Finite Group Databasebeta

← Group #13146602

Character table — Group #13146602

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222299991212121212121212181818181818181818181818181818181818181818181818181818181818181818182424242436363636363636367272727272727272
order122234466612121212444433666666448888888812121212121212122424242424242424242424242424242412121212444444441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ511111-1-1111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111-1-1111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ811111-1-1111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
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χ101-1-111i−i-11-1ii−i−iii−i−i11-1-111-1-11-111-1-1ii−i−iii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iii−i−i−ii−ii-11-11-11-11−ii−ii
χ111-1-111i−i-11-1ii−i−iii−i−i11-1-111-1-11-1-1-111−i−iiiii−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiii−i−ii−i−ii1-1-111-1-11i−i−ii
χ121-1-111i−i-11-1ii−i−iii−i−i11-1-111-1-11-1-1-111−i−iiiii−i−i11-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i−iii−i-111-1-111-1−iii−i
χ131-1-111−ii-11-1−i−iii−i−iii11-1-111-1-11-111-1-1−i−iii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−iiii−ii−i-11-11-11-11i−ii−i
χ141-1-111−ii-11-1−i−iii−i−iii11-1-111-1-11-111-1-1−i−iii−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−iii−ii−ii1-11-11-11-1−ii−ii
χ151-1-111−ii-11-1−i−iii−i−iii11-1-111-1-11-1-1-111ii−i−i−i−iii11-1-1-1-1-1-11111iiii−i−i−i−i−i−iiii−i−ii-111-1-111-1i−i−ii
χ161-1-111−ii-11-1−i−iii−i−iii11-1-111-1-11-1-1-111ii−i−i−i−iii11-1-1-1-1-1-11111iiii−i−i−i−i−i−iii−iii−i1-1-111-1-11−iii−i
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χ1822222-2-2222-2-2-2-2222222222222-2-2000000002222-2-2-2-20000000000000000-2-2-2-20000000000000000
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χ282-2-222−2i2i-22-2−2i−2i2i2i2i2i−2i−2i22-2-222-2-2-22000000002i2i−2i−2i-2-2220000000000000000−2i−2i2i2i0000000000000000
χ294444444444444400001-21-21-21-200000000000000000000000000000000001-21-20022002200-1-100-1-1
χ304444444444444400001-21-21-21-200000000000000000000000000000000001-21-200-2-200-2-200110011
χ31444444444444440000-21-21-21-210000000000000000000000000000000000-21-2122002200-1-100-1-100
χ32444444444444440000-21-21-21-210000000000000000000000000000000000-21-21-2-200-2-20011001100
χ3344444-4-4444-4-4-4-400001-21-21-21-20000000000000000000000000000000000-12-12002200-2-2001100-1-1
χ3444444-4-4444-4-4-4-400001-21-21-21-20000000000000000000000000000000000-12-1200-2-2002200-1-10011
χ3544444-4-4444-4-4-4-40000-21-21-21-2100000000000000000000000000000000002-12-12200-2-2001100-1-100
χ3644444-4-4444-4-4-4-40000-21-21-21-2100000000000000000000000000000000002-12-1-2-2002200-1-1001100
χ374-4-4444i−4i-44-44i4i−4i−4i00001-2-121-2-120000000000000000000000000000000000i−2i−i2i002i−2i002-200-1100−ii
χ384-4-4444i−4i-44-44i4i−4i−4i00001-2-121-2-120000000000000000000000000000000000i−2i−i2i00−2i2i00-22001-100i−i
χ394-4-4444i−4i-44-44i4i−4i−4i0000-212-1-212-10000000000000000000000000000000000−2ii2i−i2i−2i002-200-1100−ii00
χ404-4-4444i−4i-44-44i4i−4i−4i0000-212-1-212-10000000000000000000000000000000000−2ii2i−i−2i2i00-22001-100i−i00
χ414-4-444−4i4i-44-4−4i−4i4i4i00001-2-121-2-120000000000000000000000000000000000−i2ii−2i002i−2i00-22001-100−ii
χ424-4-444−4i4i-44-4−4i−4i4i4i00001-2-121-2-120000000000000000000000000000000000−i2ii−2i00−2i2i002-200-1100i−i
χ434-4-444−4i4i-44-4−4i−4i4i4i0000-212-1-212-100000000000000000000000000000000002i−i−2ii2i−2i00-22001-100−ii00
χ444-4-444−4i4i-44-4−4i−4i4i4i0000-212-1-212-100000000000000000000000000000000002i−i−2ii−2i2i002-200-1100i−i00
χ456666-366-3-3-3-3-3-3-32222000000002200000000-1-1-1-1-1-1-1-13−33−33−33−33−33−33−33−300000000000000000000
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χ476666-366-3-3-3-3-3-3-3-2-2-2-200000000-2-22222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ486666-366-3-3-3-3-3-3-3-2-2-2-200000000-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000000
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χ506666-3-6-6-3-3-33333222200000000-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000
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χ5966-6-6-30033-3−3333−3333-22-2200000000002−22−22−22−21-11-13−33−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ700000000000000000000
χ6066-6-6-30033-3−3333−3333-22-220000000000−22−22−22−221-11-13−33−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ700000000000000000000
χ616-66-6-300-333−3i33i33i3−3i32i−2i−2i2i00000000002−2−22−i2i2i2−i2−iii−i−333−3ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ700000000000000000000
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χ646-66-6-300-333−3i33i33i3−3i3−2i2i2i−2i0000000000−222−2−i2i2i2−i2i−i−ii3−3−33−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000000000000000
χ656-66-6-300-3333i3−3i3−3i33i32i−2i−2i2i00000000002−2−22−i2i2i2−i2−iii−i3−3−33ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000000000000000
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χ7788-8-8800-8-88000000002-42-4-24-24000000000000000000000000000000000000000000000000000000
χ7888-8-8800-8-8800000000-42-424-24-2000000000000000000000000000000000000000000000000000000
χ798-88-88008-8-8000000002-4-24-242-4000000000000000000000000000000000000000000000000000000
χ808-88-88008-8-800000000-424-24-2-42000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.