Finite Group Databasebeta

← Group #13166631

Character table — Group #13166631

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222444444448888888888888888888899991212181818181818181818181818181818181818181818181818181818181818181818182424242424242424108108108108108108
order12222236666666336666663366666666666666666644444444888888881212121212121212242424242424242424242424242424241212121212121212248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111111111-1-1-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1i−ii−i
χ6111111111111111111111111111111111111111111-1-1-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1−ii−ii
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111−ii−ii
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111i−ii−i
χ91111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-1
χ101111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111
χ111111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-111
χ121111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-1
χ131111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111ii−i−i−i−iii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11-1i−i−ii
χ141111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111−i−iiiii−i−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11-1−iii−i
χ151111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−iii−i
χ161111-1-1111-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11i−i−ii
χ17222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12222002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ18222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122220022-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000
χ19222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-22i2i2i2i−2i−2i−2i−2i11111111−i−i−i−i−i−i−i−iiiiiiiii00000000000000
χ20222222-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2−2i−2i−2i−2i2i2i2i2i11111111iiiiiiii−i−i−i−i−i−i−i−i00000000000000
χ212222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111222200-2-222-2-222-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000
χ222222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111222200-2-2-2-222-2-222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000
χ232222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-200222i2i−2i−2i−2i−2i2i2i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ242222-2-2-1-1-11111-122222222-1-1-2-2-2-2-1-1-1-1-1-111111111-2-2-2-20022−2i−2i2i2i2i2i−2i−2i11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ2522-2-20022-20000-222-2-222-2-222000022-2-2-2-2000000002i−2i2i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132i−2i00002i−2i00002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000
χ2622-2-20022-20000-222-2-222-2-222000022-2-2-2-2000000002i−2i2i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132i−2i00002i−2i0000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000
χ2722-2-20022-20000-222-2-222-2-222000022-2-2-2-200000000−2i2i−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2i2i0000−2i2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000
χ2822-2-20022-20000-222-2-222-2-222000022-2-2-2-200000000−2i2i−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2i2i0000−2i2i00002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000
χ2922-2-200-1-11−i3−i3i3i3122-2-222-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i32i−2i2i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−ii33−3−3−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000000000
χ3022-2-200-1-11−i3−i3i3i3122-2-222-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i32i−2i2i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−ii33−3−3−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000000000
χ3122-2-200-1-11−i3−i3i3i3122-2-222-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23i−i−3−333i−i−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000000000
χ3222-2-200-1-11−i3−i3i3i3122-2-222-2-2-1-10000-1-11111−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23i−i−3−333i−iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000000000
χ3322-2-200-1-11i3i3−i3−i3122-2-222-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i32i−2i2i−2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−ii−3−333−iiζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000000000
χ3422-2-200-1-11i3i3−i3−i3122-2-222-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i32i−2i2i−2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−ii−3−333−ii−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000000000
χ3522-2-200-1-11i3i3−i3−i3122-2-222-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23i−i33−3−3i−iζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000000000
χ3622-2-200-1-11i3i3−i3−i3122-2-222-2-2-1-10000-1-11111i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23i−i33−3−3i−i−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000000000
χ372-22-2002-2-20000222-2-2-2-222220000-2-222-2-20000000022-2-200002i−2i002i−2i00220000-2-22i−2i2i−2i00002i−2i2i−2i000000000000000000
χ382-22-2002-2-20000222-2-2-2-222220000-2-222-2-20000000022-2-20000−2i2i00−2i2i00220000-2-2−2i2i−2i2i0000−2i2i−2i2i000000000000000000
χ392-22-2002-2-20000222-2-2-2-222220000-2-222-2-200000000-2-22200002-200-2200-2-20000222-22-20000-22-22000000000000000000
χ402-22-2002-2-20000222-2-2-2-222220000-2-222-2-200000000-2-2220000-22002-200-2-2000022-22-2200002-22-2000000000000000000
χ412-22-200-111−i3i3−i3i3-122-2-2-2-222-1-1000011-1-111−i3−i3i3i3−i3−i3i3i322-2-200002i−2i002i−2i00-1-1−i3i3−i3i311−ii−ii3−33−3−ii−ii3−33−300000000000000
χ422-22-200-111−i3i3−i3i3-122-2-2-2-222-1-1000011-1-111−i3−i3i3i3−i3−i3i3i322-2-20000−2i2i00−2i2i00-1-1−i3i3−i3i311i−ii−i−33−33i−ii−i−33−3300000000000000
χ432-22-200-111−i3i3−i3i3-122-2-2-2-222-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-2-22200002-200-220011i3−i3i3−i3-1-1-11-11−i3i3−i3i31-11-1i3−i3i3−i300000000000000
χ442-22-200-111−i3i3−i3i3-122-2-2-2-222-1-1000011-1-111−i3−i3i3i3−i3−i3i3i3-2-2220000-22002-20011i3−i3i3−i3-1-11-11-1i3−i3i3−i3-11-11−i3i3−i3i300000000000000
χ452-22-200-111i3−i3i3−i3-122-2-2-2-222-1-1000011-1-111i3i3−i3−i3i3i3−i3−i322-2-200002i−2i002i−2i00-1-1i3−i3i3−i311−ii−ii−33−33−ii−ii−33−3300000000000000
χ462-22-200-111i3−i3i3−i3-122-2-2-2-222-1-1000011-1-111i3i3−i3−i3i3i3−i3−i322-2-20000−2i2i00−2i2i00-1-1i3−i3i3−i311i−ii−i3−33−3i−ii−i3−33−300000000000000
χ472-22-200-111i3−i3i3−i3-122-2-2-2-222-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-2-22200002-200-220011−i3i3−i3i3-1-1-11-11i3−i3i3−i31-11-1−i3i3−i3i300000000000000
χ482-22-200-111i3−i3i3−i3-122-2-2-2-222-1-1000011-1-111i3i3−i3−i3i3i3−i3−i3-2-2220000-22002-20011−i3i3−i3i3-1-11-11-1−i3i3−i3i3-11-11i3−i3i3−i300000000000000
χ492-2-222-22-222-2-22-22222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2222i−2i−2i2i002i−2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ502-2-222-22-222-2-22-22222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222−2i2i2i−2i00−2i2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ512-2-222-2-11-1-111-112222-2-2-2-2-1-122-2-21111-1-1-1-11111-1-12i−2i−2i2i002i−2i00000000−ii−iii−ii−iζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000
χ522-2-222-2-11-1-111-112222-2-2-2-2-1-122-2-21111-1-1-1-11111-1-12i−2i−2i2i002i−2i00000000−ii−iii−ii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000
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χ582-2-22-22-11-11-1-1112222-2-2-2-2-1-1-2-2221111-1-111-1-1-1-1112i−2i−2i2i00−2i2i00000000−iii−i−iii−i−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000
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χ704-4-444-44-444-4-44-41-21-2-12-121-21-2-12-12-121-21-2-12-121-20000000000000000000000000000000000000000−3i3i00−3i3i00000000
χ714-4-444-44-444-4-44-4-21-212-12-1-21-212-12-12-1-21-212-12-1-210000000000000000000000000000000000000000003i−3i003i−3i000000
χ724-4-444-44-444-4-44-4-21-212-12-1-21-212-12-12-1-21-212-12-1-21000000000000000000000000000000000000000000−3i3i00−3i3i000000
χ734-4-44-444-44-444-4-41-21-2-12-121-2-121-2-12-121-2-121-21-2-1200000000000000000000000000000000000000003i−3i00−3i3i00000000
χ744-4-44-444-44-444-4-41-21-2-12-121-2-121-2-12-121-2-121-21-2-120000000000000000000000000000000000000000−3i3i003i−3i00000000
χ754-4-44-444-44-444-4-4-21-212-12-1-212-1-212-12-1-212-1-21-212-10000000000000000000000000000000000000000003i−3i00−3i3i000000
χ764-4-44-444-44-444-4-4-21-212-12-1-212-1-212-12-1-212-1-21-212-1000000000000000000000000000000000000000000−3i3i003i−3i000000
χ77888888-4-4-4-4-4-4-4-42-42-42-42-4-122-42-4-12-12-12-12-12-12-12000000000000000000000000000000000000000000000000000000
χ78888888-4-4-4-4-4-4-4-4-42-42-42-422-1-42-422-12-12-12-12-12-12-1000000000000000000000000000000000000000000000000000000
χ798888-8-8-4-4-44444-42-42-42-42-4-12-24-24-12-12-121-21-21-21-2000000000000000000000000000000000000000000000000000000
χ808888-8-8-4-4-44444-4-42-42-42-422-14-24-22-12-12-1-21-21-21-21000000000000000000000000000000000000000000000000000000
χ8188-8-80088-80000-82-4-242-4-242-400002-4-24-2400000000000000000000000000000000000000000000000000000000000000
χ8288-8-80088-80000-8-424-2-424-2-420000-424-24-200000000000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-44−4i3−4i34i34i342-4-242-4-24-120000-121-21-2−i32i3−i32i3i3−2i3i3−2i3000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-44−4i3−4i34i34i34-424-2-424-22-100002-1-21-212i3−i32i3−i3−2i3i3−2i3i3000000000000000000000000000000000000000000000000000000
χ8588-8-800-4-444i34i3−4i3−4i342-4-242-4-24-120000-121-21-2i3−2i3i3−2i3−i32i3−i32i3000000000000000000000000000000000000000000000000000000
χ8688-8-800-4-444i34i3−4i3−4i34-424-2-424-22-100002-1-21-21−2i3i3−2i3i32i3−i32i3−i3000000000000000000000000000000000000000000000000000000
χ878-88-8008-8-8000082-4-24-242-42-40000-242-4-2400000000000000000000000000000000000000000000000000000000000000
χ888-88-8008-8-800008-424-24-2-42-4200004-2-424-200000000000000000000000000000000000000000000000000000000000000
χ898-88-800-444−4i34i3−4i34i3-42-4-24-242-4-1200001-2-121-2−i32i3i3−2i3−i32i3i3−2i3000000000000000000000000000000000000000000000000000000
χ908-88-800-444−4i34i3−4i34i3-4-424-24-2-422-10000-212-1-212i3−i3−2i3i32i3−i3−2i3i3000000000000000000000000000000000000000000000000000000
χ918-88-800-4444i3−4i34i3−4i3-42-4-24-242-4-1200001-2-121-2i3−2i3−i32i3i3−2i3−i32i3000000000000000000000000000000000000000000000000000000
χ928-88-800-4444i3−4i34i3−4i3-4-424-24-2-422-10000-212-1-21−2i3i32i3−i3−2i3i32i3−i3000000000000000000000000000000000000000000000000000000
χ938-8-888-8-44-4-444-442-42-4-24-24-122-4-241-21-2-12-121-21-2-12000000000000000000000000000000000000000000000000000000
χ948-8-888-8-44-4-444-44-42-424-24-22-1-424-2-21-212-12-1-21-212-1000000000000000000000000000000000000000000000000000000
χ958-8-88-88-44-44-4-4442-42-4-24-24-12-242-41-21-2-121-2-12-121-2000000000000000000000000000000000000000000000000000000
χ968-8-88-88-44-44-4-444-42-424-24-22-14-2-42-21-212-1-212-12-1-21000000000000000000000000000000000000000000000000000000

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