Finite Group Databasebeta

← Group #13166331

Character table — Group #13166331

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
χ2522-2-22002-2-222-2-2-2-22200000000002-20022-2-2-2-222000000002i−2i2i−2i2222-2-2-2-200000000002i−2i2i−2i000000000000002i−2i000000
χ2622-2-22002-2-222-2-2-2-22200000000002-20022-2-2-2-22200000000−2i2i−2i2i2222-2-2-2-20000000000−2i2i−2i2i00000000000000−2i2i000000
χ2722-2-22002-2-222-2-2-2-2220000000000-220022-2-2-2-222000000002i−2i2i−2i-2-2-2-2222200000000002i−2i2i−2i00000000000000−2i2i000000
χ2822-2-22002-2-222-2-2-2-2220000000000-220022-2-2-2-22200000000−2i2i−2i2i-2-2-2-222220000000000−2i2i−2i2i000000000000002i−2i000000
χ292-22-2200-22-22222-2-2-2-20000000000002i−2i2222-2-2-2-20000000022-2-2000000002i2i2i2i−2i−2i−2i−2i00-2-22200000000000000002i−2i0000
χ302-22-2200-22-22222-2-2-2-20000000000002i−2i2222-2-2-2-200000000-2-222000000002i2i2i2i−2i−2i−2i−2i0022-2-20000000000000000−2i2i0000
χ312-22-2200-22-22222-2-2-2-2000000000000−2i2i2222-2-2-2-20000000022-2-200000000−2i−2i−2i−2i2i2i2i2i00-2-2220000000000000000−2i2i0000
χ322-22-2200-22-22222-2-2-2-2000000000000−2i2i2222-2-2-2-200000000-2-22200000000−2i−2i−2i−2i2i2i2i2i0022-2-200000000000000002i−2i0000
χ332-2-2222i−2i-2-2222-2-222-2-22i−2i2i2i2i2i−2i−2i−2i−2i000022-2-222-2-22i2i2i2i−2i−2i−2i−2i2i−2i−2i2i00000000000000002-2−2i2i2i−2i00002-20000000000000000
χ342-2-2222i−2i-2-2222-2-222-2-22i−2i2i2i2i2i−2i−2i−2i−2i000022-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i2i2i−2i0000000000000000-222i−2i−2i2i0000-220000000000000000
χ352-2-222−2i2i-2-2222-2-222-2-2−2i2i−2i−2i−2i−2i2i2i2i2i000022-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i−2i−2i2i0000000000000000-22−2i2i2i−2i0000-220000000000000000
χ362-2-222−2i2i-2-2222-2-222-2-2−2i2i−2i−2i−2i−2i2i2i2i2i000022-2-222-2-2−2i−2i−2i−2i2i2i2i2i−2i2i2i−2i00000000000000002-22i−2i−2i2i00002-20000000000000000
χ372-2-22-12i−2i11-122-2-222-2-2−ii2i2i2i2i−2i−2i−2i−2i0000-1-111-1-111−i−i−i−iiiii2i−2i−2i2i00000000000000002-2i−i−ii0000-11−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ382-2-22-12i−2i11-122-2-222-2-2−ii2i2i2i2i−2i−2i−2i−2i0000-1-111-1-111−i−i−i−iiiii2i−2i−2i2i00000000000000002-2i−i−ii0000-11ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ392-2-22-12i−2i11-122-2-222-2-2−ii2i2i2i2i−2i−2i−2i−2i0000-1-111-1-111−i−i−i−iiiii−2i2i2i−2i0000000000000000-22−iii−i00001-1ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000
χ402-2-22-12i−2i11-122-2-222-2-2−ii2i2i2i2i−2i−2i−2i−2i0000-1-111-1-111−i−i−i−iiiii−2i2i2i−2i0000000000000000-22−iii−i00001-1−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000
χ412-2-22-1−2i2i11-122-2-222-2-2i−i−2i−2i−2i−2i2i2i2i2i0000-1-111-1-111iiii−i−i−i−i2i−2i−2i2i0000000000000000-22i−i−ii00001-1−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000
χ422-2-22-1−2i2i11-122-2-222-2-2i−i−2i−2i−2i−2i2i2i2i2i0000-1-111-1-111iiii−i−i−i−i2i−2i−2i2i0000000000000000-22i−i−ii00001-1ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000
χ432-2-22-1−2i2i11-122-2-222-2-2i−i−2i−2i−2i−2i2i2i2i2i0000-1-111-1-111iiii−i−i−i−i−2i2i2i−2i00000000000000002-2−iii−i0000-11ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ442-2-22-1−2i2i11-122-2-222-2-2i−i−2i−2i−2i−2i2i2i2i2i0000-1-111-1-111iiii−i−i−i−i−2i2i2i−2i00000000000000002-2−iii−i0000-11−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
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
χ5344-4-44004-4-41-2-12-121-2003-3003-3004-4001-2-12-121-23-3003-300000011-2-2-1-1223-3003-3000000000000000000000000000000
χ5444-4-44004-4-41-2-12-121-2003-3003-300-44001-2-12-121-23-3003-3000000-1-12211-2-2-3300-33000000000000000000000000000000
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χ674-44-4400-44-4-21-212-12-100003i−3i00−3i3i004i−4i-21-212-12-1003i−3i00−3i3i0000003-3003-3−2i−2iii2i2i−i−i0000000000000000000000000000
χ684-44-4400-44-4-21-212-12-100003i−3i00−3i3i00−4i4i-21-212-12-1003i−3i00−3i3i000000-3300-332i2i−i−i−2i−2iii0000000000000000000000000000
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χ704-44-4400-44-4-21-212-12-10000−3i3i003i−3i00−4i4i-21-212-12-100−3i3i003i−3i0000003-3003-32i2i−i−i−2i−2iii0000000000000000000000000000
χ714-44-4-2002-224444-4-4-4-400000000000000-2-2-2-222220000000044-4-400000000000000000022-2-20000000000000000000000
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χ794-4-444−4i4i-4-44-212-1-212-1−4i4i2i2i−i−i−2i−2iii0000-212-1-212-12i2i−i−i−2i−2iii0000003-300-3300−3i3i003i−3i0000000000000000000000000000
χ804-4-444−4i4i-4-44-212-1-212-1−4i4i2i2i−i−i−2i−2iii0000-212-1-212-12i2i−i−i−2i−2iii000000-33003-3003i−3i00−3i3i0000000000000000000000000000
χ818888-488-4-4-42-42-42-42-4-4-422-4-422-4-40000-12-12-12-12-1-122-1-122000000000000000000000000000000000000000000000000
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χ948-8-88-48i−8i44-4-424-2-424-2−4i4i−4i−4i2i2i4i4i−2i−2i00002-1-212-1-212i2i−i−i−2i−2iii000000000000000000000000000000000000000000000000
χ958-8-88-4−8i8i44-42-4-242-4-244i−4i−2i−2i4i4i2i2i−4i−4i0000-121-2-121-2ii−2i−2i−i−i2i2i000000000000000000000000000000000000000000000000
χ968-8-88-4−8i8i44-4-424-2-424-24i−4i4i4i−2i−2i−4i−4i2i2i00002-1-212-1-21−2i−2iii2i2i−i−i000000000000000000000000000000000000000000000000

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