Finite Group Databasebeta

← Group #13168212

Character table — Group #13168212

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222244444444444444444444446666666666888888888888121212121212121212121212121212121212121212121212121212121218181818181824242424242424242424363636363636363636363654547272108
order12223334466666666633366666666612121212121212121212224444121212123666121212121212121224466666666666612121212121212121212121212124412121212661212121212121212444441212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-111111111111111-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11-1-11-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-1-11-1-1-1-1-1-111111
χ51111111111111111111111111111111111111111-1-111-1-11111111111111111111-1-111-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11111-11-1-11-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-11-111-1-11111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-11-1-1-1-111111-1-1-1-11111-1-1-111
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-11-1-1-11-1-1-1-111111-1-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-11111111-1-1111-1-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1-111-1-1-11-11-111-1-1-1-1-1-1-111
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111111111-1-1-1111-1-111-11-11-111-1-1-1-111-11-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11-11111-1-1-1-11111111-1-1-1-11-11
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1111-1-1111-1-1-11-1-1-1-111-1-11-11
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1111-1-1-1-1111111-11-1
χ17222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-12002222-1-1-1-1-1-1-1-1-1-100220022-1-1-1-1000000-1-100-1-1000020020-1-100-1-100000
χ18222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-122-2-2221111-1-1-1-1-1-122-1-1-1-1-20022-2-2-1-1111111-1-1002200-2-21111000000-1-100-1-10000-200-2011001100000
χ19222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-1-122-1-1-1-1200-2-22211-1-1-1-1-1-11100-2-20022-1-1-1-10000001100110000-200-2011001100000
χ20222222-1222-12-1222-122-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-1-122-1-1-1-1-200-2-2-2-2111111111100-2-200-2-21111000000110011000020020-1-100-1-100000
χ21222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-211112222-2-2-1-1-1-1-1-1-1-111-2-21111-20022-2-2-1-11111111100-2-20022-1-1-1-1000000-1-100110000200-201100-1-100000
χ22222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-2111122-2-2-2-21111-1-1-1-111-2-211112002222-1-1-1-1-1-1-1-11100-2-200-2-21111000000-1-100110000-20020-1-1001100000
χ23222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111-2-22222-1-1-1-1-1-1-1-111-2-21111-200-2-2-2-211111111-1-100220022-1-1-1-10000001100-1-10000-20020-1-1001100000
χ24222222-1-2-22-12-1222-122-1-12-1-1-1-12-12-1-2-211-2-21111-2-2-2-2221111-1-1-1-111-2-21111200-2-22211-1-1-1-1-1-1-1-1002200-2-211110000001100-1-10000200-201100-1-100000
χ2522222-122222-122-1-122-12-1-122-1-1-1-1-12-1-1222222222200220000-1-1-1-1-1-1-1-1-1-1-1-1022-1-1002200000022-1-1-1-1-1-100000022-1-1-1-1-1-122-1-1-1-1-1-10020000-1-10000000
χ2622222-122222-122-1-122-12-1-122-1-1-1-1-12-1-1222222222200220000-1-1-1-1-1-1-1-1-1-1-1-10-2-2-1-100220000002211-1-111000000-2-21111-1-1-2-2-1-1111100-20000110000000
χ2722222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222-2-200-2-20000-1-1-1-1-1-1-1-1-1-1-1-10221100-2-2000000-2-2-1-111-1-1000000-2-21111112211-1-1-1-100-20000110000000
χ2822222-122222-122-1-122-12-1-122-1-1-1-1-12-1-122222222-2-200-2-20000-1-1-1-1-1-1-1-1-1-1-1-10-2-21100-2-2000000-2-211111100000022-1-1-1-111-2-21111110020000-1-10000000
χ2922222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-22200-2-20000-1-1-1-11111111102-2-1-10022000000-2-2-1-11111000000-2-21111-1-1-221111-1-10020000-1-10000000
χ3022222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-22200-2-20000-1-1-1-1111111110-22-1-10022000000-2-21111-1-100000022-1-1-1-1-1-12-211-1-11100-20000110000000
χ3122222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2-2-200220000-1-1-1-11111111102-21100-2-200000022-1-1-1-11100000022-1-1-1-111-22-1-111-1-100-20000110000000
χ3222222-12-2-222-122-1-122-12-1-122-1-1-1-1-1211-2-2-2-2-2-2-2-2-2-200220000-1-1-1-1111111110-221100-2-20000002211-1-1-1-1000000-2-21111112-2-1-1-1-1110020000-1-10000000
χ332222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-10022002222-1-1-1-122-1-1-1-1-1-122200-1-10022-1-1-1-100220022-1-1-1-1-1-100000000-1-100-1-1-1-10200200000000-1-10
χ342222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-10022002222-1-1-1-122-1-1-1-1-1-12-2-200-1-10022-1-1-1-100-2-200-2-2-1-1-1-1-1-100000000110011110-200-200000000110
χ352222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-100-2-200-2-2-2-2-1-1-1-122-1-1-1-1-1-1-222001100-2-211110022002211111100000000-1-100-1-1-1-10-200-200000000110
χ362222-12222-1222-1222-1-1-12-1-1-122-12-1-12222-1-1-1-1-1-100-2-200-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2001100-2-2111100-2-200-2-211111100000000110011110200200000000-1-10
χ372222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-21111110022002222-1-1-1-1-2-2111111-22-2001100-2-21111002200-2-2-1-1-1-1-1-1000000001-10011-1-10200-2000000001-10
χ382222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-21111110022002222-1-1-1-1-2-2111111-2-22001100-2-2111100-2-20022-1-1-1-1-1-100000000-1100-1-1110-200200000000-110
χ392222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-211111100-2-200-2-2-2-2-1-1-1-1-2-211111122-200-1-10022-1-1-1-1002200-2-2111111000000001-10011-1-10-200200000000-110
χ402222-122-2-2-1222-1222-1-1-12-1-1-122-12-1-1-2-2-2-211111100-2-200-2-2-2-2-1-1-1-1-2-21111112-2200-1-10022-1-1-1-100-2-2002211111100000000-1100-1-1110200-2000000001-10
χ4122-2-222200-2-22-2-2-2-222222-2-2-2-22-2-2220000000000002-20022-2-22-2-2200000000000000000000000000000002-222-2-22i−2i2i2i−2i−2i0000000000000000000002i−2i000
χ4222-2-222200-2-22-2-2-2-222222-2-2-2-22-2-2220000000000002-20022-2-22-2-2200000000000000000000000000000002-222-2-2−2i2i−2i−2i2i2i000000000000000000000−2i2i000
χ4322-2-222200-2-22-2-2-2-222222-2-2-2-22-2-222000000000000-2200-2-2222-2-220000000000000000000000000000000-22-2-2222i−2i2i2i−2i−2i000000000000000000000−2i2i000
χ4422-2-222200-2-22-2-2-2-222222-2-2-2-22-2-222000000000000-2200-2-2222-2-220000000000000000000000000000000-22-2-222−2i2i−2i−2i2i2i0000000000000000000002i−2i000
χ452-2-222222i−2i-2-2-2222-2-2-2222-22-22-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i2-2002i−2i000022-2-22i−2i2i−2i2i2i−2i−2i0002-2002-20000002i−2i002i−2i000000000000002-2002i−2i00000000000000000000
χ462-2-222222i−2i-2-2-2222-2-2-2222-22-22-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i-2200−2i2i000022-2-22i−2i2i−2i2i2i−2i−2i000-2200-22000000−2i2i00−2i2i00000000000000-2200−2i2i00000000000000000000
χ472-2-22222−2i2i-2-2-2222-2-2-2222-22-22-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i2-200−2i2i000022-2-2−2i2i−2i2i−2i−2i2i2i0002-2002-2000000−2i2i00−2i2i000000000000002-200−2i2i00000000000000000000
χ482-2-22222−2i2i-2-2-2222-2-2-2222-22-22-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i-22002i−2i000022-2-2−2i2i−2i2i−2i−2i2i2i000-2200-220000002i−2i002i−2i00000000000000-22002i−2i00000000000000000000
χ492-2-2222-12i−2i-21-2-122-21-22-1-1-2-11-1121-212i−2i−ii2i−2i−i−iii2-2002i−2i3−33−3-1-111−ii2i−2i−i−iii0002-200-11−i3i3−i3−i3i3i3−ii002i−2i00003−33−3000000-1100−ii000000000−i3i3003−300000
χ502-2-2222-12i−2i-21-2-122-21-22-1-1-2-11-1121-212i−2i−ii2i−2i−i−iii2-2002i−2i−33−33-1-111−ii2i−2i−i−iii0002-200-11i3−i3i3i3−i3−i3−ii002i−2i0000−33−33000000-1100−ii000000000i3−i300−3300000
χ512-2-2222-12i−2i-21-2-122-21-22-1-1-2-11-1121-212i−2i−ii2i−2i−i−iii-2200−2i2i3−33−3-1-111−ii2i−2i−i−iii000-22001-1−i3i3−i3−i3i3i3i−i00−2i2i00003−33−30000001-100i−i000000000i3−i300−3300000
χ522-2-2222-12i−2i-21-2-122-21-22-1-1-2-11-1121-212i−2i−ii2i−2i−i−iii-2200−2i2i−33−33-1-111−ii2i−2i−i−iii000-22001-1i3−i3i3i3−i3−i3i−i00−2i2i0000−33−330000001-100i−i000000000−i3i3003−300000
χ532-2-2222-1−2i2i-21-2-122-21-22-1-1-2-11-1121-21−2i2ii−i−2i2iii−i−i2-200−2i2i3−33−3-1-111i−i−2i2iii−i−i0002-200-11i3−i3i3i3−i3−i3i−i00−2i2i00003−33−3000000-1100i−i000000000i3−i3003−300000
χ542-2-2222-1−2i2i-21-2-122-21-22-1-1-2-11-1121-21−2i2ii−i−2i2iii−i−i2-200−2i2i−33−33-1-111i−i−2i2iii−i−i0002-200-11−i3i3−i3−i3i3i3i−i00−2i2i0000−33−33000000-1100i−i000000000−i3i300−3300000
χ552-2-2222-1−2i2i-21-2-122-21-22-1-1-2-11-1121-21−2i2ii−i−2i2iii−i−i-22002i−2i3−33−3-1-111i−i−2i2iii−i−i000-22001-1i3−i3i3i3−i3−i3−ii002i−2i00003−33−30000001-100−ii000000000−i3i300−3300000
χ562-2-2222-1−2i2i-21-2-122-21-22-1-1-2-11-1121-21−2i2ii−i−2i2iii−i−i-22002i−2i−33−33-1-111i−i−2i2iii−i−i000-22001-1−i3i3−i3−i3i3i3−ii002i−2i0000−33−330000001-100−ii000000000i3−i3003−300000
χ572-2-222-122i−2i-2-2122-11-2-2-12-112-2-11-111-2−ii2i−2i2i−2i2i2i−2i−2i2-2002i−2i0000-1-111−ii−ii−i−iii000-11002-20000002i−2i3−3−ii−i3i300000000−i3i3−i3i3-1100−ii−i3i33−300000003−30000000
χ582-2-222-122i−2i-2-2122-11-2-2-12-112-2-11-111-2−ii2i−2i2i−2i2i2i−2i−2i2-2002i−2i0000-1-111−ii−ii−i−iii000-11002-20000002i−2i−33−iii3−i300000000i3−i3i3−i3-1100−iii3−i3−330000000−330000000
χ592-2-222-122i−2i-2-2122-11-2-2-12-112-2-11-111-2−ii2i−2i2i−2i2i2i−2i−2i-2200−2i2i0000-1-111−ii−ii−i−iii0001-100-22000000−2i2i3−3i−i−i3i300000000i3−i3i3−i31-100i−i−i3i33−30000000−330000000
χ602-2-222-122i−2i-2-2122-11-2-2-12-112-2-11-111-2−ii2i−2i2i−2i2i2i−2i−2i-2200−2i2i0000-1-111−ii−ii−i−iii0001-100-22000000−2i2i−33i−ii3−i300000000−i3i3−i3i31-100i−ii3−i3−3300000003−30000000
χ612-2-222-12−2i2i-2-2122-11-2-2-12-112-2-11-111-2i−i−2i2i−2i2i−2i−2i2i2i2-200−2i2i0000-1-111i−ii−iii−i−i000-11002-2000000−2i2i3−3i−ii3−i300000000i3−i3i3−i3-1100i−ii3−i33−300000003−30000000
χ622-2-222-12−2i2i-2-2122-11-2-2-12-112-2-11-111-2i−i−2i2i−2i2i−2i−2i2i2i2-200−2i2i0000-1-111i−ii−iii−i−i000-11002-2000000−2i2i−33i−i−i3i300000000−i3i3−i3i3-1100i−i−i3i3−330000000−330000000
χ632-2-222-12−2i2i-2-2122-11-2-2-12-112-2-11-111-2i−i−2i2i−2i2i−2i−2i2i2i-22002i−2i0000-1-111i−ii−iii−i−i0001-100-220000002i−2i3−3−iii3−i300000000−i3i3−i3i31-100−iii3−i33−30000000−330000000
χ642-2-222-12−2i2i-2-2122-11-2-2-12-112-2-11-111-2i−i−2i2i−2i2i−2i−2i2i2i-22002i−2i0000-1-111i−ii−iii−i−i0001-100-220000002i−2i−33−ii−i3i300000000i3−i3i3−i31-100−ii−i3i3−3300000003−30000000
χ6544444-2-2444-2-2-24-2-2-24-2-21-2-2-211-21-2-2-2-2-2-244-2-2-2-24400440000111111-2-21111000-2-200-2-2000000-2-200-2-20000000000000011001100000000000000000000
χ6644444-2-2444-2-2-24-2-2-24-2-21-2-2-211-21-2-2-2-2-2-244-2-2-2-2-4-400-4-40000111111-2-2111100022002200000022002200000000000000-1-100-1-100000000000000000000
χ6744444-2-2-4-44-2-2-24-2-2-24-2-21-2-2-211-21-2-22222-4-422224400-4-400001111-1-122-1-1-1-1000-2-200-2-2000000220022000000000000001100-1-100000000000000000000
χ6844444-2-2-4-44-2-2-24-2-2-24-2-21-2-2-211-21-2-22222-4-42222-4-4004400001111-1-122-1-1-1-1000220022000000-2-200-2-200000000000000-1-1001100000000000000000000
χ694444-24-244-2-24-2-244-2-2-21-2-211-2-2-2-2-2144-2-2-2-21111004400-2-2-2-21111-2-2-2-2111140000-2-200-2-2111100000000-2-2111100000000000000000000000000000000
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χ904-44-44-2400442-4-42-2-4-4-24-2-2-44222-22-400000000000000000000-22-2200000000000000000000000000000000000000023−23−232300000000000000000000000000
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χ994-4-444-2-24i−4i-422-24-222-4-2-212-221-1-2-122−2i2i−2i2i4i−4i−2i−2i2i2i-4400−4i4i000011-1-1i−i−2i2iii−i−i0002-2002-20000002i−2i002i−2i00000000000000-1100−ii00000000000000000000
χ1004-4-444-2-2−4i4i-422-24-222-4-2-212-221-1-2-1222i−2i2i−2i−4i4i2i2i−2i−2i4-400−4i4i000011-1-1−ii2i−2i−i−iii000-2200-220000002i−2i002i−2i000000000000001-100−ii00000000000000000000
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χ1034-4-44-244−4i4i2-4-44-24-4-42-2-242-224-4-2-422−4i4i−4i4i2i−2i2i2i−2i−2i0000000000-2-222−4i4i2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-24-24i−4i22-4-2-24-422-21-221-1-22-222-14i−4i−2i2i−2i2iii−i−i00000023−2323−2311-1-1−2i2i−2i2iii−i−i000000000−2i32i3i3i3−i3−i30000000000−33−3300000000000000000000000000000000
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χ1094-4-44-2-244i−4i2-424-2-22-421-2-2-1-22-2212-12−2i2i4i−4i−2i2i−2i−2i2i2i000000000011-1-1−2i2ii−iii−i−i00000000000000000−2323002i3−2i3000000000000000000−i3i33−30000000000000000
χ1104-4-44-2-24−4i4i2-424-2-22-421-2-2-1-22-2212-122i−2i−4i4i2i−2i2i2i−2i−2i000000000011-1-12i−2i−ii−i−iii0000000000000000023−23002i3−2i3000000000000000000−i3i3−330000000000000000
χ1114-4-44-2-24−4i4i2-424-2-22-421-2-2-1-22-2212-122i−2i−4i4i2i−2i2i2i−2i−2i000000000011-1-12i−2i−ii−i−iii00000000000000000−232300−2i32i3000000000000000000i3−i33−30000000000000000
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χ1138888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-20000000000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000000
χ11488-8-88-4-400-84-44-844-48-4-42444-224-2-4-4000000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
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χ11788-8-8-4-4-40044-44444-4-4222-2-2-2-22-2-222000000-66-660000000000-111-100003-33-30000000000000000000000000000000000000000000000000000000000000
χ1188-88-88-4-4008-444-84-44-8-4-42-44-4-2-24244000000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1198-88-8-4-4800-484-844-4-842-4-424-444-2-4-24000000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
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χ1218-88-8-4-4-400-4-44444-4442222-22-2-2-22-2-2000000−6i6i6i−6i0000000000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000000
χ1228-8-88-4-4-48i−8i444-4-4-4444222-22-22-22-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i0000000000-1-1112i−2i2i−2i−i−iii0000000000000000000000000000000000000000000000000000000000000
χ1238-8-88-4-4-4−8i8i444-4-4-4444222-22-22-22-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i0000000000-1-111−2i2i−2i2iii−i−i0000000000000000000000000000000000000000000000000000000000000

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