Finite Group Databasebeta

← Group #13168577

Character table — Group #13168577

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order12223336666666663334666666666121244444436661212121212121212121212124441212121212121212121212121212121222446666121212121212121212121212121212122444121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111111111111111111-11-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1111-1-111-1-111111-1-1111-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111-1-111111111111111111111-111-1-111-1-11111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-1111111-111-1-1-111-1-1-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-111111111111111111111-1111111-1-11111-1-1111111111111-111-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-1-111-1-1-111-1-111-111
χ71111111111111111111111111111111-1-1-1-1111111111111111111-11-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-11-1-1111-1-1-1-1111-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111111111-1-11111-1-11-1-1-1-1-1111111-1-1-11-1111-1-1-1-111-11-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-111-1-11111-11-1-11111-1-1-1-111-1-11-11-1-1-111-1-1111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-111-111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-11-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1-111111-111-1-1-1-11111-1-1111-11-1-1-111-1-1-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-1-1-111-1-1111111-111111-1-1-1-1-1-111-11-1111-1-1-1-1-1-1-111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111111111-1-1-1
χ17222222-122-12-1-12222-1-122-1-1-12-12-1-122222200-1-1-1-1-12-1-122-1-1-1-1-1-120200-1-1-1-1220022220000000000-1-102-1-100-1-100-1-1-1-12002-1-1000000-100
χ18222222-122-12-1-12222-1-122-1-1-12-12-1-12222-2-200-1-1-1-1-12-1-122-1-1-1-1-1-120-20011-1-1-2-20022-2-20000000000-110211001100-1-1-1-1-200-211000000100
χ19222222-122-12-1-12222-1-122-1-1-12-12-1-122-2-22200-1-1-1-1-12-1-122-1-1-1-1-1-1-20200-1-1112200-2-22200000000001-10-2-1-100-1-1001111-200-211000000100
χ20222222-122-12-1-12222-1-122-1-1-12-12-1-122-2-2-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-20-2001111-2-200-2-2-2-20000000000110-21100110011112002-1-1000000-100
χ21222222-122-12-1-12222-1-1-22-1-1-12-12-1-1-2-2222200-1-1-1-11-211-2-2111111-20-200-1-1-1-1-2-20022220000000000110-21100-1-100-1-111-2002-1-1000000100
χ22222222-122-12-1-12222-1-1-22-1-1-12-12-1-1-2-222-2-200-1-1-1-11-211-2-2111111-2020011-1-1220022-2-200000000001-10-2-1-1001100-1-111200-211000000-100
χ23222222-122-12-1-12222-1-1-22-1-1-12-12-1-1-2-2-2-22200-1-1-1-11-211-2-211111120-200-1-111-2-200-2-2220000000000-11021100-1-10011-1-1200-211000000-100
χ24222222-122-12-1-12222-1-1-22-1-1-12-12-1-1-2-2-2-2-2-200-1-1-1-11-211-2-21111112020011112200-2-2-2-20000000000-1-102-1-100110011-1-1-2002-1-1000000100
χ2522222-12-122-12222-1-12-12-12-12-1-1-1-12-1-1002222-1-1-1-12222-1-1-1-1-1-1-1-1022222200-1-1-1-100-1-1-1-12222-1-1-1-10220-1-1-1-1-1-1-1-1000000000000-1-100000
χ2622222-12-122-12222-1-12-12-12-12-1-1-1-12-1-10022-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-22-2-22200-1-11100-1-111-2-2-2-2111102-20-1-111-1-1110000000000001100000
χ2722222-12-122-12222-1-12-12-12-12-1-1-1-12-1-100-2-222-1-1-1-12222-1-1-1-1-1-1-1-102-222-2-20011-1-10011-1-1-2-2-2-211110-22011-1-111-1-10000000000001100000
χ2822222-12-122-12222-1-12-12-12-12-1-1-1-12-1-100-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-2-2-20011110011112222-1-1-1-10-2-2011111111000000000000-1-100000
χ2922222-12-122-12222-1-12-1-2-12-12-1-1-1-1211002222-1-1-1-1-2-2-2-2111111110-2-222220011-1-100-1-111-2-22211110-2-2011-1-1-1-111000000000000-1-100000
χ3022222-12-122-12222-1-12-1-2-12-12-1-1-1-12110022-2-2-1-1-1-1-2-2-2-21111111102-2-2-22200111100-1-1-1-122-2-2-1-1-1-10-2201111-1-1-1-10000000000001100000
χ3122222-12-122-12222-1-12-1-2-12-12-1-1-1-121100-2-222-1-1-1-1-2-2-2-2111111110-2222-2-200-1-1-1-100111122-2-2-1-1-1-102-20-1-1-1-111110000000000001100000
χ3222222-12-122-12222-1-12-1-2-12-12-1-1-1-121100-2-2-2-2-1-1-1-1-2-2-2-211111111022-2-2-2-200-1-1110011-1-1-2-22211110220-1-11111-1-1000000000000-1-100000
χ332222-1222-12222-1-12-1-122-1-12-1-12-12-122220022-1-1-1-12-1-1-1-1-122-1-1-1-1220-1-100220022-1-100220000000020-1-100-1-100-1-1-1-1-1-1022000-1-100000-10
χ342222-1222-12222-1-12-1-122-1-12-1-12-12-1222200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-12-2011002200-2-2-1-100-2-200000000201-100110011-1-1-1-10-2-2000110000010
χ352222-1222-12222-1-12-1-122-1-12-1-12-12-122-2-20022-1-1-1-12-1-1-1-1-122-1-1-1-1-220-1-100-2-2002211002200000000-20-1100-1-100-1-111110-2-2000110000010
χ362222-1222-12222-1-12-1-122-1-12-1-12-12-122-2-200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-2-201100-2-200-2-21100-2-200000000-2011001100111111022000-1-100000-10
χ372222-1222-12222-1-12-1-12-2-1-12-1-12-12-1-2-2220022-1-1-1-1-211111-2-21111-2-20-1-100220022-1-100-2-200000000-201100-1-10011-1-1110-22000-1-10000010
χ382222-1222-12222-1-12-1-12-2-1-12-1-12-12-1-2-22200-2-2-1-1-1-1-211111-2-21111-22011002200-2-2-1-1002200000000-20-11001100-1-1-1-11102-20001100000-10
χ392222-1222-12222-1-12-1-12-2-1-12-1-12-12-1-2-2-2-20022-1-1-1-1-211111-2-211112-20-1-100-2-200221100-2-200000000201-100-1-1001111-1-102-20001100000-10
χ402222-1222-12222-1-12-1-12-2-1-12-1-12-12-1-2-2-2-200-2-2-1-1-1-1-211111-2-211112201100-2-200-2-21100220000000020-1-1001100-1-111-1-10-22000-1-10000010
χ412-22-2222-2-22-2-2-22-222220-2-2-22-2-222-2002i−2i00002-2-2200000000000000000002i−2i00002i−2i00002-20022-2-20000000000002i−2i0000000000002i−2i000
χ422-22-2222-2-22-2-2-22-222220-2-2-22-2-222-2002i−2i00002-2-2200000000000000000002i−2i00002i−2i0000-2200-2-2220000000000002i−2i000000000000−2i2i000
χ432-22-2222-2-22-2-2-22-222220-2-2-22-2-222-200−2i2i00002-2-220000000000000000000−2i2i0000−2i2i00002-20022-2-2000000000000−2i2i000000000000−2i2i000
χ442-22-2222-2-22-2-2-22-222220-2-2-22-2-222-200−2i2i00002-2-220000000000000000000−2i2i0000−2i2i0000-2200-2-222000000000000−2i2i0000000000002i−2i000
χ452-2-22222-22-22-22-2-2-22220-22-2-222-2-2-200002i−2i2-222-2-20000000000000002-22i−2i00002-2002i−2i00002i−2i00000000002-22i−2i000000000000002i−2i00000
χ462-2-22222-22-22-22-2-2-22220-22-2-222-2-2-200002i−2i-2222-2-2000000000000000-222i−2i0000-22002i−2i0000−2i2i0000000000-222i−2i00000000000000−2i2i00000
χ472-2-22222-22-22-22-2-2-22220-22-2-222-2-2-20000−2i2i2-222-2-20000000000000002-2−2i2i00002-200−2i2i0000−2i2i00000000002-2−2i2i00000000000000−2i2i00000
χ482-2-22222-22-22-22-2-2-22220-22-2-222-2-2-20000−2i2i-2222-2-2000000000000000-22−2i2i0000-2200−2i2i00002i−2i0000000000-22−2i2i000000000000002i−2i00000
χ492-2-222-1212-2-1-22-2-21-12-10121-2-1-111-23−3002i−2i2-2-1-11100003−33−333−3−30002-22i−2i00−i3i3-1100−ii3−3002i−2i−i3i3−i3i30000−i3i3-11−ii3−3000000000000−ii00000
χ502-2-222-1212-2-1-22-2-21-12-10121-2-1-111-23−3002i−2i-22-1-11100003−33−333−3−3000-222i−2i00−i3i31-100−ii−3300−2i2ii3−i3i3−i30000−i3i31-1−ii−33000000000000i−i00000
χ512-2-222-1212-2-1-22-2-21-12-10121-2-1-111-23−300−2i2i2-2-1-11100003−33−333−3−30002-2−2i2i00i3−i3-1100i−i3−300−2i2ii3−i3i3−i30000i3−i3-11i−i3−3000000000000i−i00000
χ522-2-222-1212-2-1-22-2-21-12-10121-2-1-111-23−300−2i2i-22-1-11100003−33−333−3−3000-22−2i2i00i3−i31-100i−i−33002i−2i−i3i3−i3i30000i3−i31-1i−i−33000000000000−ii00000
χ532-2-222-1212-2-1-22-2-21-12-10121-2-1-111-2−33002i−2i2-2-1-1110000−33−33−3−3330002-22i−2i00i3−i3-1100−ii−33002i−2ii3−i3i3−i30000i3−i3-11−ii−33000000000000−ii00000
χ542-2-222-1212-2-1-22-2-21-12-10121-2-1-111-2−33002i−2i-22-1-1110000−33−33−3−333000-222i−2i00i3−i31-100−ii3−300−2i2i−i3i3−i3i30000i3−i31-1−ii3−3000000000000i−i00000
χ552-2-222-1212-2-1-22-2-21-12-10121-2-1-111-2−3300−2i2i2-2-1-1110000−33−33−3−3330002-2−2i2i00−i3i3-1100i−i−3300−2i2i−i3i3−i3i30000−i3i3-11i−i−33000000000000i−i00000
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χ5744444-2-2-24-2-2-2-244-2-2-214-2-21-2-21-21-2-2-20044001111-24-2-2-2-211111100400-2-200-2-20000-2-200000000000-200110011000000000000000000000
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χ5944444-2-2-24-2-2-2-244-2-2-21-4-2-21-2-21-21-22200440011112-42222-1-1-1-1-1-100-400-2-200220000-2-200000000000200-1-10011000000000000000000000
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χ624444-24-24-2-24-2-2-2-24-21-24-21-21-2-2-2-2144-4-400001111-2-211-2-2-2-21111-400000022000022000000000000200200000000-1-1-1-1000000000000000
χ634444-24-24-2-24-2-2-2-24-21-2-4-21-21-2-2-2-21-4-4440000111122-1-12222-1-1-1-1-4000000-2-20000-2-200000000000020020000000011-1-1000000000000000
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χ884-4-444-2-2242-22-2-4-42-2-2102-2-12-212-1223−23004i−4i0011-1-1000023−23−33−3−33300000−2i2i00−2i32i30000−2i2i00000000000000i3−i300i−i000000000000000000000
χ894-4-444-2-2242-22-2-4-42-2-2102-2-12-212-1223−2300−4i4i0011-1-1000023−23−33−3−333000002i−2i002i3−2i300002i−2i00000000000000−i3i300−ii000000000000000000000
χ904-4-444-2-2242-22-2-4-42-2-2102-2-12-212-12−2323004i−4i0011-1-10000−23233−333−3−300000−2i2i002i3−2i30000−2i2i00000000000000−i3i300i−i000000000000000000000
χ914-4-444-2-2242-22-2-4-42-2-2102-2-12-212-12−232300−4i4i0011-1-10000−23233−333−3−3000002i−2i00−2i32i300002i−2i00000000000000i3−i300−ii000000000000000000000
χ924-4-44-244-4-2-44-4422-4-2-2402-2-42-242-420000004-4-2-222000000000000000-220000004-400000000000000000000-2200000000000000000000000
χ934-4-44-244-4-2-44-4422-4-2-2402-2-42-242-42000000-44-2-2220000000000000002-2000000-44000000000000000000002-200000000000000000000000
χ944-4-44-2-242-2-4-2-442221-2-20-1-2221-2-12223−2300004-411-1-10000−3323−23−3−333000-22000000-22000023−23000000000000001-100−330000000000000000000
χ954-4-44-2-242-2-4-2-442221-2-20-1-2221-2-12223−230000-4411-1-10000−3323−23−3−3330002-20000002-20000−232300000000000000-11003−30000000000000000000
χ964-4-44-2-242-2-4-2-442221-2-20-1-2221-2-122−232300004-411-1-100003−3−232333−3−3000-22000000-220000−2323000000000000001-1003−30000000000000000000
χ974-4-44-2-242-2-4-2-442221-2-20-1-2221-2-122−23230000-4411-1-100003−3−232333−3−30002-20000002-2000023−2300000000000000-1100−330000000000000000000
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
χ10088-8-88-4-4-4-844-44-884-4-420-44244-24-2-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4844-8-444-4-8-42-40-4-2-4-244442000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48-44-848-84-442-4-4024-44-24-24-4000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4444-444-4422202-22-2-2-2-2-2200000000-11-110000000033−33−33330000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-4-4444-444-4422202-22-2-2-2-2-2200000000-11-1100000000−333333−330000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-44-8-44448-8-4-4-42044-2-44-2-424000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-484484-8-8-44-42-4-40-244-4-242-44000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-444-4444-44-42220-2-2-22-2-222-200000000-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-444-4444-44-42220-2-2-22-2-222-200000000-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-8-4484-444-8-42-40424-2-4-444-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44-44-44-44442220-22-2-222-2-2-243−43000000-1-1110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44-44-44-44442220-22-2-222-2-2-2−4343000000-1-111000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000

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