Finite Group Databasebeta

← Group #13155709

Character table — Group #13155709

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order1222333446666666661212121233366666666612121212121212121212121236661212121212124488882424242424242424242424242424242424242424242424242424242424242424444412121212121212124444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1
χ91-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1i−i1-1i−i11-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−ii−iii−i−iii−i−ii−i1-1ii−i−ii−i1-11-1
χ101-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1i−i1-1−ii11-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−iiii−i−iii−i−ii−i-11−i−iiii−i-11-11
χ111-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1i−i-11i−i-1-111ii−i−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−iiii−i−iii−i−i−ii1-1−i−iii−ii1-1-11
χ121-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1i−i-11−ii-1-111−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−ii−iii−i−iii−i−i−ii-11ii−i−i−ii-111-1
χ131-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1−ii1-1i−i11-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−ii−i−i−iii−i−iii−ii-11ii−i−i−ii-11-11
χ141-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1−ii1-1−ii11-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−ii−i−iii−i−iii−ii1-1−i−iii−ii1-11-1
χ151-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1−ii-11i−i-1-111ii−i−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−ii−i−iii−i−iiii−i-11−i−iiii−i-111-1
χ161-1-111111-1-111-1-1-1-1-1111-1-1111-1-1-1-1-1111-1-1111-1-11-111-1-11-1-111-111-1-1−ii-11−ii-1-111−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−ii−i−i−iii−i−iiii−i1-1ii−i−ii−i1-1-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000022-2-20000000000002-22-2000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-222000000000000-22-22000000
χ19222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ20222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000000001111000000
χ21222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ22222222-12222-122-1-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222000000000000-1-1-1-1000000
χ23222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−33−33−30033−3−30033−3−30033−3−30033−3−322-2-2000000000000-11-11000000
χ24222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-2-2220000000000001-11-1000000
χ25222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-2-2220000000000001-11-1000000
χ26222222-1-2-222-122-1-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−33−33−3300−3−33300−3−33300−3−33300−3−33322-2-2000000000000-11-11000000
χ2722222-12222-122-122-122222-12-1-122-1-1-12-1-1-1222-1-1-12-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002-12-1-1-1-1-122000000-1-10000
χ2822222-12222-122-122-122222-12-1-122-1-1-12-1-1-1222-1-1-12-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-2000011111111111100000000000000002-12-1-1-1-1-1-2-2000000110000
χ2922222-12222-122-122-122222-12-1-122-1-1-12-1-1-1222-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-21-211111-2-2000000110000
χ3022222-12222-122-122-122222-12-1-122-1-1-12-1-1-1222-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200001111111111110000000000000000-21-21111122000000-1-10000
χ312222-12222-122-12222-12222-1-12-1-1-122-1-12-12-1-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-12-12-1-1-1-10022000000-1-100
χ322222-12222-122-12222-12222-1-12-1-1-122-1-12-12-1-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-20000000000001111111111110000-12-12-1-1-1-100-2-20000001100
χ332222-12222-122-12222-12222-1-12-1-1-122-1-12-12-1-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100001-21-2111100-2-20000001100
χ342222-12222-122-12222-12222-1-12-1-1-122-1-12-12-1-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-200000000000011111111111100001-21-211110022000000-1-100
χ352-2-22222-22-222-2-2-2-2-22-2-222222-2-2-2-2-2222-22-2-2-222-22-2-2222-2-22-22-2-222000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000
χ362-2-22222-22-222-2-2-2-2-22-2-222222-2-2-2-2-2222-22-2-2-222-22-2-2222-2-22-22-2-22200000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000
χ372-2-2222-12-2-22-1-2-211-22-1-1112-1-1-211112-1-1-2-22-1-1112-2-1-111-111-12-2-1-111002-22i−2i-1-111−i−iii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i−2i2i−2i000000000000−i−iii000000
χ382-2-2222-12-2-22-1-2-211-22-1-1112-1-1-211112-1-1-2-22-1-1112-2-1-111-111-12-2-1-111002-2−2i2i-1-111ii−i−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i2i−2i2i000000000000ii−i−i000000
χ392-2-2222-12-2-22-1-2-211-22-1-1112-1-1-211112-1-1-2-22-1-1112-2-1-111-111-12-2-1-11100-222i−2i11-1-1−i−iii-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i2i−2i2i000000000000ii−i−i000000
χ402-2-2222-12-2-22-1-2-211-22-1-1112-1-1-211112-1-1-2-22-1-1112-2-1-111-111-12-2-1-11100-22−2i2i11-1-1ii−i−i-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i−2i2i−2i000000000000−i−iii000000
χ412-2-2222-1-22-22-1-2-211-2211-1-12-1-1-211112-1-1-22-211-1-1-2211-1-1-111-1-2211-1-10000003−3−33−i3i3i3−i30033−3−300−3−33300−i3−i3i3i300i3i3−i3−i3−2i2i2i−2i000000000000i−i−ii000000
χ422-2-2222-1-22-22-1-2-211-2211-1-12-1-1-211112-1-1-22-211-1-1-2211-1-1-111-1-2211-1-10000003−3−33i3−i3−i3i30033−3−300−3−33300i3i3−i3−i300−i3−i3i3i32i−2i−2i2i000000000000−iii−i000000
χ432-2-2222-1-22-22-1-2-211-2211-1-12-1-1-211112-1-1-22-211-1-1-2211-1-1-111-1-2211-1-1000000−333−3−i3i3i3−i300−3−3330033−3−300−i3−i3i3i300i3i3−i3−i32i−2i−2i2i000000000000−iii−i000000
χ442-2-2222-1-22-22-1-2-211-2211-1-12-1-1-211112-1-1-22-211-1-1-2211-1-1-111-1-2211-1-1000000−333−3i3−i3−i3i300−3−3330033−3−300i3i3−i3−i300−i3−i3i3i3−2i2i2i−2i000000000000i−i−ii000000
χ452-2-222-122-2-2-12-21-2-21222-2-2-12-11-2-211-12-11122211-1-2-1-1-2-2-111-1-11-1-1112i−2i2-20022-2-20000-1-1-1-1-1-111111100000000000000002i−i−2ii−i−iii2i−2i000000−ii0000
χ462-2-222-122-2-2-12-21-2-21222-2-2-12-11-2-211-12-11122211-1-2-1-1-2-2-111-1-11-1-1112i−2i-2200-2-2220000111111-1-1-1-1-1-100000000000000002i−i−2ii−i−iii−2i2i000000i−i0000
χ472-2-222-122-2-2-12-21-2-21222-2-2-12-11-2-211-12-11122211-1-2-1-1-2-2-111-1-11-1-111−2i2i2-20022-2-20000-1-1-1-1-1-11111110000000000000000−2ii2i−iii−i−i−2i2i000000i−i0000
χ482-2-222-122-2-2-12-21-2-21222-2-2-12-11-2-211-12-11122211-1-2-1-1-2-2-111-1-11-1-111−2i2i-2200-2-2220000111111-1-1-1-1-1-10000000000000000−2ii2i−iii−i−i2i−2i000000−ii0000
χ492-2-22-1222-21221-2-2-2-2-122-2-2-1-12111-2-2-1-121-2-1-1-1-2-2212211-111-1-11-1-1112i−2i002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000−i2ii−2i−i−iii002-2000000-1100
χ502-2-22-1222-21221-2-2-2-2-122-2-2-1-12111-2-2-1-121-2-1-1-1-2-2212211-111-1-11-1-1112i−2i00−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000−i2ii−2i−i−iii00-220000001-100
χ512-2-22-1222-21221-2-2-2-2-122-2-2-1-12111-2-2-1-121-2-1-1-1-2-2212211-111-1-11-1-111−2i2i002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000i−2i−i2iii−i−i00-220000001-100
χ522-2-22-1222-21221-2-2-2-2-122-2-2-1-12111-2-2-1-121-2-1-1-1-2-2212211-111-1-11-1-111−2i2i00−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000i−2i−i2iii−i−i002-2000000-1100
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χ624444-24-2-4-4-24-2-24-2-24-22222-21-2-211-2-2-21-2-2-42-1-122-4222-1-1111122-1-1-1-10000000000−2323−23230000000000000033−3−30033−3−300000000000000000000000000
χ634444-2-2444-2-24-2-244-2-244441-2-21-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111440000000000000000000000000000000000000000-2-2-2-2111100000000000000
χ644444-2-2444-2-24-2-244-2-244441-2-21-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111-4-400000000000000000000000000000000000000002222-1-1-1-100000000000000
χ654444-2-24-4-4-2-24-2-244-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000003-33-300000000000000
χ664444-2-24-4-4-2-24-2-244-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000000-33-3300000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.