-2222-1-11100-2-211-1-100-2-222-1-1-1-1-1-10-22011-1-1110000000000110000000
χ3122222-1222-122-1-1222-1-1-222-1-1-1-1-1-1211-2-20022-1-1-1-1-2-21111-2-2111102-2-2-211-1-10022-1-11100-2-222-1-1-1-11102-20-1-111-1-10000000000110000000
χ3222222-1222-122-1-1222-1-1-222-1-1-1-1-1-1211-2-200-2-2-1-1-1-1-2-21111-2-21111022-2-2111100-2-2-1-1-1-10022-2-21111110220-1-1-1-1110000000000-1-10000000
χ332222-122-1222-1222-1-12-12-1-12-1-12-12-122222200-1-1-1-12-1-1-122-1-1-1-1-1-1220-1-1220022002200-1-100000000-1-12-10-1-1-10000-1-1-1-102200000-1-100-100
χ342222-122-1222-1222-1-12-12-1-12-1-12-12-12222-2-200-1-1-1-12-1-1-122-1-1-1-1-1-1-220-1-12200-2-20022001100000000-1-1-2-101-1-1000011110-2-2000001100100
χ352222-122-1222-1222-1-12-12-1-12-1-12-12-122-2-22200-1-1-1-12-1-1-122-1-1-1-1-1-12-2011-2-2002200-2-200-1-10000000011210-1110000-1-1-1-10-2-2000001100100
χ362222-122-1222-1222-1-12-12-1-12-1-12-12-122-2-2-2-200-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2011-2-200-2-200-2-200110000000011-2101110000111102200000-1-100-100
χ372222-122-1222-1222-1-12-1-2-1-12-1-12-12-1-2-2222200-1-1-1-1-2111-2-2111111-2-20-1-122002200-2-200-1-100000000-1-1-2101110000-1-11102-200000-1-100100
χ382222-122-1222-1222-1-12-1-2-1-12-1-12-12-1-2-222-2-200-1-1-1-1-2111-2-21111112-20-1-12200-2-200-2-2001100000000-1-1210-111000011-1-10-22000001100-100
χ392222-122-1222-1222-1-12-1-2-1-12-1-12-12-1-2-2-2-22200-1-1-1-1-2111-2-2111111-22011-2-20022002200-1-10000000011-2-101-1-10000-1-1110-22000001100-100
χ402222-122-1222-1222-1-12-1-2-1-12-1-12-12-1-2-2-2-2-2-200-1-1-1-1-2111-2-211111122011-2-200-2-20022001100000000112-10-1-1-1000011-1-102-200000-1-100100
χ4122-2-2222-2-222-2-2-2-222220-2-2-2-22-2-22200002-2002-2-220000000000000000000002-20000002-2002i−2i2i2i−2i−2i0000000000002-20000000000002i−2i000
χ4222-2-2222-2-222-2-2-2-222220-2-2-2-22-2-22200002-2002-2-220000000000000000000002-20000002-200−2i2i−2i−2i2i2i0000000000002-2000000000000−2i2i000
χ4322-2-2222-2-222-2-2-2-222220-2-2-2-22-2-2220000-22002-2-22000000000000000000000-22000000-22002i−2i2i2i−2i−2i000000000000-22000000000000−2i2i000
χ4422-2-2222-2-222-2-2-2-222220-2-2-2-22-2-2220000-22002-2-22000000000000000000000-22000000-2200−2i2i−2i−2i2i2i000000000000-220000000000002i−2i000
χ452-2-222222-2-2-2-22-22-222202-2-22-22-2-2-2002-2002i−2i22-2-20000000000000002-22-22i−2i002i−2i0000002i−2i0000002-2000000002i−2i00000000002i−2i0000000
χ462-2-222222-2-2-2-22-22-222202-2-22-22-2-2-2002-200−2i2i22-2-20000000000000002-22-2−2i2i00−2i2i000000−2i2i0000002-200000000−2i2i0000000000−2i2i0000000
χ472-2-222222-2-2-2-22-22-222202-2-22-22-2-2-200-22002i−2i22-2-2000000000000000-22-222i−2i002i−2i000000−2i2i000000-22000000002i−2i0000000000−2i2i0000000
χ482-2-222222-2-2-2-22-22-222202-2-22-22-2-2-200-2200−2i2i22-2-2000000000000000-22-22−2i2i00−2i2i0000002i−2i000000-2200000000−2i2i00000000002i−2i0000000
χ492-2-222-122-21-2-2-112-22-1-102-21-11-111-23−32-2002i−2i-1-111003−33−30033−3−30002-2-11−ii002i−2i3−3−i3i3002i−2i00−i3i3−i3i3-1100003−3−i3i3−ii0000000000−ii0000000
χ502-2-222-122-21-2-2-112-22-1-102-21-11-111-23−32-200−2i2i-1-111003−33−30033−3−30002-2-11i−i00−2i2i3−3i3−i300−2i2i00i3−i3i3−i3-1100003−3i3−i3i−i0000000000i−i0000000
χ512-2-222-122-21-2-2-112-22-1-102-21-11-111-23−3-22002i−2i-1-111003−33−30033−3−3000-221-1−ii002i−2i−33−i3i300−2i2i00i3−i3i3−i31-10000−33−i3i3−ii0000000000i−i0000000
χ522-2-222-122-21-2-2-112-22-1-102-21-11-111-23−3-2200−2i2i-1-111003−33−30033−3−3000-221-1i−i00−2i2i−33i3−i3002i−2i00−i3i3−i3i31-10000−33i3−i3i−i0000000000−ii0000000
χ532-2-222-122-21-2-2-112-22-1-102-21-11-111-2−332-2002i−2i-1-11100−33−3300−3−3330002-2-11−ii002i−2i−33i3−i3002i−2i00i3−i3i3−i3-110000−33i3−i3−ii0000000000−ii0000000
χ542-2-222-122-21-2-2-112-22-1-102-21-11-111-2−332-200−2i2i-1-11100−33−3300−3−3330002-2-11i−i00−2i2i−33−i3i300−2i2i00−i3i3−i3i3-110000−33−i3i3i−i0000000000i−i0000000
χ552-2-222-122-21-2-2-112-22-1-102-21-11-111-2−33-22002i−2i-1-11100−33−3300−3−333000-221-1−ii002i−2i3−3i3−i300−2i2i00−i3i3−i3i31-100003−3i3−i3−ii0000000000i−i0000000
χ562-2-222-122-21-2-2-112-22-1-102-21-11-111-2−33-2200−2i2i-1-11100−33−3300−3−333000-221-1i−i00−2i2i3−3−i3i3002i−2i00i3−i3i3−i31-100003−3−i3i3i−i0000000000−ii0000000
χ5744444-2-24-2-2-24-2-2-24-21-24-2-21-2-21-21-2-2-20000441111-24-2-211-2-211110040000-2-200-2-200-2-200000000000000-200011110000000000000000000
χ5844444-2-24-2-2-24-2-2-24-21-24-2-21-2-21-21-2-2-20000-4-41111-24-2-211-2-2111100-400002200220022000000000000002000-1-1-1-10000000000000000000
χ5944444-2-24-2-2-24-2-2-24-21-2-4-2-21-2-21-21-22200004411112-422-1-122-1-1-1-100-40000-2-200-2-20022000000000000002000-1-1110000000000000000000
χ6044444-2-24-2-2-24-2-2-24-21-2-4-2-21-2-21-21-2220000-4-411112-422-1-122-1-1-1-1004000022002200-2-200000000000000-200011-1-10000000000000000000
χ614444-24-2-2-24-2-244-2-21-2-2411-2-2-2-2-2-21440044001111-2-2-2-2-2-2111111400000000-2-2000000-2-20000000000-200-20000001111000000000000000
χ624444-24-2-2-24-2-244-2-21-2-2411-2-2-2-2-2-214400-4-4001111-2-2-2-2-2-2111111-400000000220000002200000000002002000000-1-1-1-1000000000000000
χ634444-24-2-2-24-2-244-2-21-2-2-411-2-2-2-2-2-21-4-40044001111222222-1-1-1-1-1-1-400000000-2-2000000-2-20000000000200200000011-1-1000000000000000
χ644444-24-2-2-24-2-244-2-21-2-2-411-2-2-2-2-2-21-4-400-4-4001111222222-1-1-1-1-1-140000000022000000220000000000-200-2000000-1-111000000000000000
χ654444-2-24-24-24-2-2-24-2-2-214-2-2-211-21-2-2-2-244000011114-211-2-2-2-21111040-2-2-2-2000000-2-2000000000000110-2001100000000000000000000000
χ664444-2-24-24-24-2-2-24-2-2-214-2-2-211-21-2-2-2-2-4-4000011114-211-2-2-2-211110-40222200000022000000000000-1-10200-1-100000000000000000000000
χ674444-2-24-24-24-2-2-24-2-2-21-4-2-2-211-21-2-2224400001111-42-1-12222-1-1-1-10-40-2-2-2-200000022000000000000110200-1-100000000000000000000000
χ684444-2-24-24-24-2-2-24-2-2-21-4-2-2-211-21-2-222-4-400001111-42-1-12222-1-1-1-10402222000000-2-2000000000000-1-10-2001100000000000000000000000
χ6944-4-444-2-424-2-4-4-424-2-240222-442-4-2-200004-400-222-2000000000000000000000-220000004-400000000000000000000-2200000000000000000
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χ7344-4-4-2442-4442-4-4-4-2-24-2022-42-2-424-200004-400-222-20000000000000000000004-4000000-2200000000000000000000-2200000000000000000
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χ7544-4-4-24-2224-22-4-42-21-2-20-1-122-222-2100004-4001-1-110000003-33-33-3000000000-22000000-22000000000000000000001-13-3000000000000000
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χ7744-4-4-24-2224-22-4-42-21-2-20-1-122-222-210000-44001-1-110000003-33-33-30000000002-20000002-200000000000000000000-11-33000000000000000
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χ794-44-4444-44-4-44-44-4-44440-444-4-4-44-4-4000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000
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χ814-44-444-2-4-2-424-442-4-2-2402-2-2-4-4242200000000-22-22000000000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ824-44-44-24-442-442-2-4-44-2-20-44-2222-22-400000000-22-220000000000000000000000000000000000023−23−23230000000000000000000000000000000
χ834-44-44-24-442-442-2-4-44-2-20-44-2222-22-400000000-22-2200000000000000000000000000000000000−232323−230000000000000000000000000000000
χ844-44-4-24424-4-4-2-44-42-24-202-2422-4-2-4200000000-22-2200000000000000000000000000000000000000000000000000000000000000023−2300000
χ854-44-4-24424-4-4-2-44-42-24-202-2422-4-2-4200000000-22-22000000000000000000000000000000000000000000000000000000000000000−232300000
χ864-4-4444-242-42-44-4-2-4-2-240-2224-4-2-4220000004i−4i-2-22200000000000000000004i−4i00−2i2i000000000000000000000000−2i2i0000000000000000000
χ874-4-4444-242-42-44-4-2-4-2-240-2224-4-2-422000000−4i4i-2-2220000000000000000000−4i4i002i−2i0000000000000000000000002i−2i0000000000000000000
χ884-4-444-2-24222-4-22-2-4-21-20-22-1-2212-1223−2300004i−4i11-1-10023−23−3300−3−3330000000−2i2i00−2i2i00−2i32i3000000000000000000i3−i3i−i0000000000000000000
χ894-4-444-2-24222-4-22-2-4-21-20-22-1-2212-1223−230000−4i4i11-1-10023−23−3300−3−33300000002i−2i002i−2i002i3−2i3000000000000000000−i3i3−ii0000000000000000000
χ904-4-444-2-24222-4-22-2-4-21-20-22-1-2212-12−232300004i−4i11-1-100−23233−30033−3−30000000−2i2i00−2i2i002i3−2i3000000000000000000−i3i3i−i0000000000000000000
χ914-4-444-2-24222-4-22-2-4-21-20-22-1-2212-12−23230000−4i4i11-1-100−23233−30033−3−300000002i−2i002i−2i00−2i32i3000000000000000000i3−i3−ii0000000000000000000
χ924-4-44-244-2-4-4-424-442-24-20-22-4-2242-42004-40000-2-222000000000000000-224-400000000000000000000-2200000000000000000000000000000
χ934-4-44-244-2-4-4-424-442-24-20-22-4-2242-4200-440000-2-2220000000000000002-2-44000000000000000000002-200000000000000000000000000000
χ944-4-44-2-24-2-42-42-2242-2-210-2221-1-2-12223−234-4000011-1-100−3323−2300−3−333000-22-2200000023−230000000000001-10000−3300000000000000000000000
χ954-4-44-2-24-2-42-42-2242-2-210-2221-1-2-12223−23-44000011-1-100−3323−2300−3−3330002-22-2000000−2323000000000000-1100003−300000000000000000000000
χ964-4-44-2-24-2-42-42-2242-2-210-2221-1-2-122−23234-4000011-1-1003−3−23230033−3−3000-22-22000000−23230000000000001-100003−300000000000000000000000
χ974-4-44-2-24-2-42-42-2242-2-210-2221-1-2-122−2323-44000011-1-1003−3−23230033−3−30002-22-200000023−23000000000000-110000−3300000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-4-84-4-4-84448-42-4044-24-4-242-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-484-8-48444-8-4-4-420444-224-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-444-4-44444-42220-2-2-2-22-2-22200000000-111-10000006-6-33-330000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-4-44444-42220-2-2-2-22-2-22200000000-111-1000000-663-33-30000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-4-8-44484-44-8-42-404-4244-2-4-24000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-44-4-84-4-88442-4-40-22-4444-44-2000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48484-8-44-4-84-4-4204-4-4-2-24244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-444-44-4442220-222-2-2-22-2-200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-44-444-44-4442220-222-2-2-22-2-200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-44-8448-8-442-4-402-24-44-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-44444-44-4422202-2-22-22-2-2-243−43000000-1-11100−2323−23230033−3−30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-44444-44-4422202-2-22-22-2-2-2−4343000000-1-1110023−2323−2300−3−3330000000000000000000000000000000000000000000000000000000000

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