Finite Group Databasebeta

← Group #13146680

Character table — Group #13146680

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222299991212121212121212181818181818181818181818181818181818181818181818181818181818181818182424242436363636363636367272727272727272
order12222236666666444433666666448888888812121212121212122424242424242424242424242424242466662244444466121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ51111-1-1111-1-1-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111-1-1111-1-1-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111-1-1111-1-1-1-11-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111
χ81111-1-1111-1-1-1-11-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-11111-1-1
χ91-1-111-11-1-111-1-1111-1-1111-1-1-1-111-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-1i−ii−i1-11-11-1i−ii−i
χ101-1-111-11-1-111-1-1111-1-1111-1-1-1-111-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1-11−ii−ii-11-11-11−ii−ii
χ111-1-111-11-1-111-1-1111-1-1111-1-1-1-111-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−ii−ii1-11-11-1−ii−ii
χ121-1-111-11-1-111-1-1111-1-1111-1-1-1-111-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1-11i−ii−i-11-11-11i−ii−i
χ131-1-11-111-1-1-1-1111-1-111111-1-1-1-111-1ii−i−i−i−iii11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-111-1i−i−ii-111-1-11i−i−ii
χ141-1-11-111-1-1-1-1111-1-111111-1-1-1-111-1ii−i−i−i−iii11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11-11−iii−i1-1-111-1−iii−i
χ151-1-11-111-1-1-1-1111-1-111111-1-1-1-111-1−i−iiiii−i−i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-111-1−iii−i-111-1-11−iii−i
χ161-1-11-111-1-1-1-1111-1-111111-1-1-1-111-1−i−iiiii−i−i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11-11i−i−ii1-1-111-1i−i−ii
χ1722222222222222-2-2-2-222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ182222-2-2222-2-2-2-22222222222222-2-200000000-2-22222-2-20000000000000000-2-2-2-20000000000000000
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χ2122-2-20022-20000-2−2i2i−2i2i22-22-22-2-2002−22−2i2−i2i2−i200−2i2i−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ2222-2-20022-20000-2−2i2i−2i2i22-22-22-2-200−22−22−i2i2−i2i200−2i2i−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000
χ232-22-2002-220000-22i−2i−2i2i22-2-22-22-200−i2i2i2−i2−222−2002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000
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χ282-2-22-222-2-2-2-222222-2-2222-2-2-2-22-2200000000-2-222-2-2220000000000000000-22-220000000000000000
χ294444444444444400001-21-2-211-2000000000000000000000000000000000011-2-2002222000000-1-1-1-1
χ304444444444444400001-21-2-211-2000000000000000000000000000000000011-2-200-2-2-2-20000001111
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χ32444444444444440000-21-211-2-210000000000000000000000000000000000-2-211-2-20000-2-211110000
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χ344444-4-4444-4-4-4-4400001-21-2-211-20000000000000000000000000000000000-1-12200-2-22200000011-1-1
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χ374-4-444-44-4-444-4-4400001-2122-1-1-200000000000000000000000000000000001-1-22002i−2i2i−2i000000−ii−ii
χ384-4-444-44-4-444-4-4400001-2122-1-1-200000000000000000000000000000000001-1-2200−2i2i−2i2i000000i−ii−i
χ394-4-444-44-4-444-4-440000-21-2-1-12210000000000000000000000000000000000-221-12-200002-2-11-110000
χ404-4-444-44-4-444-4-440000-21-2-1-12210000000000000000000000000000000000-221-1-220000-221-11-10000
χ414-4-44-444-4-4-4-444400001-2122-1-1-20000000000000000000000000000000000-112-2002i−2i−2i2i000000−iii−i
χ424-4-44-444-4-4-4-444400001-2122-1-1-20000000000000000000000000000000000-112-200−2i2i2i−2i000000i−i−ii
χ434-4-44-444-4-4-4-44440000-21-2-1-122100000000000000000000000000000000002-2-112-20000-22-111-10000
χ444-4-44-444-4-4-4-44440000-21-2-1-122100000000000000000000000000000000002-2-11-2200002-21-1-110000
χ45666666-3-3-3-3-3-3-3-32222000000002200000000-1-1-1-1-1-1-1-13−33−33−33−33−33−33−33−300000000000000000000
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χ48666666-3-3-3-3-3-3-3-3-2-2-2-200000000-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000000
χ496666-6-6-3-3-33333-3222200000000-2-22222-2-2-2-211-1-1-1-111-1-1-1-1-1-1-1-11111111100000000000000000000
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χ5966-6-600-3-333i3−3i33i3−3i33−2i2i−2i2i00000000002−22−2−i2i2−i2i23−3i−ii−i3−3ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ2300000000000000000000
χ6066-6-600-3-333i3−3i33i3−3i33−2i2i−2i2i0000000000−22−22i2−i2i2−i23−3i−ii−i3−3−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ2300000000000000000000
χ616-66-600-33-3−3i33i33i3−3i332i−2i−2i2i0000000000−i2i2i2−i22−2−223−3−iii−i−33ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ700000000000000000000
χ626-66-600-33-3−3i33i33i3−3i332i−2i−2i2i0000000000i2−i2−i2i2−222−23−3−iii−i−33−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ700000000000000000000
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χ646-66-600-33-3−3i33i33i3−3i33−2i2i2i−2i0000000000i2−i2−i2i22−2−22−33i−i−ii3−3−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ2300000000000000000000
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χ798-88-8008-880000-800002-4-24-4-224000000000000000000000000000000000000000000000000000000
χ808-88-8008-880000-80000-424-224-4-2000000000000000000000000000000000000000000000000000000

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