Finite Group Databasebeta

← Group #13168057

Character table — Group #13168057

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222244444444444444444444446666666666888888888888121212121212121212121212121212121212121212121212121212121218181818181824242424242424242424363636363636363636363654547272108
order122233344666666666333666666666121212121212121212122222446666366612121212121212124446666666666121212121212121212121212121212124412121212661212121212121212224446612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-11-11-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111-11111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111111111111111-1-1-11-1-1-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-1-11-1-1-1-1-1-111111
χ51111111111111111111111111111111111111111-1-111-1-11111111111111111111-1-111-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-11-1-11-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111-1-111-1-111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-11
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-11-1-11111-1-111-1-11
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
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-11-111-1-111-1-11-11
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-111-1-11-1-1-1111-1-1-1-111-11-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-111-1-1111-1-1111111-11-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111-1-111-1-1-1-1111111111111111-1-1-111-1-1-111-1-1-1-111-1-1-1-11-11
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-1-111-1-11111-1-1-1-1-1-1111111-1-1-1111-1-111-111-1-1-1-111-1-1111-1-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-1-11111-1-1-111
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111111-1-1-1111-1-1111-1-1-1111-1-1-1-1-1-1-111
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-11-11111-1-111-11-111-1-111111-1-1
χ17222222-122-122-12222-12-1-12-1-1-1-12-12-122-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-122-1-1-1-12002222-1-1-1-1-1-1-1-1002222-1-100-1-1-1-1000000-1-100-1-1000020200-1-1-1-10000000
χ18222222-122-122-12222-12-1-12-1-1-1-12-12-122-1-122-1-1-1-122-2-2221111-1-1-1-1-1-122-1-1-1-1-20022-2-2-1-111111100-2-222-1-1001111000000-1-100-1-10000-20-20011110000000
χ19222222-122-122-12222-12-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-1-122-1-1-1-1200-2-22211-1-1-1-1-1-10022-2-21100-1-1-1-10000001100110000-20-20011110000000
χ20222222-122-122-12222-12-1-12-1-1-1-12-12-122-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-1-122-1-1-1-1-200-2-2-2-21111111100-2-2-2-211001111000000110011000020200-1-1-1-10000000
χ21222222-1-2-2-122-12222-12-1-12-1-1-1-12-12-1-2-211-2-211112222-2-2-1-1-1-1-1-1-1-111-2-21111-2002222-1-1-1-1-1-11100-2-2-2-211001111000000-1-10011000020-200-1-1110000000
χ22222222-1-2-2-122-12222-12-1-12-1-1-1-12-12-1-2-211-2-2111122-2-2-2-21111-1-1-1-111-2-2111120022-2-2-1-11111-1-10022-2-21100-1-1-1-1000000-1-100110000-2020011-1-10000000
χ23222222-1-2-2-122-12222-12-1-12-1-1-1-12-12-1-2-211-2-21111-2-22222-1-1-1-1-1-1-1-111-2-21111-200-2-22211-1-1-1-11100-2-222-1-10011110000001100-1-10000-2020011-1-10000000
χ24222222-1-2-2-122-12222-12-1-12-1-1-1-12-12-1-2-211-2-21111-2-2-2-2221111-1-1-1-111-2-21111200-2-2-2-2111111-1-1002222-1-100-1-1-1-10000001100-1-1000020-200-1-1110000000
χ2522222-12222-122-1-1222-12-1-12-1-12-12-1-12222-1-1-1-1-1-10022002222-1-1-1-122-1-1-1-1-1-122200-1-100-1-1-1-12222-1-1000022-1-1-1-100000000-1-100-1-1-1-10200200000000-1-10
χ2622222-12222-122-1-1222-12-1-12-1-12-12-1-12222-1-1-1-1-1-10022002222-1-1-1-122-1-1-1-1-1-12-2-200-1-100-1-1-1-122-2-2-1-10000-2-2-1-1-1-100000000110011110-200-200000000110
χ2722222-12222-122-1-1222-12-1-12-1-12-12-1-12222-1-1-1-1-1-100-2-200-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2220011001111-2-22211000022111100000000-1-100-1-1-1-10-200-200000000110
χ2822222-12222-122-1-1222-12-1-12-1-12-12-1-12222-1-1-1-1-1-100-2-200-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-20011001111-2-2-2-2110000-2-2111100000000110011110200200000000-1-10
χ2922222-12-2-22-122-1-1222-12-1-12-1-12-12-1-1-2-2-2-21111110022002222-1-1-1-1-2-2111111-22-200-1-100-1-1-1-1-2-222110000-2-21111000000001-10011-1-10200-200000000-110
χ3022222-12-2-22-122-1-1222-12-1-12-1-12-12-1-1-2-2-2-21111110022002222-1-1-1-1-2-2111111-2-2200-1-100-1-1-1-1-2-2-2-211000022111100000000-1100-1-1110-2002000000001-10
χ3122222-12-2-22-122-1-1222-12-1-12-1-12-12-1-1-2-2-2-211111100-2-200-2-2-2-2-1-1-1-1-2-211111122-200110011112222-1-10000-2-2-1-1-1-1000000001-10011-1-10-2002000000001-10
χ3222222-12-2-22-122-1-1222-12-1-12-1-12-12-1-1-2-2-2-211111100-2-200-2-2-2-2-1-1-1-1-2-21111112-22001100111122-2-2-1-1000022-1-1-1-100000000-1100-1-1110200-200000000-110
χ332222-1222222-1222-1-12-1-12-1-122-1-1-1-12-1-1222222222200220000-1-1-1-1-1-1-1-1-1-1-1-1022-1-10022000000-1-100-1-122-1-1000022-1-1-1-1-1-122-1-1-1-1-1-1000200000-1-100000
χ342222-1222222-1222-1-12-1-12-1-122-1-1-1-12-1-1222222222200220000-1-1-1-1-1-1-1-1-1-1-1-10-2-2-1-100220000001100-1-122110000-2-21111-1-1-2-2-1-11111000-2000001100000
χ352222-1222222-1222-1-12-1-12-1-122-1-1-1-12-1-122222222-2-200-2-20000-1-1-1-1-1-1-1-1-1-1-1-10221100-2-2000000-1-10011-2-2-1-10000-2-21111112211-1-1-1-1000-2000001100000
χ362222-1222222-1222-1-12-1-12-1-122-1-1-1-12-1-122222222-2-200-2-20000-1-1-1-1-1-1-1-1-1-1-1-10-2-21100-2-2000000110011-2-211000022-1-1-1-111-2-2111111000200000-1-100000
χ372222-122-2-222-1222-1-12-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-22200-2-20000-1-1-1-11111111102-2-1-10022000000-1-10011-2-2110000-2-21111-1-1-221111-1-1000200000-1-100000
χ382222-122-2-222-1222-1-12-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-22200-2-20000-1-1-1-1111111110-22-1-10022000000110011-2-2-1-1000022-1-1-1-1-1-12-211-1-111000-2000001100000
χ392222-122-2-222-1222-1-12-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2-2-200220000-1-1-1-11111111102-21100-2-2000000-1-100-1-12211000022-1-1-1-111-22-1-111-1-1000-2000001100000
χ402222-122-2-222-1222-1-12-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2-2-200220000-1-1-1-1111111110-221100-2-20000001100-1-122-1-10000-2-21111112-2-1-1-1-111000200000-1-100000
χ4122-2-222200-2-2222-2-2-2-2222-2-2-2-22-2-2220000000000002-20022-2-22-2-2200000000000002-20022-2-200000000000000002i−2i2i2i−2i−2i0000000000000000000002i−2i000
χ4222-2-222200-2-2222-2-2-2-2222-2-2-2-22-2-2220000000000002-20022-2-22-2-2200000000000002-20022-2-20000000000000000−2i2i−2i−2i2i2i000000000000000000000−2i2i000
χ4322-2-222200-2-2222-2-2-2-2222-2-2-2-22-2-222000000000000-2200-2-2222-2-220000000000000-2200-2-22200000000000000002i−2i2i2i−2i−2i000000000000000000000−2i2i000
χ4422-2-222200-2-2222-2-2-2-2222-2-2-2-22-2-222000000000000-2200-2-2222-2-220000000000000-2200-2-2220000000000000000−2i2i−2i−2i2i2i0000000000000000000002i−2i000
χ452-22-22222i−2i22-2-2-2-22-2-2222-222-2-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i2-2002i−2i000022-2-22i−2i2i−2i2i2i−2i−2i0002-2002-200000000002i−2i2i−2i0000000000002-2002i−2i00000000000000000000
χ462-22-22222i−2i22-2-2-2-22-2-2222-222-2-22-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i-2200−2i2i000022-2-22i−2i2i−2i2i2i−2i−2i000-2200-220000000000−2i2i−2i2i000000000000-2200−2i2i00000000000000000000
χ472-22-2222−2i2i22-2-2-2-22-2-2222-222-2-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i2-200−2i2i000022-2-2−2i2i−2i2i−2i−2i2i2i0002-2002-20000000000−2i2i−2i2i0000000000002-200−2i2i00000000000000000000
χ482-22-2222−2i2i22-2-2-2-22-2-2222-222-2-22-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i-22002i−2i000022-2-2−2i2i−2i2i−2i−2i2i2i000-2200-2200000000002i−2i2i−2i000000000000-22002i−2i00000000000000000000
χ492-22-222-12i−2i-12-21-2-22-212-1-1-2-1-11121-212i−2i−ii2i−2i−i−iii2-2002i−2i−i3i3−i3i3-1-111−ii2i−2i−i−iii0002-200-11−i3i3−i3i33−300002i−2i−ii0033−3−3000000-1100−ii000000000−i3i33−30000000
χ502-22-222-12i−2i-12-21-2-22-212-1-1-2-1-11121-212i−2i−ii2i−2i−i−iii2-2002i−2ii3−i3i3−i3-1-111−ii2i−2i−i−iii0002-200-11i3−i3i3−i3−3300002i−2i−ii00−3−333000000-1100−ii000000000i3−i3−330000000
χ512-22-222-12i−2i-12-21-2-22-212-1-1-2-1-11121-212i−2i−ii2i−2i−i−iii-2200−2i2i−i3i3−i3i3-1-111−ii2i−2i−i−iii000-22001-1−i3i3−i3i33−30000−2i2ii−i0033−3−30000001-100i−i000000000i3−i3−330000000
χ522-22-222-12i−2i-12-21-2-22-212-1-1-2-1-11121-212i−2i−ii2i−2i−i−iii-2200−2i2ii3−i3i3−i3-1-111−ii2i−2i−i−iii000-22001-1i3−i3i3−i3−330000−2i2ii−i00−3−3330000001-100i−i000000000−i3i33−30000000
χ532-22-222-1−2i2i-12-21-2-22-212-1-1-2-1-11121-21−2i2ii−i−2i2iii−i−i2-200−2i2i−i3i3−i3i3-1-111i−i−2i2iii−i−i0002-200-11−i3i3−i3i3−330000−2i2ii−i00−3−333000000-1100i−i000000000−i3i3−330000000
χ542-22-222-1−2i2i-12-21-2-22-212-1-1-2-1-11121-21−2i2ii−i−2i2iii−i−i2-200−2i2ii3−i3i3−i3-1-111i−i−2i2iii−i−i0002-200-11i3−i3i3−i33−30000−2i2ii−i0033−3−3000000-1100i−i000000000i3−i33−30000000
χ552-22-222-1−2i2i-12-21-2-22-212-1-1-2-1-11121-21−2i2ii−i−2i2iii−i−i-22002i−2i−i3i3−i3i3-1-111i−i−2i2iii−i−i000-22001-1−i3i3−i3i3−3300002i−2i−ii00−3−3330000001-100−ii000000000i3−i33−30000000
χ562-22-222-1−2i2i-12-21-2-22-212-1-1-2-1-11121-21−2i2ii−i−2i2iii−i−i-22002i−2ii3−i3i3−i3-1-111i−i−2i2iii−i−i000-22001-1i3−i3i3−i33−300002i−2i−ii0033−3−30000001-100−ii000000000−i3i3−330000000
χ572-22-2-1222i−2i221-2-2-2-11-2-1-121-12-21-111-2−ii2i−2i2i−2i2i2i−2i−2i2-2002i−2i0000-1-111−ii−ii−i−iii000-11002-20000003−300−ii2i−2i−i3i3000000−i3i3−i3i3-1100−ii−i3i33−30000000003−300000
χ582-22-2-1222i−2i221-2-2-2-11-2-1-121-12-21-111-2−ii2i−2i2i−2i2i2i−2i−2i2-2002i−2i0000-1-111−ii−ii−i−iii000-11002-2000000−3300−ii2i−2ii3−i3000000i3−i3i3−i3-1100−iii3−i3−33000000000−3300000
χ592-22-2-1222i−2i221-2-2-2-11-2-1-121-12-21-111-2−ii2i−2i2i−2i2i2i−2i−2i-2200−2i2i0000-1-111−ii−ii−i−iii0001-100-220000003−300i−i−2i2i−i3i3000000i3−i3i3−i31-100i−i−i3i33−3000000000−3300000
χ602-22-2-1222i−2i221-2-2-2-11-2-1-121-12-21-111-2−ii2i−2i2i−2i2i2i−2i−2i-2200−2i2i0000-1-111−ii−ii−i−iii0001-100-22000000−3300i−i−2i2ii3−i3000000−i3i3−i3i31-100i−ii3−i3−330000000003−300000
χ612-22-2-122−2i2i221-2-2-2-11-2-1-121-12-21-111-2i−i−2i2i−2i2i−2i−2i2i2i2-200−2i2i0000-1-111i−ii−iii−i−i000-11002-20000003−300i−i−2i2ii3−i3000000i3−i3i3−i3-1100i−ii3−i33−30000000003−300000
χ622-22-2-122−2i2i221-2-2-2-11-2-1-121-12-21-111-2i−i−2i2i−2i2i−2i−2i2i2i2-200−2i2i0000-1-111i−ii−iii−i−i000-11002-2000000−3300i−i−2i2i−i3i3000000−i3i3−i3i3-1100i−i−i3i3−33000000000−3300000
χ632-22-2-122−2i2i221-2-2-2-11-2-1-121-12-21-111-2i−i−2i2i−2i2i−2i−2i2i2i-22002i−2i0000-1-111i−ii−iii−i−i0001-100-220000003−300−ii2i−2ii3−i3000000−i3i3−i3i31-100−iii3−i33−3000000000−3300000
χ642-22-2-122−2i2i221-2-2-2-11-2-1-121-12-21-111-2i−i−2i2i−2i2i−2i−2i2i2i-22002i−2i0000-1-111i−ii−iii−i−i0001-100-22000000−3300−ii2i−2i−i3i3000000i3−i3i3−i31-100−ii−i3i3−330000000003−300000
χ6544444-2-244-2-24-2-2-244-2-2-21-2-211-2-2-2-2144-2-2-2-21111004400-2-2-2-21111-2-2-2-2111140000-2-2001111-2-200-2-2000000111100000000000000000000000000000000
χ6644444-2-244-2-24-2-2-244-2-2-21-2-211-2-2-2-2144-2-2-2-2111100-4-40022221111-2-2-2-21111-400002200-1-1-1-1220022000000-1-1-1-100000000000000000000000000000000
χ6744444-2-2-4-4-2-24-2-2-244-2-2-21-2-211-2-2-2-21-4-42222-1-1-1-1004400-2-2-2-211112222-1-1-1-1-40000-2-2001111220022000000-1-1-1-100000000000000000000000000000000
χ6844444-2-2-4-4-2-24-2-2-244-2-2-21-2-211-2-2-2-21-4-42222-1-1-1-100-4-400222211112222-1-1-1-1400002200-1-1-1-1-2-200-2-2000000111100000000000000000000000000000000
χ694444-24-244-24-2-244-2-2-2-21-2-21-2-21-21-2-2-2-2-2-244-2-2-2-24400440000111111-2-21111000-2-200-2-20000000000-2-2-2-200000000000011001100000000000000000000
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χ964-44-4-24-2−4i4i-2422-4-4-222-21-221-22-1-2-1222i−2i2i−2i−4i4i2i2i−2i−2i-44004i−4i000011-1-1−ii2i−2i−i−iii0002-2002-20000000000−2i2i−2i2i000000000000-1100i−i00000000000000000000
χ974-44-4-2-244i−4i4-22-422-22-41-2-2-1-2-22212-12−2i2i4i−4i−2i2i−2i−2i2i2i000000000011-1-1−2i2ii−iii−i−i00000000000000023−23000000−2i32i30000000000000000i3−i3−330000000000000000
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χ1084-4-444-2-20022-422-2-44-2-2-21-22-1122-22-1000000−3i3i3i−3i000000−2i32i32i3−2i31-11-10000−3i3i3i−3i000000000i3−i3−i3i3000023−23000000−333−300000000000000000000000000000000
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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
χ11488-8-8-48-4004-8-4-48-8444-42-44-24424-2-4-4000000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
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χ1188-88-8-4-4-48i−8i-4-44444-444222-222-2-22-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i0000000000-1-1112i−2i2i−2i−i−iii0000000000000000000000000000000000000000000000000000000000000
χ1198-88-8-4-4-4−8i8i-4-44444-444222-222-2-22-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i0000000000-1-111−2i2i−2i2iii−i−i0000000000000000000000000000000000000000000000000000000000000
χ1208-8-88-48-4004-844-884-4-4-42-4-4-24-4-24244000000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).