Finite Group Databasebeta

← Group #13166330

Character table — Group #13166330

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444466668888888888888888999912121212121212121212121212121212181818181818363636363636363636363636363654545454108108108108
order1222344666336666661212121212121212121222443366666612121212121212124444666666661212121212121212441212121288881212242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i1111−i−iii
χ81111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii1111ii−i−i
χ911111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-111-1-111-1-11-11-1
χ1011111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-11111-1-1-11-11
χ1111111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1i−i−ii11ii−i−i−i−iii-1-111i−i−ii
χ1211111-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1−iii−i11−i−iiiii−i−i-1-111−iii−i
χ1311111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111-11-1-1-111-1-111-1-1-1-111-11-11
χ1411111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-11-11-1-1-1-111-1-111-1-1111-11-1
χ1511111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1i−i−ii11ii−i−i−i−iii11-1-1−iii−i
χ1611111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−iii−i11−i−iiiii−i−i11-1-1i−i−ii
χ172222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000
χ182222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-1-2-2-2-2-1-11111111100000000
χ192222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-211112i2i−2i−2i11−i−i−i−iiiii00000000
χ202222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-21111−2i−2i2i2i11iiii−i−i−i−i00000000
χ212222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-12-22-211-1-111-1-11100000000
χ222222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-1-22-221111-1-111-1-100000000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-111111111-2-2-2-200000000000000002211112i−2i−2i2i-1-1−i−iiiii−i−i00000000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-111111111-2-2-2-20000000000000000221111−2i2i2i−2i-1-1ii−i−i−i−iii00000000
χ2522-2-222-22-2-222-2-2-2-2222-22222-2-2-2-2000022-2-2-2-2222222-2-2-2-22i−2i2i−2i00000000000000002i−2i2i−2i2i−2i00002i−2i0000000000000000
χ2622-2-222-22-2-222-2-2-2-2222-22222-2-2-2-2000022-2-2-2-2222222-2-2-2-2−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i0000−2i2i0000000000000000
χ2722-2-22-222-2-222-2-2-2-222-22-2-2-2-22222000022-2-2-2-222-2-2-2-222222i−2i2i−2i0000000000000000−2i2i2i−2i2i−2i0000−2i2i0000000000000000
χ2822-2-22-222-2-222-2-2-2-222-22-2-2-2-22222000022-2-2-2-222-2-2-2-22222−2i2i−2i2i00000000000000002i−2i−2i2i−2i2i00002i−2i0000000000000000
χ2922-2-2-12-2-11122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-111112i−2i2i−2i00000000000000002i−2i−ii−ii0000−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000
χ3022-2-2-12-2-11122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-111112i−2i2i−2i00000000000000002i−2i−ii−ii0000−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000
χ3122-2-2-12-2-11122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-11111−2i2i−2i2i0000000000000000−2i2ii−ii−i0000i−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000
χ3222-2-2-12-2-11122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-11111−2i2i−2i2i0000000000000000−2i2ii−ii−i0000i−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000
χ3322-2-2-1-22-11122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-12i−2i2i−2i0000000000000000−2i2i−ii−ii0000i−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ3422-2-2-1-22-11122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-12i−2i2i−2i0000000000000000−2i2i−ii−ii0000i−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ3522-2-2-1-22-11122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-1−2i2i−2i2i00000000000000002i−2ii−ii−i0000−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ3622-2-2-1-22-11122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-1−2i2i−2i2i00000000000000002i−2ii−ii−i0000−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ372-22-2200-22-22222-2-2-2-20000000000002i−2i2222-2-2-2-20000000022-2-2000000002i2i2i2i−2i−2i−2i−2i00-2-22200000000000000002i−2i0000
χ382-22-2200-22-22222-2-2-2-20000000000002i−2i2222-2-2-2-200000000-2-222000000002i2i2i2i−2i−2i−2i−2i0022-2-20000000000000000−2i2i0000
χ392-22-2200-22-22222-2-2-2-2000000000000−2i2i2222-2-2-2-20000000022-2-200000000−2i−2i−2i−2i2i2i2i2i00-2-2220000000000000000−2i2i0000
χ402-22-2200-22-22222-2-2-2-2000000000000−2i2i2222-2-2-2-200000000-2-22200000000−2i−2i−2i−2i2i2i2i2i0022-2-200000000000000002i−2i0000
χ412-2-22200-2-2222-2-222-2-200000000002-20022-2-222-2-2000000002i−2i−2i2i2222-2-2-2-20000000000−2i2i2i−2i000000000000002i−2i000000
χ422-2-22200-2-2222-2-222-2-200000000002-20022-2-222-2-200000000−2i2i2i−2i2222-2-2-2-200000000002i−2i−2i2i00000000000000−2i2i000000
χ432-2-22200-2-2222-2-222-2-20000000000-220022-2-222-2-2000000002i−2i−2i2i-2-2-2-222220000000000−2i2i2i−2i00000000000000−2i2i000000
χ442-2-22200-2-2222-2-222-2-20000000000-220022-2-222-2-200000000−2i2i2i−2i-2-2-2-2222200000000002i−2i−2i2i000000000000002i−2i000000
χ4544444444441-21-21-21-24411-2-211-2-244441-21-21-21-211-2-211-2-2000011-2-211-2-211-2-211-2-20000000000000000000000000000
χ4644444444441-21-21-21-24411-2-211-2-2-4-4-4-41-21-21-21-211-2-211-2-20000-1-122-1-122-1-122-1-1220000000000000000000000000000
χ474444444444-21-21-21-2144-2-211-2-2114444-21-21-21-21-2-211-2-2110000-2-211-2-211-2-211-2-2110000000000000000000000000000
χ484444444444-21-21-21-2144-2-211-2-211-4-4-4-4-21-21-21-21-2-211-2-211000022-1-122-1-122-1-122-1-10000000000000000000000000000
χ4944444-4-44441-21-21-21-2-4-4-1-122-1-12244-4-41-21-21-21-2-1-122-1-122000011-2-211-2-2-1-122-1-1220000000000000000000000000000
χ5044444-4-44441-21-21-21-2-4-4-1-122-1-122-4-4441-21-21-21-2-1-122-1-1220000-1-122-1-12211-2-211-2-20000000000000000000000000000
χ5144444-4-4444-21-21-21-21-4-422-1-122-1-144-4-4-21-21-21-2122-1-122-1-10000-2-211-2-21122-1-122-1-10000000000000000000000000000
χ5244444-4-4444-21-21-21-21-4-422-1-122-1-1-4-444-21-21-21-2122-1-122-1-1000022-1-122-1-1-2-211-2-2110000000000000000000000000000
χ5344-4-444-44-4-41-2-12-121-24-411-2-2-1-12200001-2-12-121-211-2-2-1-12200003-3003-3003-3003-3000000000000000000000000000000
χ5444-4-444-44-4-41-2-12-121-24-411-2-2-1-12200001-2-12-121-211-2-2-1-1220000-3300-3300-3300-33000000000000000000000000000000
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χ5844-4-44-444-4-41-2-12-121-2-44-1-12211-2-200001-2-12-121-2-1-12211-2-20000-3300-33003-3003-3000000000000000000000000000000
χ5944-4-44-444-4-4-212-12-1-21-4422-1-1-2-2110000-212-12-1-2122-1-1-2-2110000003-3003-300-3300-330000000000000000000000000000
χ6044-4-44-444-4-4-212-12-1-21-4422-1-1-2-2110000-212-12-1-2122-1-1-2-211000000-3300-33003-3003-30000000000000000000000000000
χ614-44-4400-44-41-21-2-12-12003i−3i003i−3i00004i−4i1-21-2-12-123i−3i003i−3i0000003-300-3300ii−2i−2i−i−i2i2i0000000000000000000000000000
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χ654-44-4400-44-4-21-212-12-100003i−3i003i−3i004i−4i-21-212-12-1003i−3i003i−3i0000003-300-33−2i−2iii2i2i−i−i0000000000000000000000000000
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χ684-44-4400-44-4-21-212-12-10000−3i3i00−3i3i00−4i4i-21-212-12-100−3i3i00−3i3i0000003-300-332i2i−i−i−2i−2iii0000000000000000000000000000
χ694-44-4-2002-224444-4-4-4-400000000000000-2-2-2-222220000000044-4-400000000000000000022-2-20000000000000000000000
χ704-44-4-2002-224444-4-4-4-400000000000000-2-2-2-2222200000000-4-444000000000000000000-2-2220000000000000000000000
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χ724-4-44400-4-441-2-121-2-12003i−3i00−3i3i00-44001-2-121-2-123i−3i00−3i3i000000-1-12211-2-2−3i3i003i−3i000000000000000000000000000000
χ734-4-44400-4-441-2-121-2-1200−3i3i003i−3i004-4001-2-121-2-12−3i3i003i−3i00000011-2-2-1-122−3i3i003i−3i000000000000000000000000000000
χ744-4-44400-4-441-2-121-2-1200−3i3i003i−3i00-44001-2-121-2-12−3i3i003i−3i000000-1-12211-2-23i−3i00−3i3i000000000000000000000000000000
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χ774-4-44400-4-44-212-1-212-10000−3i3i003i−3i4-400-212-1-212-100−3i3i003i−3i0000-2-21122-1-100−3i3i003i−3i0000000000000000000000000000
χ784-4-44400-4-44-212-1-212-10000−3i3i003i−3i-4400-212-1-212-100−3i3i003i−3i000022-1-1-2-211003i−3i00−3i3i0000000000000000000000000000
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χ804-4-44-20022-244-4-444-4-400000000000000-2-222-2-22200000000−4i4i4i−4i000000000000000000−2i2i2i−2i0000000000000000000000
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χ848888-4-8-8-4-4-4-42-42-42-424444-2-244-2-200002-12-12-12-1-2-211-2-211000000000000000000000000000000000000000000000000
χ8588-8-8-48-8-4442-4-24-242-4-4422-4-4-2-2440000-121-21-2-12-1-12211-2-2000000000000000000000000000000000000000000000000
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χ938-8-88-40044-42-4-242-4-24006i−6i00−6i6i000000-121-2-121-2−3i3i003i−3i00000000000000000000000000000000000000000000000000
χ948-8-88-40044-42-4-242-4-2400−6i6i006i−6i000000-121-2-121-23i−3i00−3i3i00000000000000000000000000000000000000000000000000
χ958-8-88-40044-4-424-2-424-200006i−6i00−6i6i00002-1-212-1-2100−3i3i003i−3i000000000000000000000000000000000000000000000000
χ968-8-88-40044-4-424-2-424-20000−6i6i006i−6i00002-1-212-1-21003i−3i00−3i3i000000000000000000000000000000000000000000000000

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