Finite Group Databasebeta

← Group #13168235

Character table — Group #13168235

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order1222333666666666333466666666612122244443666121212121212121212121212444666612121212121212121212121244441212121266121212121212121212121212121244441212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1111111-1-111111111-1-11111111111-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111111-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1-1-1-1-1-111-1-1-11-1
χ4111111111111111111111111111111111-1-1-1-11111111111111111-11-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-11
χ51111111111111111111111111111111-1-1111111111111111111111-11-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-111111111-1-111-1-111-1-1-1-11-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-11
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-111111111-1-11-1-1-11111-1-1-1-11-1-11-1-1-1-111111-1-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-111-1-1-1-111111111111-1-1-111-1-1-1-111-111-1-1-111-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1111-1-11111-1-1-111-1-1-111-1-111-11-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1111-1-1-1-111111-1-11-1-1-1-111-1-11-11
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111-11-111111111-1-1-1
χ17222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1222200-1-1-1-122-1-122-1-1-1-1-1-102222-1-100-1-122-1-1-1-1002222-1-1-1-1-1-10022-1-1-1-100-1-1000000-1-1000000000
χ18222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-122-2-200-1-1-1-122-1-122-1-1-1-1-1-102-222-1-10011-2-2-1-11100-2-2-2-21111-1-100-22-1-111001100000011000000000
χ19222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-2-22200-1-1-1-122-1-122-1-1-1-1-1-10-22-2-21100-1-12211-1-100-2-2-2-2111111002-211-1-100-1-100000011000000000
χ20222222-1222-12-1-1222-1-122-1-1-12-1-12-1-1-1-2-2-2-200-1-1-1-122-1-122-1-1-1-1-1-10-2-2-2-2110011-2-21111002222-1-1-1-11100-2-211110011000000-1-1000000000
χ21222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111222200-1-1-1-1-2-211-2-21111110-2-222-1-100-1-12211110022-2-21111-1-100-2-2111100-1-1000000-1-1000000000
χ22222222-1222-12-1-1222-1-1-22-1-1-12-1-12-11122-2-200-1-1-1-1-2-211-2-21111110-2222-1-10011-2-211-1-100-2-222-1-1-1-1-1-1002-211-1-1001100000011000000000
χ23222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-2-22200-1-1-1-1-2-211-2-211111102-2-2-21100-1-122-1-11100-2-222-1-1-1-11100-22-1-11100-1-100000011000000000
χ24222222-1222-12-1-1222-1-1-22-1-1-12-1-12-111-2-2-2-200-1-1-1-1-2-211-2-2111111022-2-2110011-2-2-1-1-1-10022-2-21111110022-1-1-1-10011000000-1-1000000000
χ2522222-12-12-122222-1-12-12-12-1-1-12-1-1222220022-1-1-1-1-12-1-1-1-122-1-1-1-1220-1-1222200002200-1-100000000-1-1-120-1-1-100-1-100-1-122000000-1-1000-10
χ2622222-12-12-122222-1-12-12-12-1-1-12-1-12222200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-220-1-122-2-2000022001100000000-1-11-20-1-1-100110011-2-20000001100010
χ2722222-12-12-122222-1-12-12-12-1-1-12-1-1222-2-20022-1-1-1-1-12-1-1-1-122-1-1-1-12-2011-2-2220000-2-200-1-10000000011-12011100-1-100-1-1-2-20000001100010
χ2822222-12-12-122222-1-12-12-12-1-1-12-1-1222-2-200-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2011-2-2-2-20000-2-2001100000000111-201110011001122000000-1-1000-10
χ2922222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2220022-1-1-1-11-21111-2-21111-2-20-1-122220000-2-200-1-100000000-1-11-2011100-1-100112-2000000-1-100010
χ3022222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-22200-2-2-1-1-1-11-21111-2-211112-20-1-122-2-20000-2-2001100000000-1-1-120111001100-1-1-2200000011000-10
χ3122222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2-2-20022-1-1-1-11-21111-2-21111-22011-2-22200002200-1-100000000111-20-1-1-100-1-10011-2200000011000-10
χ3222222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2-2-200-2-2-1-1-1-11-21111-2-2111122011-2-2-2-200002200110000000011-120-1-1-1001100-1-12-2000000-1-100010
χ332222-1222-122-122-12-1-122-1-122-1-12-1-122002222-1-1-1-12-122-1-1-1-1-1-1-1-12020000-1-122-1-100222200000000002-1-1000-1-1-1-1-1-1-1-1002200-1-10000-100
χ342222-1222-122-122-12-1-122-1-122-1-12-1-1220022-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20200001122-1-10022-2-20000000000-21-1000-1-111-1-11100-2-200110000100
χ352222-1222-122-122-12-1-122-1-122-1-12-1-12200-2-222-1-1-1-12-122-1-1-1-1-1-1-1-120-20000-1-1-2-21100-2-22200000000002-1100011-1-111-1-100-2-200110000100
χ362222-1222-122-122-12-1-122-1-122-1-12-1-12200-2-2-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-20-2000011-2-21100-2-2-2-20000000000-21100011111111002200-1-10000-100
χ372222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-2002222-1-1-1-1-21-2-211111111-20-20000-1-122-1-100-2-2220000000000-21100011-1-1-1-111002-200-1-10000100
χ382222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-20022-2-2-1-1-1-1-21-2-21111111120-200001122-1-100-2-2-2-200000000002-110001111-1-1-1-100-2200110000-100
χ392222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-200-2-222-1-1-1-1-21-2-211111111-2020000-1-1-2-2110022220000000000-21-1000-1-1-1-1111100-2200110000-100
χ402222-1222-122-122-12-1-12-2-1-122-1-12-1-1-2-200-2-2-2-2-1-1-1-1-21-2-211111111202000011-2-2110022-2-200000000002-1-1000-1-11111-1-1002-200-1-10000100
χ412-22-2222-22-2-2-22-2-222220-22-2-22-22-2-20000002-222-2-200000000000000000002-2000000002-2002i−2i2i2i−2i−2i00000000002-2000000000000002i−2i000
χ422-22-2222-22-2-2-22-2-222220-22-2-22-22-2-20000002-222-2-200000000000000000002-2000000002-200−2i2i−2i−2i2i2i00000000002-200000000000000−2i2i000
χ432-22-2222-22-2-2-22-2-222220-22-2-22-22-2-2000000-2222-2-20000000000000000000-2200000000-22002i−2i2i2i−2i−2i0000000000-2200000000000000−2i2i000
χ442-22-2222-22-2-2-22-2-222220-22-2-22-22-2-2000000-2222-2-20000000000000000000-2200000000-2200−2i2i−2i−2i2i2i0000000000-22000000000000002i−2i000
χ452-2-222222-2-2-2-2-222-222202-22-2-22-2-2-2002-22i−2i002-22-20000000000000002-22-2002i−2i2i−2i0000002i−2i0000002-200000000002i−2i0000002i−2i000000000
χ462-2-222222-2-2-2-2-222-222202-22-2-22-2-2-2002-2−2i2i002-22-20000000000000002-22-200−2i2i−2i2i000000−2i2i0000002-20000000000−2i2i000000−2i2i000000000
χ472-2-222222-2-2-2-2-222-222202-22-2-22-2-2-200-222i−2i002-22-2000000000000000-22-22002i−2i2i−2i000000−2i2i000000-2200000000002i−2i000000−2i2i000000000
χ482-2-222222-2-2-2-2-222-222202-22-2-22-2-2-200-22−2i2i002-22-2000000000000000-22-2200−2i2i−2i2i0000002i−2i000000-220000000000−2i2i0000002i−2i000000000
χ492-2-2222-12-2-21-21-12-22-1-1021-11-2-11-213−32-22i−2i00-11-11003−3003−333−3−30002-2-1100−ii2i−2i3−3−i3i3002i−2i00−i3i3−i3i3-1100003−3−i3i300−ii000000−ii000000000
χ502-2-2222-12-2-21-21-12-22-1-1021-11-2-11-213−32-2−2i2i00-11-11003−3003−333−3−30002-2-1100i−i−2i2i3−3i3−i300−2i2i00i3−i3i3−i3-1100003−3i3−i300i−i000000i−i000000000
χ512-2-2222-12-2-21-21-12-22-1-1021-11-2-11-213−3-222i−2i00-11-11003−3003−333−3−3000-221-100−ii2i−2i−33−i3i300−2i2i00i3−i3i3−i31-10000−33−i3i300−ii000000i−i000000000
χ522-2-2222-12-2-21-21-12-22-1-1021-11-2-11-213−3-22−2i2i00-11-11003−3003−333−3−3000-221-100i−i−2i2i−33i3−i3002i−2i00−i3i3−i3i31-10000−33i3−i300i−i000000−ii000000000
χ532-2-2222-12-2-21-21-12-22-1-1021-11-2-11-21−332-22i−2i00-11-1100−3300−33−3−3330002-2-1100−ii2i−2i−33i3−i3002i−2i00i3−i3i3−i3-110000−33i3−i300−ii000000−ii000000000
χ542-2-2222-12-2-21-21-12-22-1-1021-11-2-11-21−332-2−2i2i00-11-1100−3300−33−3−3330002-2-1100i−i−2i2i−33−i3i300−2i2i00−i3i3−i3i3-110000−33−i3i300i−i000000i−i000000000
χ552-2-2222-12-2-21-21-12-22-1-1021-11-2-11-21−33-222i−2i00-11-1100−3300−33−3−333000-221-100−ii2i−2i3−3i3−i300−2i2i00−i3i3−i3i31-100003−3i3−i300−ii000000i−i000000000
χ562-2-2222-12-2-21-21-12-22-1-1021-11-2-11-21−33-22−2i2i00-11-1100−3300−33−3−333000-221-100i−i−2i2i3−3−i3i3002i−2i00i3−i3i3−i31-100003−3−i3i300i−i000000−ii000000000
χ5744444-2-2-24-2-24-2-24-2-2-214-2-211-2-21-2-2-2-24400001111-2411-2-2-2-21111040-2-2-2-2000000-2-200000000000011000-21100000000000000000000000
χ5844444-2-2-24-2-24-2-24-2-2-214-2-211-2-21-2-2-2-2-4-400001111-2411-2-2-2-211110-40222200000022000000000000-1-10002-1-100000000000000000000000
χ5944444-2-2-24-2-24-2-24-2-2-21-4-2-211-2-21-2-22244000011112-4-1-12222-1-1-1-10-40-2-2-2-200000022000000000000110002-1-100000000000000000000000
χ6044444-2-2-24-2-24-2-24-2-2-21-4-2-211-2-21-2-222-4-4000011112-4-1-12222-1-1-1-10402222000000-2-2000000000000-1-1000-21100000000000000000000000
χ614444-24-24-24-2-2-2-2-24-21-24-21-2-2-21-2-21-2-200440011114-2-2-2-2-2111111004000000-2-2-2-200-2-200000000000000-200011001100000000000000000
χ624444-24-24-24-2-2-2-2-24-21-24-21-2-2-21-2-21-2-200-4-40011114-2-2-2-2-211111100-400000022220022000000000000002000-1-100-1-100000000000000000
χ634444-24-24-24-2-2-2-2-24-21-2-4-21-2-2-21-2-21220044001111-422222-1-1-1-1-1-100-4000000-2-2-2-20022000000000000002000-1-1001100000000000000000
χ644444-24-24-24-2-2-2-2-24-21-2-4-21-2-2-21-2-212200-4-4001111-422222-1-1-1-1-1-1004000000222200-2-200000000000000-20001100-1-100000000000000000
χ654444-2-24-2-2-24-244-2-21-2-241-2-2-21-2-21-2440000441111-2-2-2-211-2-211114000000-2-200000000-2-20000000000-2-2000000110011000000000000000
χ664444-2-24-2-2-24-244-2-21-2-241-2-2-21-2-21-2440000-4-41111-2-2-2-211-2-21111-4000000220000000022000000000022000000-1-100-1-1000000000000000
χ674444-2-24-2-2-24-244-2-21-2-2-41-2-2-21-2-21-2-4-400004411112222-1-122-1-1-1-1-4000000-2-200000000-2-20000000000220000001100-1-1000000000000000
χ684444-2-24-2-2-24-244-2-21-2-2-41-2-2-21-2-21-2-4-40000-4-411112222-1-122-1-1-1-140000002200000000220000000000-2-2000000-1-10011000000000000000
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χ814-44-4-244-4-2-4-424-424-2-2402-2-4-4-22422000000-44-2-22200000000000000000002-200000000-440000000000000000002-20000000000000000000
χ824-44-4-2-242-22-424-42-21-2-20-1-22212-2-120000004-411-1-100003i−3i003i−3i3i−3i0000000-2200000000-220000000000000000001-1003i−3i000000000000000
χ834-44-4-2-242-22-424-42-21-2-20-1-22212-2-120000004-411-1-10000−3i3i00−3i3i−3i3i0000000-2200000000-220000000000000000001-100−3i3i000000000000000
χ844-44-4-2-242-22-424-42-21-2-20-1-22212-2-12000000-4411-1-100003i−3i003i−3i3i−3i00000002-2000000002-2000000000000000000-1100−3i3i000000000000000
χ854-44-4-2-242-22-424-42-21-2-20-1-22212-2-12000000-4411-1-10000−3i3i00−3i3i−3i3i00000002-2000000002-2000000000000000000-11003i−3i000000000000000
χ864-4-444-24-2-42-4-4-4442-24-20-2-4-222422-4004-40000-22-22000000000000000-224-400000000000000000000-2200000000000000000000000000000
χ874-4-444-24-2-42-4-4-4442-24-20-2-4-222422-400-440000-22-220000000000000002-2-44000000000000000000002-200000000000000000000000000000
χ884-4-444-2-2-2-422-42-242-2-210-221-12-2-12223−234-400001-11-100−330023−23−3−333000-22-2200000023−230000000000001-10000−3300000000000000000000000
χ894-4-444-2-2-2-422-42-242-2-210-221-12-2-12223−23-4400001-11-100−330023−23−3−3330002-22-2000000−2323000000000000-1100003−300000000000000000000000
χ904-4-444-2-2-2-422-42-242-2-210-221-12-2-122−23234-400001-11-1003−300−232333−3−3000-22-22000000−23230000000000001-100003−300000000000000000000000
χ914-4-444-2-2-2-422-42-242-2-210-221-12-2-122−2323-4400001-11-1003−300−232333−3−30002-22-200000023−23000000000000-110000−3300000000000000000000000
χ924-4-44-24442-4-42-44-2-4-2-240-224-42-2-42200004i−4i00-22-220000000000000000000004i−4i−2i2i00000000000000000000000000−2i2i00000000000000000
χ934-4-44-24442-4-42-44-2-4-2-240-224-42-2-4220000−4i4i00-22-22000000000000000000000−4i4i2i−2i000000000000000000000000002i−2i00000000000000000
χ944-4-44-24-242-4222-2-2-4-21-20-2-1-222122-123−23004i−4i001-11-10023−2300−33−3−333000000000−2i2i−2i2i00−2i32i3000000000000000000i3−i300i−i00000000000000000
χ954-4-44-24-242-4222-2-2-4-21-20-2-1-222122-123−2300−4i4i001-11-10023−2300−33−3−3330000000002i−2i2i−2i002i3−2i3000000000000000000−i3i300−ii00000000000000000
χ964-4-44-24-242-4222-2-2-4-21-20-2-1-222122-1−2323004i−4i001-11-100−2323003−333−3−3000000000−2i2i−2i2i002i3−2i3000000000000000000−i3i300i−i00000000000000000
χ974-4-44-24-242-4222-2-2-4-21-20-2-1-222122-1−232300−4i4i001-11-100−2323003−333−3−30000000002i−2i2i−2i00−2i32i3000000000000000000i3−i300−ii00000000000000000
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
χ10088-8-88-4-44-8-4-4844-84-4-42044-2244-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-848-4-4444-8-42-404-24-44-24-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4844-48-4-8-8442-4-40-244-4-2442-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-444-4-4-444442220-2-2-22-2-2-22200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-444-4-4-444442220-2-2-22-2-2-22200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000
χ1058-88-88-4-44844-8-44-8-4-4-4204-4-2-2-442440000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-48-4-8-4-844-4448-42-404244-4-2-44-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44-4444-444-42220-22-2-22-22-2-200000000-1-11100006i−6i00−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-44-4444-444-42220-22-2-22-22-2-200000000-1-1110000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-444-84-88-442-4-4024-44-2-44-24000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-444444-4-4422202-22-2-22-2-2-243−43000000-11-1100−232300−232333−3−30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-444444-4-4422202-22-2-22-2-2-2−4343000000-11-110023−230023−23−3−3330000000000000000000000000000000000000000000000000000000000

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