Finite Group Databasebeta

← Group #13155415

Character table — Group #13155415

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order12223334466666666612121212333666666666121212121212121212121212366612121212121244888824242424242424242424242424242424242424242424242424242424242424242244121212121212121244446612121212121244
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
χ91-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-11-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11-111-1-111-1-1i−ii−i1-11-1i−ii−i1-1
χ101-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-11-1i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-1111-1-111-1-1i−i−ii-11-11i−i−ii-11
χ111-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-11-1−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-1111-1-111-1-1−iii−i-11-11−iii−i-11
χ121-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-11-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11-111-1-111-1-1−ii−ii1-11-1−ii−ii1-1
χ131-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-1-11i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11-1-1-111-1-111−ii−ii1-11-1−ii−ii-11
χ141-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-1-11i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11-1-111-1-111−iii−i-11-11−iii−i1-1
χ151-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-1-11−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11-1-111-1-111i−i−ii-11-11i−i−ii1-1
χ161-1-111111-1-1-1-1-1111-1-111-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-111-111-1-1-11−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11-1-1-111-1-111i−ii−i1-11-1i−ii−i-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000022-2-200000000000022-2-2000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-222000000000000-2-222000000
χ19222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ20222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000000001111000000
χ21222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ22222222-12222-1-122-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222000000000000-1-1-1-1000000
χ23222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−33−33−30033−3−30033−3−30033−3−30033−3−322-2-2000000000000-1-111000000
χ24222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-2-22200000000000011-1-1000000
χ25222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-2-22200000000000011-1-1000000
χ26222222-1-2-222-1-122-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−33−33−3300−3−33300−3−33300−3−33300−3−33322-2-2000000000000-1-111000000
χ2722222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-10022000000-1-100
χ2822222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-200000000000011111111111100002-12-1-1-1-1-100-2-20000001100
χ2922222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-21-21111100-2-20000001100
χ3022222-12222-1222-122-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-20000000000001111111111110000-21-2111110022000000-1-100
χ312222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12-12-1-1-1-122000000-1-10000
χ322222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-200001111111111110000000000000000-12-12-1-1-1-1-2-2000000110000
χ332222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-21-21111-2-2000000110000
χ342222-12222-1222-122-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000011111111111100000000000000001-21-2111122000000-1-10000
χ352-2-22222-22-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-2-222000000000000000000000000000000000000002-2-220000000000002-2-22000000
χ362-2-22222-22-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-2-22200000000000000000000000000000000000000-222-2000000000000-222-2000000
χ372-2-2222-12-2-2-21122-1-2-2-1-1112-1-1-2-21111-1-1222-1-1-1-1-2-21111-111-12-2-1-111002i−2i2i−2i−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2-22-2000000000000-11-11000000
χ382-2-2222-12-2-2-21122-1-2-2-1-1112-1-1-2-21111-1-1222-1-1-1-1-2-21111-111-12-2-1-111002i−2i−2i2i−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-22-220000000000001-11-1000000
χ392-2-2222-12-2-2-21122-1-2-2-1-1112-1-1-2-21111-1-1222-1-1-1-1-2-21111-111-12-2-1-11100−2i2i2i−2iii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-22-220000000000001-11-1000000
χ402-2-2222-12-2-2-21122-1-2-2-1-1112-1-1-2-21111-1-1222-1-1-1-1-2-21111-111-12-2-1-11100−2i2i−2i2iii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2-22-2000000000000-11-11000000
χ412-2-2222-1-22-2-21122-1-2-211-1-12-1-1-2-21111-1-12-2-2111122-1-1-1-1-111-1-2211-1-1000000−i3i3i3−i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i32-2-22000000000000-111-1000000
χ422-2-2222-1-22-2-21122-1-2-211-1-12-1-1-2-21111-1-12-2-2111122-1-1-1-1-111-1-2211-1-1000000−i3i3i3−i3i3−i3−i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i3-222-20000000000001-1-11000000
χ432-2-2222-1-22-2-21122-1-2-211-1-12-1-1-2-21111-1-12-2-2111122-1-1-1-1-111-1-2211-1-1000000i3−i3−i3i3−i3i3i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i3-222-20000000000001-1-11000000
χ442-2-2222-1-22-2-21122-1-2-211-1-12-1-1-2-21111-1-12-2-2111122-1-1-1-1-111-1-2211-1-1000000i3−i3−i3i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i32-2-22000000000000-111-1000000
χ452-2-222-122-2-21-2-22-12-2122-2-2-12-111-2-2112-1-12-122-1-1-21-2-211-111-1-11-1-1112-2002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii00002-1-21-1-111002i−2i000000−ii00
χ462-2-222-122-2-21-2-22-12-2122-2-2-12-111-2-2112-1-12-122-1-1-21-2-211-111-1-11-1-1112-200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i00002-1-21-1-11100−2i2i000000i−i00
χ472-2-222-122-2-21-2-22-12-2122-2-2-12-111-2-2112-1-12-122-1-1-21-2-211-111-1-11-1-111-22002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000-212-111-1-100−2i2i000000i−i00
χ482-2-222-122-2-21-2-22-12-2122-2-2-12-111-2-2112-1-12-122-1-1-21-2-211-111-1-11-1-111-2200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000-212-111-1-1002i−2i000000−ii00
χ492-2-22-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-12-1-1221-211-2-2-111-1-11-1-1112-22i−2i002i2i−2i−2i0000−i−i−i−i−i−iiiiiii0000000000000000-121-2-1-1112i−2i000000−ii0000
χ502-2-22-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-12-1-1221-211-2-2-111-1-11-1-1112-2−2i2i00−2i−2i2i2i0000iiiiii−i−i−i−i−i−i0000000000000000-121-2-1-111−2i2i000000i−i0000
χ512-2-22-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-12-1-1221-211-2-2-111-1-11-1-111-222i−2i002i2i−2i−2i0000−i−i−i−i−i−iiiiiii00000000000000001-2-1211-1-1−2i2i000000i−i0000
χ522-2-22-1222-21-2-2-2-1221-222-2-2-1-121111-2-2-12-1-12-1-1221-211-2-2-111-1-11-1-111-22−2i2i00−2i−2i2i2i0000iiiiii−i−i−i−i−i−i00000000000000001-2-1211-1-12i−2i000000−ii0000
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χ5644444-2-2-4-44-2-2-24-2-24-22222-2-21-2-2-2-211-21-2-4222-1-1-4222-1-1111122-1-1-1-1000000000023−2323−2300000000000000−3−33300−3−33300000000000000000000000000
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χ624444-24-2-4-4-24-2-2-24-2-242222-21-2-2-211-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-1000000−2323−232300000033−3−30033−3−300000000000000000000000000000000000000
χ634444-2-2444-2-244-2-24-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111440000000000000000000000000000000000000000-2-2-2-2111100000000000000
χ644444-2-2444-2-244-2-24-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111-4-400000000000000000000000000000000000000002222-1-1-1-100000000000000
χ654444-2-24-4-4-2-244-2-24-2-2-4-4-4-41-2-211-2-2-2-2-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000003-33-300000000000000
χ664444-2-24-4-4-2-244-2-24-2-2-4-4-4-41-2-211-2-2-2-2-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000000-33-3300000000000000
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χ7044-4-44-2400424-4-42-4-4-20000-24-2-224-4-22-422000000000000-2-222000000000000000000000000000000006−66−66−66−66−66−600000000000000000000000000
χ7144-4-44-2400424-4-42-4-4-20000-24-2-224-4-22-422000000000000-2-22200000000000000000000000000000000−66−66−66−66−66−6600000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.