Finite Group Databasebeta

← Group #13168194

Character table — Group #13168194

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666668888888888888888121212121212121212121212121212121212121818181818181818242424242424242424242424242424243636363636363636363654547272108
order122233366666666633346666666661212224444366612121212121212121212121244466661212121212121212121212122244666666121212121212121212121212121244441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111111111111111111-11111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-111111-1-111-1-111-1-1-1-1-1-111-1-1-11-1
χ3111111111111111111111111111111111-1-111111111111111111111-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-111111-1-111-1-111-1-111-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-111111111111111111111-111-1-1-1-111111111111111111111-1-11-11-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1-1-11111-111
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
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-11-1111111-1-1-1-11
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-11111-1-1111111-1-11-1-1-11111-1-1-1-11-1-11-1-1-1-111111-1-1
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111-1-11111111-1-1-1-1-1-1-1-1-11111-111-1-1-111-1-111-11-1
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-11-1-1-1-1-11111-1-1-11-1111-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-11-111111-1-1-1-111-11-1111-1-1-1-11111-1
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1111111111-1-1-1-1-111-1-1-111-1-1-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-111-1111-1-1-1-111111-1-11-1-1-1-111-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-11-11-111111111-1-1-1
χ17222222-122-122-1-122-1-122-1-122-1-12-1-1-1-1002222-1-1-1-12222-1-1-1-1-1-1-1-10220000-1-1-1-1-1-1-1-122222222-1-1-1-100202000-1-1-1-1-1-1-1-10000-1-1000000000
χ18222222-122-122-1-122-1-122-1-122-1-12-1-1-1-10022-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-220000-1-111-1-111-2-222-2-2-2-211110020-2000-1-111-1-111000011000000000
χ19222222-122-122-1-122-1-122-1-122-1-12-1-1-1-100-2-222-1-1-1-12222-1-1-1-1-1-1-1-102-2000011-1-111-1-122-2-2-2-2-2-2111100-20200011-1-111-1-1000011000000000
χ20222222-122-122-1-122-1-122-1-122-1-12-1-1-1-100-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2000011111111-2-2-2-22222-1-1-1-100-20-2000111111110000-1-1000000000
χ21222222-122-122-1-122-1-12-2-1-122-1-12-1-111002222-1-1-1-1-2-2-2-2111111110-2-20000-1-11111-1-12222-2-222111100-20-2000-1-11111-1-10000-1-1000000000
χ22222222-122-122-1-122-1-12-2-1-122-1-12-1-1110022-2-2-1-1-1-1-2-2-2-21111111102-20000-1-1-1-11111-2-22222-2-2-1-1-1-100-202000-1-1-1-11111000011000000000
χ23222222-122-122-1-122-1-12-2-1-122-1-12-1-11100-2-222-1-1-1-1-2-2-2-2111111110-2200001111-1-1-1-122-2-222-2-2-1-1-1-10020-20001111-1-1-1-1000011000000000
χ24222222-122-122-1-122-1-12-2-1-122-1-12-1-11100-2-2-2-2-1-1-1-1-2-2-2-211111111022000011-1-1-1-111-2-2-2-2-2-22211110020200011-1-1-1-1110000-1-1000000000
χ2522222-122-122-122-122-1-122-1-1-12-1-12-122220022-1-1-1-12-1-1-122-1-1-1-1-1-122022-1-100220022-1-10000000000-1-10-1-12-1-100-1-100-1-1002200-1-10000-100
χ2622222-122-122-122-122-1-122-1-1-12-1-12-1222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-12-2022-1-100-2-200-2-2110000000000-1-10-112-1-10011001100-2-200110000100
χ2722222-122-122-122-122-1-122-1-1-12-1-12-122-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-1-220-2-21100220022-1-100000000001101-1-21100-1-100-1-100-2-200110000100
χ2822222-122-122-122-122-1-122-1-1-12-1-12-122-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-20-2-21100-2-200-2-211000000000011011-21100110011002200-1-10000-100
χ2922222-122-122-122-122-1-1-22-1-1-12-1-12-1-2-2220022-1-1-1-1-2111-2-2111111-2-2022-1-100-2-20022-1-10000000000-1-1011-211001100-1-1002-200-1-10000100
χ3022222-122-122-122-122-1-1-22-1-1-12-1-12-1-2-22200-2-2-1-1-1-1-2111-2-2111111-22022-1-1002200-2-2110000000000-1-101-1-21100-1-1001100-2200110000-100
χ3122222-122-122-122-122-1-1-22-1-1-12-1-12-1-2-2-2-20022-1-1-1-1-2111-2-21111112-20-2-21100-2-20022-1-10000000000110-112-1-1001100-1-100-2200110000-100
χ3222222-122-122-122-122-1-1-22-1-1-12-1-12-1-2-2-2-200-2-2-1-1-1-1-2111-2-2111111220-2-211002200-2-2110000000000110-1-12-1-100-1-10011002-200-1-10000100
χ332222-122-122-12222-1-12-12-12-1-1-12-1-1222222200-1-1-1-1-12-1-1-1-122-1-1-1-1202-1-1222200220000-1-100000000-1-1-120-1-1-1-1-100-1-10022000000-1-1000-10
χ342222-122-122-12222-1-12-12-12-1-1-12-1-122222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-120-2-1-122-2-200-2-200001100000000-1-1120-1-1-111001100-2-20000001100010
χ352222-122-122-12222-1-12-12-12-1-1-12-1-1222-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-1-20211-2-22200220000-1-10000000011-1-20111-1-100-1-100-2-20000001100010
χ362222-122-122-12222-1-12-12-12-1-1-12-1-1222-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-211-2-2-2-200-2-200001100000000111-201111100110022000000-1-1000-10
χ372222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2222200-1-1-1-11-21111-2-21111-20-2-1-1222200-2-20000-1-100000000-1-11-20111-1-10011002-2000000-1-100010
χ382222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-222-2-200-1-1-1-11-21111-2-21111-202-1-122-2-2002200001100000000-1-1-1-201111100-1-100-2200000011000-10
χ392222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-2-22200-1-1-1-11-21111-2-2111120-211-2-22200-2-20000-1-10000000011120-1-1-1-1-1001100-2200000011000-10
χ402222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-2-2-2-2-200-1-1-1-11-21111-2-2111120211-2-2-2-200220000110000000011-120-1-1-11100-1-1002-2000000-1-100010
χ4122-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-2002-2000022-2-20000000000000002-22-20000000000002-20022-2-22-20000000000000000000000002-2000
χ4222-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-2002-2000022-2-20000000000000002-22-2000000000000-2200-2-2222-2000000000000000000000000-22000
χ4322-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000000-22-220000000000002-20022-2-2-22000000000000000000000000-22000
χ4422-2-2222222-2-2-2-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000000-22-22000000000000-2200-2-222-220000000000000000000000002-2000
χ452-22-2222-2-2-2-222-2-222220-2-2-2-2222-2-200002-22i−2i2-22-200000000000000000002-200002i−2i2i−2i2-2002i−2i0000000000002-200002i−2i00002i−2i000000000
χ462-22-2222-2-2-2-222-2-222220-2-2-2-2222-2-200002-2−2i2i2-22-200000000000000000002-20000−2i2i−2i2i2-200−2i2i0000000000002-20000−2i2i0000−2i2i000000000
χ472-22-2222-2-2-2-222-2-222220-2-2-2-2222-2-20000-222i−2i2-22-20000000000000000000-2200002i−2i2i−2i-2200−2i2i000000000000-2200002i−2i0000−2i2i000000000
χ482-22-2222-2-2-2-222-2-222220-2-2-2-2222-2-20000-22−2i2i2-22-20000000000000000000-220000−2i2i−2i2i-22002i−2i000000000000-220000−2i2i00002i−2i000000000
χ492-22-222-1-2-21-22-11-22-1-12011-2-2-1-12113−3002-22i−2i-11-1100003−33−333−3−30000000-11−i3i33−3−ii2i−2i2-2002i−2i−i3i3−i3i300000000-11−i3i33−3−ii0000−ii000000000
χ502-22-222-1-2-21-22-11-22-1-12011-2-2-1-12113−3002-2−2i2i-11-1100003−33−333−3−30000000-11i3−i33−3i−i−2i2i2-200−2i2ii3−i3i3−i300000000-11i3−i33−3i−i0000i−i000000000
χ512-22-222-1-2-21-22-11-22-1-12011-2-2-1-12113−300-222i−2i-11-1100003−33−333−3−300000001-1−i3i3−33−ii2i−2i-2200−2i2ii3−i3i3−i3000000001-1−i3i3−33−ii0000i−i000000000
χ522-22-222-1-2-21-22-11-22-1-12011-2-2-1-12113−300-22−2i2i-11-1100003−33−333−3−300000001-1i3−i3−33i−i−2i2i-22002i−2i−i3i3−i3i3000000001-1i3−i3−33i−i0000−ii000000000
χ532-22-222-1-2-21-22-11-22-1-12011-2-2-1-1211−33002-22i−2i-11-110000−33−33−3−3330000000-11i3−i3−33−ii2i−2i2-2002i−2ii3−i3i3−i300000000-11i3−i3−33−ii0000−ii000000000
χ542-22-222-1-2-21-22-11-22-1-12011-2-2-1-1211−33002-2−2i2i-11-110000−33−33−3−3330000000-11−i3i3−33i−i−2i2i2-200−2i2i−i3i3−i3i300000000-11−i3i3−33i−i0000i−i000000000
χ552-22-222-1-2-21-22-11-22-1-12011-2-2-1-1211−3300-222i−2i-11-110000−33−33−3−33300000001-1i3−i33−3−ii2i−2i-2200−2i2i−i3i3−i3i3000000001-1i3−i33−3−ii0000i−i000000000
χ562-22-222-1-2-21-22-11-22-1-12011-2-2-1-1211−3300-22−2i2i-11-110000−33−33−3−33300000001-1−i3i33−3i−i−2i2i-22002i−2ii3−i3i3−i3000000001-1−i3i33−3i−i0000−ii000000000
χ5744444-2-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-200004411114-2-2-2-2-2111111040000000-2-200-2-2-2-200000000000000-200000110011000000000000000
χ5844444-2-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-20000-4-411114-2-2-2-2-21111110-400000002200222200000000000000200000-1-100-1-1000000000000000
χ5944444-2-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-21220000441111-422222-1-1-1-1-1-10-400000002200-2-2-2-200000000000000200000-1-10011000000000000000
χ6044444-2-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-21220000-4-41111-422222-1-1-1-1-1-1040000000-2-200222200000000000000-2000001100-1-1000000000000000
χ614444-24-2-24-2-24-2-24-21-2-241-2-2-21-2-21-2-2-20044001111-24-2-211-2-211110040000-2-200-2-20000-2-20000000000-20000011001100000000000000000
χ624444-24-2-24-2-24-2-24-21-2-241-2-2-21-2-21-2-2-200-4-4001111-24-2-211-2-2111100-400002200220000220000000000200000-1-100-1-100000000000000000
χ634444-24-2-24-2-24-2-24-21-2-2-41-2-2-21-2-21-22200440011112-422-1-122-1-1-1-100-40000-2-200220000-2-200000000002000001100-1-100000000000000000
χ644444-24-2-24-2-24-2-24-21-2-2-41-2-2-21-2-21-22200-4-40011112-422-1-122-1-1-1-100400002200-2-20000220000000000-200000-1-1001100000000000000000
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χ664444-2-24-2-24-2-244-2-2-2-214-2-211-2-21-2-244-4-400001111-2-211-2-2-2-21111-400222200000000000000000000-1-10202-1-100000000000000000000000
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χ7644-4-4-2-24-2-2422-4-422-2-210-2-21-122-122004-4000011-1-100−3i3i0000−3i3i−3i3i000-22-22000000000000000000001-10000−3i3i00000000000000000000000
χ7744-4-4-2-24-2-2422-4-422-2-210-2-21-122-12200-44000011-1-1003i−3i00003i−3i3i−3i0002-22-200000000000000000000-110000−3i3i00000000000000000000000
χ7844-4-4-2-24-2-2422-4-422-2-210-2-21-122-12200-44000011-1-100−3i3i0000−3i3i−3i3i0002-22-200000000000000000000-1100003i−3i00000000000000000000000
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χ804-44-44-24-42-4-4-24-4244-2-20-42224-2-2-42000000−4i4i-22-220000000000000000000000000−4i4i2i−2i0000000000000000000000002i−2i000000000000000
χ814-44-44-2-2-422-4-2-2224-21-202-122-21-22-123−2300004i−4i1-11-1000023−23−33−3−333000000000−2i32i300−2i2i−2i2i00000000000000000000i3−i300i−i000000000000000
χ824-44-44-2-2-422-4-2-2224-21-202-122-21-22-123−230000−4i4i1-11-1000023−23−33−3−3330000000002i3−2i3002i−2i2i−2i00000000000000000000−i3i300−ii000000000000000
χ834-44-44-2-2-422-4-2-2224-21-202-122-21-22-1−232300004i−4i1-11-10000−23233−333−3−30000000002i3−2i300−2i2i−2i2i00000000000000000000−i3i300i−i000000000000000
χ844-44-44-2-2-422-4-2-2224-21-202-122-21-22-1−23230000−4i4i1-11-10000−23233−333−3−3000000000−2i32i3002i−2i2i−2i00000000000000000000i3−i300−ii000000000000000
χ854-44-4-2442-4-4244-4-4-2-24-202-422-24-22-400004-400-22-2200000000000000000004-400000000-220000000000000000-22000000000000000000000
χ864-44-4-2442-4-4244-4-4-2-24-202-422-24-22-40000-4400-22-220000000000000000000-44000000002-200000000000000002-2000000000000000000000
χ874-44-4-24-22-4224-22-4-21-2-20-12221-2-2-1223−23004-4001-11-10000−3323−23−3−3330000000-220023−230000-2200000000000000001-100−3300000000000000000
χ884-44-4-24-22-4224-22-4-21-2-20-12221-2-2-1223−2300-44001-11-10000−3323−23−3−33300000002-200−232300002-20000000000000000-11003−300000000000000000
χ894-44-4-24-22-4224-22-4-21-2-20-12221-2-2-12−2323004-4001-11-100003−3−232333−3−30000000-2200−23230000-2200000000000000001-1003−300000000000000000
χ904-44-4-24-22-4224-22-4-21-2-20-12221-2-2-12−232300-44001-11-100003−3−232333−3−300000002-20023−2300002-20000000000000000-1100−3300000000000000000
χ914-4-44444-4-4-44-4-444-44440-4-4-44-4-4-444000000004-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4444-2-4-424-42-24-4-2-24022-4422-4-2-200000000-222-200000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ934-4-4444-2-4-424-42-24-4-2-24022-4422-4-2-200000000-222-2000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ944-4-444-24-42-442-44-2-44-2-20-422-2-4224-200000000-222-20000000000000000000000000000000000000000000000000000000000000−2i32i30000000
χ954-4-444-24-42-442-44-2-44-2-20-422-2-4224-200000000-222-200000000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ964-4-44-2442-4-4-2-4-4442-24-202-42-22-42-2400000000-222-200000000000000000000000000000000000000000000000000000000000000023−2300000
χ974-4-44-2442-4-4-2-4-4442-24-202-42-22-42-2400000000-222-2000000000000000000000000000000000000000000000000000000000000000−232300000
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
χ10088-8-88-4-48-4-4-84444-8-42-40-42-444-244-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-48-44-844-842-4-402-4-44-244-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200000000-1-111006i−6i0000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-4-4-4-44444442220222-2-2-2-2-2-200000000-1-11100−6i6i00003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4844-84-48-84-4-4-42044-2-2-4-4244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-44444-4-444-42220-2-2-2-2222-2-243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44444-4-444-42220-2-2-2-2222-2-2−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-844844-4-4-8-42-404-24-44-24-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-44-84-4-84-4842-4-40-244-4-2442-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4844-8-44-88-44-4-42044-2244-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-444-4-442220-2-2-22-2-2-22200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-444-4-442220-2-2-22-2-2-22200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000

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