Finite Group Databasebeta

← Group #13155675

Character table — Group #13155675

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order12223334466666666612121212333666666666121212121212121212121212366612121212121222888824242424242424242424242424242424242424242424242424242424242424244444666666664444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1
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
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
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
χ91-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-11-1i−i11-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−ii−i11-1-111-1-11-1i−iii−i−ii−i1-1i−i
χ101-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-11-1−ii11-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−ii11-1-111-1-11-1−ii−i−iii−ii1-1−ii
χ111-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-1-11i−i-1-111ii−i−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−ii11-1-111-1-1-11i−i−i−iiii−i-11−ii
χ121-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-11-1-11−ii-1-111−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−ii−i11-1-111-1-1-11−iiii−i−i−ii-11i−i
χ131-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-111-1i−i11-1-1ii−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−ii−ii−i-1-111-1-111-11−iiii−i−i−ii-11−ii
χ141-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-111-1−ii11-1-1−i−iii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−ii−ii-1-111-1-111-11i−i−i−iiii−i-11i−i
χ151-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-11-11i−i-1-111ii−i−i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−ii−ii-1-111-1-1111-1−ii−i−iii−ii1-1i−i
χ161-11-11111-1-1-1-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-1-1-1111-1-11-1-111-111-1-1-11-11−ii-1-111−i−iii-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiii−ii−i-1-111-1-1111-1i−iii−i−ii−i1-1−ii
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
χ19222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-100220000-1-10000
χ20222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-200000000000011111111111100002-12-1-1-1-1-100-2-20000110000
χ21222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-21-21111100-2-20000110000
χ22222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-12-1-122-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-20000000000001111111111110000-21-21111100220000-1-10000
χ2322222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12-12-1-1-1-12200000000-1-100
χ2422222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-200001111111111110000000000000000-12-12-1-1-1-1-2-2000000001100
χ2522222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-21-21111-2-2000000001100
χ2622222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000011111111111100000000000000001-21-211112200000000-1-100
χ272222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ282222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000000001111000000
χ292222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ302222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222000000000000-1-1-1-1000000
χ312222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−33−33−30033−3−30033−3−30033−3−30033−3−322-2-2000000000000-11-11000000
χ322222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-2-2220000000000001-11-1000000
χ332222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-2-2220000000000001-11-1000000
χ342222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−33−33−3300−3−33300−3−33300−3−33300−3−33322-2-2000000000000-11-11000000
χ352-22-2222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-22-2-2222-2-2-2222-2-22-22-2-222000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000
χ362-22-2222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-22-2-2222-2-2-2222-2-22-22-2-22200000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000
χ372-22-222-12-2-2-212-1-2-21222-2-22-1-1-2-211112-1-1-1-2-1-1-2-2122211-111-1-11-1-1112-2002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii00002-1-21-1-111002i−2i0000−ii0000
χ382-22-222-12-2-2-212-1-2-21222-2-22-1-1-2-211112-1-1-1-2-1-1-2-2122211-111-1-11-1-1112-200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i00002-1-21-1-11100−2i2i0000i−i0000
χ392-22-222-12-2-2-212-1-2-21222-2-22-1-1-2-211112-1-1-1-2-1-1-2-2122211-111-1-11-1-111-22002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000-212-111-1-100−2i2i0000i−i0000
χ402-22-222-12-2-2-212-1-2-21222-2-22-1-1-2-211112-1-1-1-2-1-1-2-2122211-111-1-11-1-111-2200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000-212-111-1-1002i−2i0000−ii0000
χ412-22-22-122-211-222-2-2-2-122-2-2-12-111-2-211-12-1212211-2-1-1-1-2-2-111-1-11-1-1112-22-20022-2-20000-1-1-1-1-1-11111110000000000000000-121-2-1-1112-200000000-1100
χ422-22-22-122-211-222-2-2-2-122-2-2-12-111-2-211-12-1212211-2-1-1-1-2-2-111-1-11-1-1112-2-2200-2-2220000111111-1-1-1-1-1-10000000000000000-121-2-1-111-22000000001-100
χ432-22-22-122-211-222-2-2-2-122-2-2-12-111-2-211-12-1212211-2-1-1-1-2-2-111-1-11-1-111-222-20022-2-20000-1-1-1-1-1-111111100000000000000001-2-1211-1-1-22000000001-100
χ442-22-22-122-211-222-2-2-2-122-2-2-12-111-2-211-12-1212211-2-1-1-1-2-2-111-1-11-1-111-22-2200-2-2220000111111-1-1-1-1-1-100000000000000001-2-1211-1-12-200000000-1100
χ452-22-2-1222-2-2-2-2-1211-22-1-111-1-121111-2-2-1-122-2-1-111-22-1-111-111-12-2-1-111002-22i−2i-1-111−i−iii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i−2i2i−2i000000000000−i−iii000000
χ462-22-2-1222-2-2-2-2-1211-22-1-111-1-121111-2-2-1-122-2-1-111-22-1-111-111-12-2-1-111002-2−2i2i-1-111ii−i−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i2i−2i2i000000000000ii−i−i000000
χ472-22-2-1222-2-2-2-2-1211-22-1-111-1-121111-2-2-1-122-2-1-111-22-1-111-111-12-2-1-11100-222i−2i11-1-1−i−iii-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i2i−2i2i000000000000ii−i−i000000
χ482-22-2-1222-2-2-2-2-1211-22-1-111-1-121111-2-2-1-122-2-1-111-22-1-111-111-12-2-1-11100-22−2i2i11-1-1ii−i−i-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i−2i2i−2i000000000000−i−iii000000
χ492-22-2-122-22-2-2-2-1211-2211-1-1-1-121111-2-2-1-12-2211-1-12-211-1-1-111-1-2211-1-10000003−3−33−i3i3i3−i30033−3−300−3−33300−i3−i3i3i300i3i3−i3−i3−2i2i2i−2i000000000000i−i−ii000000
χ502-22-2-122-22-2-2-2-1211-2211-1-1-1-121111-2-2-1-12-2211-1-12-211-1-1-111-1-2211-1-10000003−3−33i3−i3−i3i30033−3−300−3−33300i3i3−i3−i300−i3−i3i3i32i−2i−2i2i000000000000−iii−i000000
χ512-22-2-122-22-2-2-2-1211-2211-1-1-1-121111-2-2-1-12-2211-1-12-211-1-1-111-1-2211-1-1000000−333−3−i3i3i3−i300−3−3330033−3−300−i3−i3i3i300i3i3−i3−i32i−2i−2i2i000000000000−iii−i000000
χ522-22-2-122-22-2-2-2-1211-2211-1-1-1-121111-2-2-1-12-2211-1-12-211-1-1-111-1-2211-1-1000000−333−3i3−i3−i3i300−3−3330033−3−300i3i3−i3−i300−i3−i3i3i3−2i2i2i−2i000000000000i−i−ii000000
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χ5644444-2-244-2-2-24-244-2-24444-2-21-2-2-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111-4-400000000000000000000000000000000000000002222-1-1-1-100000000000000
χ5744444-2-2-4-4-2-2-24-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000003-33-300000000000000
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χ664444-2-24-4-4-2-24-24-2-24-222221-2-211-2-2-2-21-2-2-4222-1-1-42-1-122111122-1-1-1-1000000−2323−232300000033−3−30033−3−300000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.