Finite Group Databasebeta

← Group #13154846

Character table — Group #13154846

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444444444444444888888888888888812121212121212121212121212121212121218181818181818183636363636363636363636363636108108108108108108
order122222366633666666666666666633666666666666664412121212121212121212121212121212444412121212888812122424242424242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ91-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1i−ii−iii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ101-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1i−ii−iii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ111-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1−ii−ii−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
χ121-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1−ii−ii−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ131-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111i−ii−iii−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13
χ141-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111i−ii−iii−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13
χ151-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111−ii−ii−i−iii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23
χ161-11-11-111-1-1111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111−ii−ii−i−iiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23
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χ212222-2-2222222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000022-2-222220000-2-200000000000000
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χ252222-2-2-1-1-1-12211-2-2-2-22222-2-2-2-222-1-1-1-11111-1-1-1-11111000000000000000000-2-22211110000-1-13−33−3−33−33000000
χ262222-2-2-1-1-1-12211-2-2-2-22222-2-2-2-222-1-1-1-11111-1-1-1-11111000000000000000000-2-22211110000-1-1−33−333−33−3000000
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χ282-22-22-2-1-11122-112222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1111111110000000000000000002i−2i2i−2i−i−iii−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000
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χ302-22-22-2-1-11122-112222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-111111111000000000000000000−2i2i−2i2iii−i−i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000
χ312-22-2-2222-2-222-22-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222220000000000000000002i−2i−2i2i2i2i−2i−2i0000−2i2i00000000000000
χ322-22-2-2222-2-222-22-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-22222000000000000000000−2i2i2i−2i−2i−2i2i2i00002i−2i00000000000000
χ332-22-2-22-1-111221-1-2-2-2-2-2-2-2-2222222-1-1-1-111111111-1-1-1-10000000000000000002i−2i−2i2i−i−iii0000i−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000
χ342-22-2-22-1-111221-1-2-2-2-2-2-2-2-2222222-1-1-1-111111111-1-1-1-10000000000000000002i−2i−2i2i−i−iii0000i−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000
χ352-22-2-22-1-111221-1-2-2-2-2-2-2-2-2222222-1-1-1-111111111-1-1-1-1000000000000000000−2i2i2i−2iii−i−i0000−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000
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χ584-44-44-444-4-4-214-4-2-21122-1-122-1-1-21-21-21-2-21122-1-122-1-14-4-2-2-2-211112222-1-1-1-10000000000000000000000000000
χ594-44-44-444-4-4-214-4-2-21122-1-122-1-1-21-21-21-2-21122-1-122-1-1-442222-1-1-1-1-2-2-2-211110000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.