Finite Group Databasebeta

← Group #13154806

Character table — Group #13154806

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444466668888888888888888999912121212121212121212121212121212181818181818363636363636363636363636363654545454108108108108
order12223446663366666612121212121212121212888833666666121212121212121222222424242424242424242424242424242444666644441212121212121212121288884444
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
χ91-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1ii−i−i11-1-1-1-1111111-1-1-1-11-11-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-111-11-11-111-1-111-1-1ii−i−ii−ii−i
χ101-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1ii−i−i11-1-1-1-1111111-1-1-1-11-11-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1-11-11-111-1-1-111-1-111ii−i−i−ii−ii
χ111-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1ii−i−i11-1-1-1-1111111-1-1-1-1-11-11iiiiiiii−i−i−i−i−i−i−i−i-11-111-1i−i−ii-11ii−i−i−i−iii−i−iii-111-1
χ121-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1ii−i−i11-1-1-1-1111111-1-1-1-1-11-11iiiiiiii−i−i−i−i−i−i−i−i-11-111-1−iii−i-11−i−iiiii−i−i−i−iii1-1-11
χ131-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1−i−iii11-1-1-1-1111111-1-1-1-11-11-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-111-11-11-111-1-111-1-1−i−iii−ii−ii
χ141-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1−i−iii11-1-1-1-1111111-1-1-1-11-11-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1-11-11-111-1-1-111-1-111−i−iiii−ii−i
χ151-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1−i−iii11-1-1-1-1111111-1-1-1-1-11-11−i−i−i−i−i−i−i−iiiiiiiii-11-111-1i−i−ii-11ii−i−i−i−iiiii−i−i1-1-11
χ161-1-1111-1-1-1111-1-1-1-1111-11111-1-1-1-1−i−iii11-1-1-1-1111111-1-1-1-1-11-11−i−i−i−i−i−i−i−iiiiiiiii-11-111-1−iii−i-11−i−iiiii−i−iii−i−i-111-1
χ1722222-2-222222222222-2-2-2-2-2-2-2-2-2-2000022222222-2-2-2-2-2-2-2-222220000000000000000-2-222220000-2-20000000000000000
χ1822222-2-222222222222-2-2-2-2-2-2-2-2-2-2000022222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2-2-20000220000000000000000
χ192222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000
χ202222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-1-2-2-2-2-1-11111111100000000
χ212222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-211112i2i−2i−2i11−i−i−i−iiiii00000000
χ222222-122-1-1-122222222-1-1222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-21111−2i−2i2i2i11iiii−i−i−i−i00000000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-1000011−i3i3−i3i3−i3i3−i3i300000000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-1000011i3−i3i3−i3i3−i3i3−i300000000
χ252222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-111111111-2-2-2-200000000000000002211110000-1-13−33−3−33−3300000000
χ262222-1-2-2-1-1-12222222211-2-2-2-2-2-2-2-20000-1-1-1-1-1-1-1-111111111-2-2-2-200000000000000002211110000-1-1−33−333−33−300000000
χ2722-2-22002-2-22222-2-2-2-200000000002−22−22222-2-2-2-20000000022-2-22222−2−2−2−22222−2−2−2−20022-2-2000000000000002−22−20000
χ2822-2-22002-2-22222-2-2-2-200000000002−22−22222-2-2-2-200000000-2-2222222−2−2−2−22222−2−2−2−200-2-22200000000000000−22−220000
χ2922-2-22002-2-22222-2-2-2-20000000000−22−222222-2-2-2-20000000022-2-2−2−2−2−22222−2−2−2−222220022-2-200000000000000−22−220000
χ3022-2-22002-2-22222-2-2-2-20000000000−22−222222-2-2-2-200000000-2-222−2−2−2−22222−2−2−2−2222200-2-222000000000000002−22−20000
χ312-22-2200-22-222-2-222-2-20000000000−i2i2i2−i222-2-222-2-2000000002-2-22−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2002-22-200000000000000−i2i2i2−i20000
χ322-22-2200-22-222-2-222-2-20000000000−i2i2i2−i222-2-222-2-200000000-222-2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200-22-2200000000000000i2−i2−i2i20000
χ332-22-2200-22-222-2-222-2-20000000000i2−i2−i2i222-2-222-2-2000000002-2-22i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2002-22-200000000000000i2−i2−i2i20000
χ342-22-2200-22-222-2-222-2-20000000000i2−i2−i2i222-2-222-2-200000000-222-2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200-22-2200000000000000−i2i2i2−i20000
χ352-2-222-22-2-2222-2-2-2-222-22-2-2-2-22222000022-2-2-2-222-2-2-2-222222-22-20000000000000000-222-2-220000-220000000000000000
χ362-2-222-22-2-2222-2-2-2-222-22-2-2-2-22222000022-2-2-2-222-2-2-2-22222-22-2200000000000000002-2-222-200002-20000000000000000
χ372-2-22-12-211-122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-111112-22-200000000000000002-2-111-12-22-2-11-1-111-1-11100000000
χ382-2-22-12-211-122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-111112-22-200000000000000002-2-111-1-22-22-1111-1-111-1-100000000
χ392-2-22-12-211-122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-11111-22-220000000000000000-221-1-112i−2i−2i2i1-1−i−iiiii−i−i00000000
χ402-2-22-12-211-122-2-2-2-222-112222-2-2-2-20000-1-11111-1-1-1-1-1-11111-22-220000000000000000-221-1-11−2i2i2i−2i1-1ii−i−i−i−iii00000000
χ412-2-22-1-2211-122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-12-22-20000000000000000-22-111-100001-1−i3i3i3−i3−i3i3i3−i300000000
χ422-2-22-1-2211-122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-12-22-20000000000000000-22-111-100001-1i3−i3−i3i3i3−i3−i3i300000000
χ432-2-22-1-2211-122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-1-22-2200000000000000002-21-1-110000-113−3−33−333−300000000
χ442-2-22-1-2211-122-2-2-2-2221-1-2-2-2-222220000-1-11111-1-11111-1-1-1-1-22-2200000000000000002-21-1-110000-11−333−33−3−3300000000
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
χ4944444-4-44441-21-21-21-2-4-4-1-122-1-12200001-21-21-21-2-1-122-1-12200003i−3i003i−3i003i−3i003i−3i000000000000000000000000000000
χ5044444-4-44441-21-21-21-2-4-4-1-122-1-12200001-21-21-21-2-1-122-1-1220000−3i3i00−3i3i00−3i3i00−3i3i000000000000000000000000000000
χ5144444-4-4444-21-21-21-21-4-422-1-122-1-10000-21-21-21-2122-1-122-1-10000003i−3i003i−3i003i−3i003i−3i0000000000000000000000000000
χ5244444-4-4444-21-21-21-21-4-422-1-122-1-10000-21-21-21-2122-1-122-1-1000000−3i3i00−3i3i00−3i3i00−3i3i0000000000000000000000000000
χ5344-4-44004-4-41-21-2-12-12003i−3i003i−3i0022−2222−221-21-2-12-123i−3i003i−3i000000−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2322−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23220000000000000000000000000000
χ5444-4-44004-4-41-21-2-12-12003i−3i003i−3i00−2222−22221-21-2-12-123i−3i003i−3i0000002ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2322−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2322−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2−20000000000000000000000000000
χ5544-4-44004-4-41-21-2-12-1200−3i3i00−3i3i0022−2222−221-21-2-12-12−3i3i00−3i3i000000ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2322ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23220000000000000000000000000000
χ5644-4-44004-4-41-21-2-12-1200−3i3i00−3i3i00−2222−22221-21-2-12-12−3i3i00−3i3i000000−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2322ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2322ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2−20000000000000000000000000000
χ5744-4-44004-4-4-21-212-12-100003i−3i003i−3i22−2222−22-21-212-12-1003i−3i003i−3i0000−2−2−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23222ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2−2−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23222ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ230000000000000000000000000000
χ5844-4-44004-4-4-21-212-12-100003i−3i003i−3i−2222−2222-21-212-12-1003i−3i003i−3i0000222ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2−2−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23222ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2−2−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ230000000000000000000000000000
χ5944-4-44004-4-4-21-212-12-10000−3i3i00−3i3i22−2222−22-21-212-12-100−3i3i00−3i3i0000−2−2ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ2322−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−2−2ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ2322−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ230000000000000000000000000000
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χ644-44-4400-44-41-2-121-2-12003i−3i00−3i3i002i2−2i2−2i22i21-2-121-2-123i−3i00−3i3i000000−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−i2−i20000000000000000000000000000
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χ704-44-4400-44-4-212-1-212-10000−3i3i003i−3i2i2−2i2−2i22i2-212-1-212-100−3i3i003i−3i0000−i2−i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23i2i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23i2i2−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−i2−i22ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ230000000000000000000000000000
χ714-44-4-2002-2244-4-444-4-400000000000000-2-222-2-222000000004-4-44000000000000000000-22-220000000000000000000000
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χ754-4-4444-4-4-44-212-12-1-214-4-2-21122-1-14i4i−4i−4i-212-12-1-21-2-21122-1-10000−2i−2iii−2i−2iii2i2i−i−i2i2i−i−i0000000000000000000000000000
χ764-4-4444-4-4-44-212-12-1-214-4-2-21122-1-1−4i−4i4i4i-212-12-1-21-2-21122-1-100002i2i−i−i2i2i−i−i−2i−2iii−2i−2iii0000000000000000000000000000
χ774-4-444-44-4-441-2-12-121-2-44-1-12211-2-200001-2-12-121-2-1-12211-2-200003-3003-300-3300-33000000000000000000000000000000
χ784-4-444-44-4-441-2-12-121-2-44-1-12211-2-200001-2-12-121-2-1-12211-2-20000-3300-33003-3003-3000000000000000000000000000000
χ794-4-444-44-4-44-212-12-1-21-4422-1-1-2-2110000-212-12-1-2122-1-1-2-2110000003-3003-300-3300-330000000000000000000000000000
χ804-4-444-44-4-44-212-12-1-21-4422-1-1-2-2110000-212-12-1-2122-1-1-2-211000000-3300-33003-3003-30000000000000000000000000000
χ818888-488-4-4-42-42-42-42-4-4-422-4-422-4-40000-12-12-12-12-1-122-1-122000000000000000000000000000000000000000000000000
χ828888-488-4-4-4-42-42-42-42-4-4-4-422-4-42200002-12-12-12-122-1-122-1-1000000000000000000000000000000000000000000000000
χ838888-4-8-8-4-4-42-42-42-42-444-2-244-2-2440000-12-12-12-1211-2-211-2-2000000000000000000000000000000000000000000000000
χ848888-4-8-8-4-4-4-42-42-42-424444-2-244-2-200002-12-12-12-1-2-211-2-211000000000000000000000000000000000000000000000000
χ8588-8-8-400-4442-42-4-24-24006i−6i006i−6i000000-12-121-21-2−3i3i00−3i3i00000000000000000000000000000000000000000000000000
χ8688-8-8-400-4442-42-4-24-2400−6i6i00−6i6i000000-12-121-21-23i−3i003i−3i00000000000000000000000000000000000000000000000000
χ8788-8-8-400-444-42-424-24-200006i−6i006i−6i00002-12-1-21-2100−3i3i00−3i3i000000000000000000000000000000000000000000000000
χ8888-8-8-400-444-42-424-24-20000−6i6i00−6i6i00002-12-1-21-21003i−3i003i−3i000000000000000000000000000000000000000000000000
χ898-88-8-4004-442-4-242-4-24006i−6i00−6i6i000000-121-2-121-2−3i3i003i−3i00000000000000000000000000000000000000000000000000
χ908-88-8-4004-442-4-242-4-2400−6i6i006i−6i000000-121-2-121-23i−3i00−3i3i00000000000000000000000000000000000000000000000000
χ918-88-8-4004-44-424-2-424-200006i−6i00−6i6i00002-1-212-1-2100−3i3i003i−3i000000000000000000000000000000000000000000000000
χ928-88-8-4004-44-424-2-424-20000−6i6i006i−6i00002-1-212-1-21003i−3i00−3i3i000000000000000000000000000000000000000000000000
χ938-8-88-48-844-42-4-24-242-4-4422-4-4-2-2440000-121-21-2-12-1-12211-2-2000000000000000000000000000000000000000000000000
χ948-8-88-48-844-4-424-24-2-42-44-4-42244-2-200002-1-21-212-122-1-1-2-211000000000000000000000000000000000000000000000000
χ958-8-88-4-8844-42-4-24-242-44-4-2-24422-4-40000-121-21-2-1211-2-2-1-122000000000000000000000000000000000000000000000000
χ968-8-88-4-8844-4-424-24-2-424-444-2-2-4-42200002-1-21-212-1-2-21122-1-1000000000000000000000000000000000000000000000000

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