Finite Group Databasebeta

← Group #13168624

Character table — Group #13168624

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121222446666121212121212121212121212444444441212121266666612121212121212121212221212121212126644
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-11111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11-111-1-11111-1-111111-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-111111111111111111-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111-1111-1-111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-11-1-11111-1-1111111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-11-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1111111-1-1-111111-1-1-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1111-111-1-1111-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-111-1-111-1-111111111-11-1-1111-111-1-111-1-1-1-1-1-11111-1-1-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-11-1-111-1111-1-1-1-11111-1-1-1-1-1-1111-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-111-1-11-1-1-11111-1-111-1-1-1-1-1-111-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111-1-11111-1-1111111111-111-1-1-11-1-111-1-111-1-1-1-11111-1-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111-1-1-1-1-111-1-11-111-1-1111-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-11-1-1-1-1-1-111-111111-1-1-11-11
χ17222222-122-12-122-12-12-12-1-12-12-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-10222002200-1-122-1-100220000002200000-100-1-1-1200-1-1-1-1-1-1020000-1-10-100
χ18222222-122-12-122-12-12-12-1-12-12-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-102-2-2002200-1-1-2-2110022000000-2-200000-100-1-11-200-1-111110-20000110100
χ19222222-122-12-122-12-12-12-1-12-12-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-22200-2-2001122-1-100-2-2000000-2-20000010011-120011-1-1-1-10-20000110100
χ20222222-122-12-122-12-12-12-1-12-12-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-10-2-2-200-2-20011-2-21100-2-20000002200000100111-200111111020000-1-10-100
χ21222222-122-12-122-12-12-1-2-1-12-12-12-1-1-2-20022-1-1-1-1-21-2-2111111110-22-200-2-200-1-122110022000000-2-20000010011-1-200-1-1-1-111020000110-100
χ22222222-122-12-122-12-12-1-2-1-12-12-12-1-1-2-20022-1-1-1-1-21-2-2111111110-2-2200-2-200-1-1-2-2-1-100220000002200000100111200-1-111-1-10-20000-1-10100
χ23222222-122-12-122-12-12-1-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111022-200220011221100-2-20000002200000-100-1-1-1-20011-1-1110-20000-1-10100
χ24222222-122-12-122-12-12-1-2-1-12-12-12-1-1-2-200-2-2-1-1-1-1-21-2-21111111102-2200220011-2-2-1-100-2-2000000-2-200000-100-1-112001111-1-1020000110-100
χ2522222-122-12-122-122-1-122-1-1-12-12-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-120222200-1-100-1-1222200000022000000-10-1-1002-1-1-100-1-1-1-12000-1-100-1000
χ2622222-122-12-122-122-1-122-1-1-12-12-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-120-2-22200-1-10011-2-222000000-2-2000000-10-1-100-21-1-1001111-200011001000
χ2722222-122-12-122-122-1-122-1-1-12-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2022-2-2001100-1-122-2-2000000-2-20000001011002-11100-1-1-1-1-200011001000
χ2822222-122-12-122-122-1-122-1-1-12-12-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2-2-2-200110011-2-2-2-200000022000000101100-21110011112000-1-100-1000
χ2922222-122-12-122-122-1-12-2-1-1-12-12-12-1-2-22200-1-1-1-11-211-2-2111111-202-2-2-200-1-100-1-1-2-2220000002200000010110021-1-100-1-111-2000-1-1001000
χ3022222-122-12-122-122-1-12-2-1-1-12-12-12-1-2-22200-1-1-1-11-211-2-2111111-20-22-2-200-1-100112222000000-2-2000000101100-2-1-1-10011-1-120001100-1000
χ3122222-122-12-122-122-1-12-2-1-1-12-12-12-1-2-2-2-200-1-1-1-11-211-2-2111111202-222001100-1-1-2-2-2-2000000-2-2000000-10-1-100211100-1-11120001100-1000
χ3222222-122-12-122-122-1-12-2-1-1-12-12-12-1-2-2-2-200-1-1-1-11-211-2-211111120-22220011001122-2-200000022000000-10-1-100-2-1110011-1-1-2000-1-1001000
χ332222-122-12222-122-12-1-1222-1-1-1-1-1-12-1-12222-1-1-1-122-1-1-1-122-1-1-1-12200-1-1-1-122220000-1-1-1-122220000-1-1-1-122-1-1-1-100-1-1-1-1000000-1-100000000
χ342222-122-12222-122-12-1-1222-1-1-1-1-1-12-1-122-2-2-1-1-1-122-1-1-1-122-1-1-1-12-200-1-11122-2-20000-1-111-2-2-2-2000011112-2-1-11100-1-1110000001100000000
χ352222-122-12222-122-12-1-1222-1-1-1-1-1-12-1-1-2-222-1-1-1-122-1-1-1-122-1-1-1-1-220011-1-1-2-222000011-1-1-2-2-2-200001111-2211-1-10011-1-10000001100000000
χ362222-122-12222-122-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-122-1-1-1-1-2-2001111-2-2-2-20000111122220000-1-1-1-1-2-21111001111000000-1-100000000
χ372222-122-12222-122-12-1-1-222-1-1-1-1-1-12112222-1-1-1-1-2-21111-2-21111-2-200111122220000-1-1-1-1-2-22200001111-2-2111100-1-1-1-1000000-1-100000000
χ382222-122-12222-122-12-1-1-222-1-1-1-1-1-121122-2-2-1-1-1-1-2-21111-2-21111-220011-1-122-2-20000-1-11122-2-20000-1-1-1-1-2211-1-100-1-1110000001100000000
χ392222-122-12222-122-12-1-1-222-1-1-1-1-1-1211-2-222-1-1-1-1-2-21111-2-211112-200-1-111-2-222000011-1-122-2-20000-1-1-1-12-2-1-1110011-1-10000001100000000
χ402222-122-12222-122-12-1-1-222-1-1-1-1-1-1211-2-2-2-2-1-1-1-1-2-21111-2-211112200-1-1-1-1-2-2-2-200001111-2-2220000111122-1-1-1-1001111000000-1-100000000
χ4122-2-2222-222-2-2-2-2-2222202-2-2-2-2-222-200000022-2-2000000000000000000000000000000002-2002i−2i2i−2i22-2-2000000000000000000002i−2i2i−2i0000
χ4222-2-2222-222-2-2-2-2-2222202-2-2-2-2-222-200000022-2-2000000000000000000000000000000002-200−2i2i−2i2i22-2-200000000000000000000−2i2i−2i2i0000
χ4322-2-2222-222-2-2-2-2-2222202-2-2-2-2-222-200000022-2-200000000000000000000000000000000-22002i−2i−2i2i-2-222000000000000000000002i−2i−2i2i0000
χ4422-2-2222-222-2-2-2-2-2222202-2-2-2-2-222-200000022-2-200000000000000000000000000000000-2200−2i2i2i−2i-2-22200000000000000000000−2i2i2i−2i0000
χ452-22-2222-2-2-2-2-2222-22220-2222-2-2-2-2-2002i−2i2i−2i2-22-2000000000000000000002i−2i2i−2i00002i−2i2i−2i002-200000000000000002i−2i2i−2i0000002-200000000
χ462-22-2222-2-2-2-2-2222-22220-2222-2-2-2-2-2002i−2i−2i2i2-22-2000000000000000000002i−2i−2i2i00002i−2i−2i2i00-2200000000000000002i−2i−2i2i000000-2200000000
χ472-22-2222-2-2-2-2-2222-22220-2222-2-2-2-2-200−2i2i2i−2i2-22-200000000000000000000−2i2i2i−2i0000−2i2i2i−2i00-220000000000000000−2i2i2i−2i000000-2200000000
χ482-22-2222-2-2-2-2-2222-22220-2222-2-2-2-2-200−2i2i−2i2i2-22-200000000000000000000−2i2i−2i2i0000−2i2i−2i2i002-20000000000000000−2i2i−2i2i0000002-200000000
χ492-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-23−32i−2i2i−2i-11-11003−33−30033−3−30000−i3i3−i3i32i−2i2i−2i0000−ii−ii002-200003−33−300−i3i3−i3i300−ii−ii000000-1100000000
χ502-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-23−32i−2i−2i2i-11-11003−33−30033−3−30000−i3i3i3−i32i−2i−2i2i0000−iii−i00-220000−33−3300−i3i3i3−i300−iii−i0000001-100000000
χ512-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-23−3−2i2i2i−2i-11-11003−33−30033−3−30000i3−i3−i3i3−2i2i2i−2i0000i−i−ii00-220000−33−3300i3−i3−i3i300i−i−ii0000001-100000000
χ522-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-23−3−2i2i−2i2i-11-11003−33−30033−3−30000i3−i3i3−i3−2i2i−2i2i0000i−ii−i002-200003−33−300i3−i3i3−i300i−ii−i000000-1100000000
χ532-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-2−332i−2i2i−2i-11-1100−33−3300−3−3330000i3−i3i3−i32i−2i2i−2i0000−ii−ii002-20000−33−3300i3−i3i3−i300−ii−ii000000-1100000000
χ542-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-2−332i−2i−2i2i-11-1100−33−3300−3−3330000i3−i3−i3i32i−2i−2i2i0000−iii−i00-2200003−33−300i3−i3−i3i300−iii−i0000001-100000000
χ552-22-2-1221-2-2-2-2-12212-1-10-22-1-11111-2−33−2i2i2i−2i-11-1100−33−3300−3−3330000−i3i3i3−i3−2i2i2i−2i0000i−i−ii00-2200003−33−300−i3i3i3−i300i−i−ii0000001-100000000
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χ5744444-2-24-2-2-2-24-2-241-2-2411-2-2-2-2-2-214400001111-2-2-2-2-2-2111111004400000000-2-2-2-20000000000000000000000-2-200001111000000000000
χ5844444-2-24-2-2-2-24-2-241-2-2411-2-2-2-2-2-214400001111-2-2-2-2-2-211111100-4-40000000022220000000000000000000000220000-1-1-1-1000000000000
χ5944444-2-24-2-2-2-24-2-241-2-2-411-2-2-2-2-2-21-4-400001111222222-1-1-1-1-1-1004-400000000-2-2220000000000000000000000-22000011-1-1000000000000
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χ614444-24-2-24-24-2-24-2-2-2-214-2-2-21-21-21-2-2-2004411114-2-2-211-2-21111040000-2-200-2-2000000-2-20000000000000-200110000110000000000000000
χ624444-24-2-24-24-2-24-2-2-2-214-2-2-21-21-21-2-2-200-4-411114-2-2-211-2-211110-40000220022000000220000000000000200-1-10000-1-10000000000000000
χ634444-24-2-24-24-2-24-2-2-2-21-4-2-2-21-21-21-22200441111-4222-1-122-1-1-1-10-400002200-2-2000000-2-20000000000000200-1-10000110000000000000000
χ644444-24-2-24-24-2-24-2-2-2-21-4-2-2-21-21-21-22200-4-41111-4222-1-122-1-1-1-1040000-2-20022000000220000000000000-200110000-1-10000000000000000
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χ664444-2-24-2-24-24-2-24-2-21-24-2-21-21-21-2-2-2-2-4-4001111-2411-2-2-2-21111-4000220022000000220000000000000020-1-10000-1-1000000000000000000
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χ814-44-4-24-22-42-42-24-22-2-2102-2-212-12-12−2323004i−4i1-11-100−23233−30033−3−30000002i3−2i300−2i2i000000−2i2i0000000000000000−i3i30000i−i0000000000000000
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χ874-4-444444-4-444-4-4-4-44440-4-4-4-444-4-440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ884-4-4444-24-424-2-4-42-4-24-2022-424-2-42-2000000-222-200000000000000000000000000−2i32i3000000000000000000000000000000−2i32i3000000000000
χ894-4-4444-24-424-2-4-42-4-24-2022-424-2-42-2000000-222-2000000000000000000000000002i3−2i30000000000000000000000000000002i3−2i3000000000000
χ904-4-444-2442-4-24-42-4-4-2-240222-4-242-4-2000000-222-2000000000000000000000000−2i32i3000000000000000000000000000000−2i32i300000000000000
χ914-4-444-2442-4-24-42-4-4-2-240222-4-242-4-2000000-222-20000000000000000000000002i3−2i30000000000000000000000000000002i3−2i300000000000000
χ924-4-444-2-2422-2-2-422-41-2-20-1-122-2-22210000001-1-110000003-33-33-3000000000000−2i32i3−2i32i30000000000000000000000000000i3−i3i3−i3000000000000
χ934-4-444-2-2422-2-2-422-41-2-20-1-122-2-22210000001-1-110000003-33-33-30000000000002i3−2i32i3−2i30000000000000000000000000000−i3i3−i3i3000000000000
χ944-4-444-2-2422-2-2-422-41-2-20-1-122-2-22210000001-1-11000000-33-33-33000000000000−2i32i32i3−2i30000000000000000000000000000i3−i3−i3i3000000000000
χ954-4-444-2-2422-2-2-422-41-2-20-1-122-2-22210000001-1-11000000-33-33-330000000000002i3−2i3−2i32i30000000000000000000000000000−i3i3i3−i3000000000000
χ964-4-44-244-2-4-4442-4-424-2-20-4-422-2-2224000000-222-2000000000000000000000000000000000000000023−23−23230000000000000000000000000000
χ974-4-44-244-2-4-4442-4-424-2-20-4-422-2-2224000000-222-20000000000000000000000000000000000000000−232323−230000000000000000000000000000
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
χ10088-8-88-4-4-8-4-444-84482-4-402-24444-4-4-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-448-4-844-84-4-4-420-444-24-2-42400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-484-484-844-8-4-42-40-44-24-242-4400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-4-444444-422202-2-2-2-2-222-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-4-444444-422202-2-2-2-2-222-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-4-844448-4-4-82-4-40-22-4-44444-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-444444-4-4-442220-2222-2-2-2-2-243−430000-11-1100−2323−23230033−3−3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444444-4-4-442220-2222-2-2-2-2-2−43430000-11-110023−2323−2300−3−333000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4-4-848-44-844-4-420444-2-424-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-44-8-4844-84-42-4044-242-4-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444-4-444442220-2-2-2-222-2-22000000-111-10000006-6-33-33000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444-4-444442220-2-2-2-222-2-22000000-111-1000000-663-33-3000000000000000000000000000000000000000000000000000000000000

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