Finite Group Databasebeta

← Group #13167922

Character table — Group #13167922

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order1222333666666666333466666666612122244443666121212121212121212121212444444466661212121212121212121212124444121212126612121212121212121212121212124441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-11-11111111-1-111-1-1-1-11111-1-1-1-1-1-11111-111111-1-111-1-11-1-1-1-1-1-111-1-1-11-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-111-11111-1-111-1-11111-1-1-1-111-1-1-1-111-111111-1-111-1-111-1-11-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-1111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1111-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111111111-111-1-1-1-1111111111111-1-1-1-11111-1-11-11-1-1-111111111-11-111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11-1-1-1-1-111-1-111-1-1-1-11-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1111-1-1-1-1-1-11111-111
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111111-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1111111-1-1-1
χ101111111111111111111-1111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11-1-1-11111-1-1-1-1-11111-1-111-1-11-11
χ111111111111111111111-1111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-111
χ121111111111111111111-1111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-11-1-1-1-1-11111-1-11-11-1-1-1-1-1-11111-1
χ131111111111111111111-1111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-11-111111-1-1-1-1111-11-1-1-1-1-1-1-1-1111
χ141111111111111111111-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1111111111-1-1-1-111-11111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1111-1-1-1-11111-11111-1-111111-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1111111-1-11111-1-1-1-1-1-1-11111-1-1-1-11
χ17222222-12-12-1222-122-1-122-1-1-12-1-12-122220022-1-1-1-12-1-1-122-1-1-1-1-1-1000022022-1-100220022-1-10000220000-1-10-1-12-1-100-1-100-1-100200-1-10000-100
χ18222222-12-12-1222-122-1-122-1-1-12-1-12-1222200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-100002-2022-1-100-2-200-2-2110000-2-20000-1-10-112-1-10011001100-200110000100
χ19222222-12-12-1222-122-1-122-1-1-12-1-12-122-2-20022-1-1-1-12-1-1-122-1-1-1-1-1-10000-220-2-21100220022-1-10000-2-200001101-1-21100-1-100-1-100-200110000100
χ20222222-12-12-1222-122-1-122-1-1-12-1-12-122-2-200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10000-2-20-2-21100-2-200-2-211000022000011011-2110011001100200-1-10000-100
χ21222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-2220022-1-1-1-1-2111-2-21111110000-2-2022-1-1002200-2-2-1-10000220000-1-1011-211001100-1-100-200-1-10000100
χ22222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-22200-2-2-1-1-1-1-2111-2-21111110000-22022-1-100-2-20022110000-2-20000-1-101-1-21100-1-1001100200110000-100
χ23222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-2-2-20022-1-1-1-1-2111-2-211111100002-20-2-211002200-2-2-1-10000-2-20000110-112-1-1001100-1-100200110000-100
χ24222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-2-2-200-2-2-1-1-1-1-2111-2-21111110000220-2-21100-2-20022110000220000110-1-12-1-100-1-1001100-200-1-10000100
χ2522222-12-12-122222-1-12-12-12-1-1-12-1-1222222200-1-1-1-1-12-1-1-1-122-1-1-1-10000202-1-1222200220000-1-122000000-1-1-120-1-1-1-1-100-1-1002000000-1-1000-10
χ2622222-12-12-122222-1-12-12-12-1-1-12-1-122222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1000020-2-1-122-2-200-2-2000011-2-2000000-1-1120-1-1-111001100-20000001100010
χ2722222-12-12-122222-1-12-12-12-1-1-12-1-1222-2-22200-1-1-1-1-12-1-1-1-122-1-1-1-10000-20211-2-22200220000-1-1-2-200000011-1-20111-1-100-1-100-20000001100010
χ2822222-12-12-122222-1-12-12-12-1-1-12-1-1222-2-2-2-200-1-1-1-1-12-1-1-1-122-1-1-1-10000-20-211-2-2-2-200-2-200001122000000111-20111110011002000000-1-1000-10
χ2922222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2222200-1-1-1-11-21111-2-211110000-20-2-1-122-2-200220000-1-122000000-1-11-20111-1-1001100-2000000-1-100010
χ3022222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-222-2-200-1-1-1-11-21111-2-211110000-202-1-1222200-2-2000011-2-2000000-1-1-1-201111100-1-100200000011000-10
χ3122222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2-2-22200-1-1-1-11-21111-2-21111000020-211-2-2-2-200220000-1-1-2-200000011120-1-1-1-1-1001100200000011000-10
χ3222222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-2-2-2-2-200-1-1-1-11-21111-2-21111000020211-2-22200-2-20000112200000011-120-1-1-11100-1-100-2000000-1-100010
χ332222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-1002222-1-1-1-12222-1-1-1-1-1-1-1-122220220000-1-1-1-1-1-1-1-122220000-1-1-1-100202000-1-1-1-1-1-1-1-1020-1-1000000000
χ342222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-10022-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20-220000-1-111-1-111-2-222000011110020-2000-1-111-1-1110-2011000000000
χ352222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-100-2-222-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-202-2000011-1-111-1-122-2-20000111100-20200011-1-111-1-10-2011000000000
χ362222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-100-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-122220-2-2000011111111-2-2-2-20000-1-1-1-100-20-200011111111020-1-1000000000
χ372222-1222222-1-1-122-1-12-2-1-122-1-12-1-111002222-1-1-1-1-2-2-2-21111111122220-2-2000011-1-1-1-11122220000-1-1-1-100-20-2000-1-11111-1-10-2011000000000
χ382222-1222222-1-1-122-1-12-2-1-122-1-12-1-1110022-2-2-1-1-1-1-2-2-2-211111111-2-2-2-202-200001111-1-1-1-1-2-2220000111100-202000-1-1-1-11111020-1-1000000000
χ392222-1222222-1-1-122-1-12-2-1-122-1-12-1-11100-2-222-1-1-1-1-2-2-2-211111111-2-2-2-20-220000-1-1-1-1111122-2-2000011110020-20001111-1-1-1-1020-1-1000000000
χ402222-1222222-1-1-122-1-12-2-1-122-1-12-1-11100-2-2-2-2-1-1-1-1-2-2-2-21111111122220220000-1-11111-1-1-2-2-2-20000-1-1-1-10020200011-1-1-1-1110-2011000000000
χ4122-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-2002-2000022-2-200000000000022-2-20002-22-2000000000000000022-2-22-2000000000000000000000002-2000
χ4222-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-2002-2000022-2-2000000000000-2-2220002-22-20000000000000000-2-2222-200000000000000000000000-22000
χ4322-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-200-22000022-2-200000000000022-2-2000-22-22000000000000000022-2-2-2200000000000000000000000-22000
χ4422-2-222222-2-2-22-2-2-22220222-2-2-2-2-2-200-22000022-2-2000000000000-2-222000-22-220000000000000000-2-222-22000000000000000000000002-2000
χ452-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-200002-22i−2i2-22-20000000000002i−2i2i−2i0000000002i−2i2-2002i−2i2-200002i−2i2i−2i000000002-200002i−2i00000000000000
χ462-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-200002-2−2i2i2-22-2000000000000−2i2i−2i2i000000000−2i2i2-200−2i2i2-20000−2i2i−2i2i000000002-20000−2i2i00000000000000
χ472-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-20000-222i−2i2-22-2000000000000−2i2i−2i2i0000000002i−2i-22002i−2i-220000−2i2i−2i2i00000000-2200002i−2i00000000000000
χ482-22-2222-2-2-22-2-22-222220-2-2-2-2222-2-20000-22−2i2i2-22-20000000000002i−2i2i−2i000000000−2i2i-2200−2i2i-2200002i−2i2i−2i00000000-220000−2i2i00000000000000
χ492-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−3002-22i−2i-11-1100003−33−333−3−32i−2i2i−2i00000003−3−ii-11−i3i32i−2i2-20000−ii−ii00000000-11−i3i33−3−ii000−i3i3000000000
χ502-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−3002-2−2i2i-11-1100003−33−333−3−3−2i2i−2i2i00000003−3i−i-11i3−i3−2i2i2-20000i−ii−i00000000-11i3−i33−3i−i000i3−i3000000000
χ512-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−300-222i−2i-11-1100003−33−333−3−3−2i2i−2i2i0000000−33−ii1-1−i3i32i−2i-220000i−ii−i000000001-1−i3i3−33−ii000i3−i3000000000
χ522-22-2-122-2-2-2211-1-22-1-12011-2-2-1-12113−300-22−2i2i-11-1100003−33−333−3−32i−2i2i−2i0000000−33i−i1-1i3−i3−2i2i-220000−ii−ii000000001-1i3−i3−33i−i000−i3i3000000000
χ532-22-2-122-2-2-2211-1-22-1-12011-2-2-1-1211−33002-22i−2i-11-110000−33−33−3−3332i−2i2i−2i0000000−33−ii-11i3−i32i−2i2-20000−ii−ii00000000-11i3−i3−33−ii000i3−i3000000000
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χ562-22-2-122-2-2-2211-1-22-1-12011-2-2-1-1211−3300-22−2i2i-11-110000−33−33−3−3332i−2i2i−2i00000003−3i−i1-1−i3i3−2i2i-220000−ii−ii000000001-1−i3i33−3i−i000i3−i3000000000
χ572-2-22222-2-22-22-2-22-22220-2-2-22-2-2-222000000002-2-220000000000002i−2i−2i2i00000000000000000002i−2i2-22i−2i−2i2i0000000000000000000002-22i−2i00000
χ582-2-22222-2-22-22-2-22-22220-2-2-22-2-2-222000000002-2-220000000000002i−2i−2i2i0000000000000000000−2i2i-222i−2i−2i2i000000000000000000000-22−2i2i00000
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χ602-2-22222-2-22-22-2-22-22220-2-2-22-2-2-222000000002-2-22000000000000−2i2i2i−2i0000000000000000000−2i2i2-2−2i2i2i−2i0000000000000000000002-2−2i2i00000
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χ6344444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-4440000111122-1-12222-1-1-1-10000-400-2-2-2-200000000000000000000110202-1-10000000000000000000000
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χ854-44-44-242-424-4-44-4-2-24-202-422-24-22-400004-400-22-220000000000000000000000000004-40000-220000000000000000-2200000000000000000000
χ864-44-44-242-424-4-44-4-2-24-202-422-24-22-40000-4400-22-22000000000000000000000000000-4400002-200000000000000002-200000000000000000000
χ874-44-4-24-2-42-4-222-224-21-202-122-21-22-123−2300004i−4i1-11-1000023−23−33−3−3330000000000000−2i2i00−2i32i3−2i2i00000000000000000000i3−i300i−i00000000000000
χ884-44-4-24-2-42-4-222-224-21-202-122-21-22-123−230000−4i4i1-11-1000023−23−33−3−33300000000000002i−2i002i3−2i32i−2i00000000000000000000−i3i300−ii00000000000000
χ894-44-4-24-2-42-4-222-224-21-202-122-21-22-1−232300004i−4i1-11-10000−23233−333−3−30000000000000−2i2i002i3−2i3−2i2i00000000000000000000−i3i300i−i00000000000000
χ904-44-4-24-2-42-4-222-224-21-202-122-21-22-1−23230000−4i4i1-11-10000−23233−333−3−300000000000002i−2i00−2i32i32i−2i00000000000000000000i3−i300−ii00000000000000
χ914-44-4-2-242-42422-2-4-21-2-20-12221-2-2-1223−23004-4001-11-10000−3323−23−3−3330000000000023−2300-220000-2200000000000000001-100−330000000000000000
χ924-44-4-2-242-42422-2-4-21-2-20-12221-2-2-1223−2300-44001-11-10000−3323−23−3−33300000000000−2323002-200002-20000000000000000-11003−30000000000000000
χ934-44-4-2-242-42422-2-4-21-2-20-12221-2-2-12−2323004-4001-11-100003−3−232333−3−300000000000−232300-220000-2200000000000000001-1003−30000000000000000
χ944-44-4-2-242-42422-2-4-21-2-20-12221-2-2-12−232300-44001-11-100003−3−232333−3−30000000000023−23002-200002-20000000000000000-1100−330000000000000000
χ954-4-4444-2-42424-4-4-2-44-2-20-422-2-4224-200000000-222-200000000000000000000000000000000000004-40000000000000000000000000-220000000
χ964-4-4444-2-42424-4-4-2-44-2-20-422-2-4224-200000000-222-20000000000000000000000000000000000000-4400000000000000000000000002-20000000
χ974-4-444-242-4-2-44-4-442-24-202-42-22-42-2400000000-222-2000000000000000000000000000000000004i−4i00000000000000000000000000000−2i2i00000
χ984-4-444-242-4-2-44-4-442-24-202-42-22-42-2400000000-222-200000000000000000000000000000000000−4i4i000000000000000000000000000002i−2i00000
χ994-4-44-244-4-44-4-2224-4-2-24022-4422-4-2-200000000-222-20000000000004i−4i−4i4i00000000000000000000000−2i2i2i−2i000000000000000000000000000000
χ1004-4-44-244-4-44-4-2224-4-2-24022-4422-4-2-200000000-222-2000000000000−4i4i4i−4i000000000000000000000002i−2i−2i2i000000000000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4000000-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244000000-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-48-4-844-444-8-42-40-42-444-244-20000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-48-484-84-44-842-4-402-4-44-244-240000000022-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-4-4-4444-44442220222-2-2-2-2-2-200000000-1-111006i−6i0000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-4-4444-44442220222-2-2-2-2-2-200000000-1-11100−6i6i00003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000
χ1078-88-88-4-4444-4-8-884-4-4-42044-2-2-4-4244000000002-22-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4444-444-44-42220-2-2-2-2222-2-243−43000000-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4444-444-44-42220-2-2-2-2222-2-2−4343000000-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-4-444-448-8-8-44-4-42044-2244-2-4-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4-8484-444-4-8-42-404-24-44-24-42000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-484-8-4-8-444842-4-40-244-4-2442-4000000002-2-220000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444-44-444-442220-2-2-22-2-2-22200000000-111-100000000−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444-44-444-442220-2-2-22-2-2-22200000000-111-1000000003i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000

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