Finite Group Databasebeta

← Group #13166582

Character table — Group #13166582

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444466668888888888888888999912121212121212121212121212121212181818181818363636363636363636363636363654545454108108108108
order122222366633666666666666666644443366666666666666444412121212121212121212121212121212441212121288881212242424242424242444448888
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
χ91111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-111-1-111-1-11-11-1
χ101111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1-11111-1-1-11-11
χ111111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1i−i−ii11ii−i−i−i−iii-1-111i−i−ii
χ121111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1−iii−i11−i−iiiii−i−i-1-111−iii−i
χ131111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111111-11-1-1-111-1-111-1-1-1-111-11-11
χ141111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-11-11-1-1-1-111-1-111-1-1111-11-1
χ151111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1i−i−ii11ii−i−i−i−iii11-1-1−iii−i
χ161111-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−iii−i11−i−iiiii−i−i11-1-1i−i−ii
χ17222222-1-1-1-122-1-1222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000
χ18222222-1-1-1-122-1-1222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-1-2-2-2-2-1-11111111100000000
χ19222222-1-1-1-122-1-1222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-211112i2i−2i−2i11−i−i−i−iiiii00000000
χ20222222-1-1-1-122-1-1222222222222220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000000000000000-2-21111−2i−2i2i2i11iiii−i−i−i−i00000000
χ212222-2-2-1-1-1-122112222-2-2-2-2-2-2-2-2220000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-12-22-211-1-111-1-11100000000
χ222222-2-2-1-1-1-122112222-2-2-2-2-2-2-2-2220000-1-1-1-1-1-1-1-11111111122220000000000000000-2-2-1-1-1-1-22-221111-1-111-1-100000000
χ232222-2-2-1-1-1-122112222-2-2-2-2-2-2-2-2220000-1-1-1-1-1-1-1-111111111-2-2-2-200000000000000002211112i−2i−2i2i-1-1−i−iiiii−i−i00000000
χ242222-2-2-1-1-1-122112222-2-2-2-2-2-2-2-2220000-1-1-1-1-1-1-1-111111111-2-2-2-20000000000000000221111−2i2i2i−2i-1-1ii−i−i−i−iii00000000
χ2522-2-22-222-2-2222-2-2-2-2-22222-2-2-2-22200002222-2-2-2-22222-2-2-2-22i2i−2i−2i00000000000000002i−2i2i2i−2i−2i00002i−2i0000000000000000
χ2622-2-22-222-2-2222-2-2-2-2-22222-2-2-2-22200002222-2-2-2-22222-2-2-2-2−2i−2i2i2i0000000000000000−2i2i−2i−2i2i2i0000−2i2i0000000000000000
χ2722-2-22-2-1-11122-11-2-2-2-22222-2-2-2-2220000-1-1-1-11111-1-1-1-111112i2i−2i−2i00000000000000002i−2i−i−iii0000−ii−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000
χ2822-2-22-2-1-11122-11-2-2-2-22222-2-2-2-2220000-1-1-1-11111-1-1-1-111112i2i−2i−2i00000000000000002i−2i−i−iii0000−iiζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000
χ2922-2-22-2-1-11122-11-2-2-2-22222-2-2-2-2220000-1-1-1-11111-1-1-1-11111−2i−2i2i2i0000000000000000−2i2iii−i−i0000i−iζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000
χ3022-2-22-2-1-11122-11-2-2-2-22222-2-2-2-2220000-1-1-1-11111-1-1-1-11111−2i−2i2i2i0000000000000000−2i2iii−i−i0000i−i−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000
χ3122-2-2-2222-2-222-22-2-2-2-2-2-2-2-222222200002222-2-2-2-2-2-2-2-222222i2i−2i−2i0000000000000000−2i2i2i2i−2i−2i0000−2i2i0000000000000000
χ3222-2-2-2222-2-222-22-2-2-2-2-2-2-2-222222200002222-2-2-2-2-2-2-2-22222−2i−2i2i2i00000000000000002i−2i−2i−2i2i2i00002i−2i0000000000000000
χ3322-2-2-22-1-111221-1-2-2-2-2-2-2-2-22222220000-1-1-1-111111111-1-1-1-12i2i−2i−2i0000000000000000−2i2i−i−iii0000i−i−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ3422-2-2-22-1-111221-1-2-2-2-2-2-2-2-22222220000-1-1-1-111111111-1-1-1-12i2i−2i−2i0000000000000000−2i2i−i−iii0000i−iζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ3522-2-2-22-1-111221-1-2-2-2-2-2-2-2-22222220000-1-1-1-111111111-1-1-1-1−2i−2i2i2i00000000000000002i−2iii−i−i0000−iiζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ3622-2-2-22-1-111221-1-2-2-2-2-2-2-2-22222220000-1-1-1-111111111-1-1-1-1−2i−2i2i2i00000000000000002i−2iii−i−i0000−ii−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ372-22-2002-2-22220022-2-200000000-2-2002i−2i22-2-222-2-2000000002-22-2000000002i2i2i2i−2i−2i−2i−2i002-22-200000000000000002i−2i0000
χ382-22-2002-2-22220022-2-200000000-2-2002i−2i22-2-222-2-200000000-22-22000000002i2i2i2i−2i−2i−2i−2i00-22-220000000000000000−2i2i0000
χ392-22-2002-2-22220022-2-200000000-2-200−2i2i22-2-222-2-2000000002-22-200000000−2i−2i−2i−2i2i2i2i2i002-22-20000000000000000−2i2i0000
χ402-22-2002-2-22220022-2-200000000-2-200−2i2i22-2-222-2-200000000-22-2200000000−2i−2i−2i−2i2i2i2i2i00-22-2200000000000000002i−2i0000
χ412-2-22002-22-22200-2-22200000000-2-22i−2i0022-2-2-2-222000000002i−2i−2i2i2i2i2i2i−2i−2i−2i−2i00000000002i−2i−2i2i000000000000002-2000000
χ422-2-22002-22-22200-2-22200000000-2-22i−2i0022-2-2-2-22200000000−2i2i2i−2i2i2i2i2i−2i−2i−2i−2i0000000000−2i2i2i−2i00000000000000-22000000
χ432-2-22002-22-22200-2-22200000000-2-2−2i2i0022-2-2-2-222000000002i−2i−2i2i−2i−2i−2i−2i2i2i2i2i00000000002i−2i−2i2i00000000000000-22000000
χ442-2-22002-22-22200-2-22200000000-2-2−2i2i0022-2-2-2-22200000000−2i2i2i−2i−2i−2i−2i−2i2i2i2i2i0000000000−2i2i2i−2i000000000000002-2000000
χ4544444444441-2441-21-211-2-211-2-21-244441-21-21-21-211-2-211-2-2000011-2-211-2-211-2-211-2-20000000000000000000000000000
χ4644444444441-2441-21-211-2-211-2-21-2-4-4-4-41-21-21-21-211-2-211-2-20000-1-122-1-122-1-122-1-1220000000000000000000000000000
χ474444444444-2144-21-21-2-211-2-211-214444-21-21-21-21-2-211-2-2110000-2-211-2-211-2-211-2-2110000000000000000000000000000
χ484444444444-2144-21-21-2-211-2-211-21-4-4-4-4-21-21-21-21-2-211-2-211000022-1-122-1-122-1-122-1-10000000000000000000000000000
χ494444-4-444441-2-4-41-21-2-1-122-1-1221-244-4-41-21-21-21-2-1-122-1-122000011-2-211-2-2-1-122-1-1220000000000000000000000000000
χ504444-4-444441-2-4-41-21-2-1-122-1-1221-2-4-4441-21-21-21-2-1-122-1-1220000-1-122-1-12211-2-211-2-20000000000000000000000000000
χ514444-4-44444-21-4-4-21-2122-1-122-1-1-2144-4-4-21-21-21-2122-1-122-1-10000-2-211-2-21122-1-122-1-10000000000000000000000000000
χ524444-4-44444-21-4-4-21-2122-1-122-1-1-21-4-444-21-21-21-2122-1-122-1-1000022-1-122-1-1-2-211-2-2110000000000000000000000000000
χ5344-4-44-444-4-41-24-4-12-1211-2-2-1-1221-200001-21-2-12-1211-2-2-1-12200003-3003-3003-3003-3000000000000000000000000000000
χ5444-4-44-444-4-41-24-4-12-1211-2-2-1-1221-200001-21-2-12-1211-2-2-1-1220000-3300-3300-3300-33000000000000000000000000000000
χ5544-4-44-444-4-4-214-42-12-1-2-21122-1-1-210000-21-212-12-1-2-21122-1-10000003-3003-3003-3003-30000000000000000000000000000
χ5644-4-44-444-4-4-214-42-12-1-2-21122-1-1-210000-21-212-12-1-2-21122-1-1000000-3300-3300-3300-330000000000000000000000000000
χ5744-4-4-4444-4-41-2-44-12-12-1-12211-2-21-200001-21-2-12-12-1-12211-2-200003-3003-300-3300-33000000000000000000000000000000
χ5844-4-4-4444-4-41-2-44-12-12-1-12211-2-21-200001-21-2-12-12-1-12211-2-20000-3300-33003-3003-3000000000000000000000000000000
χ5944-4-4-4444-4-4-21-442-12-122-1-1-2-211-210000-21-212-12-122-1-1-2-2110000003-3003-300-3300-330000000000000000000000000000
χ6044-4-4-4444-4-4-21-442-12-122-1-1-2-211-210000-21-212-12-122-1-1-2-211000000-3300-33003-3003-30000000000000000000000000000
χ614-44-4004-4-441-2001-2-123-3003-300-12004i−4i1-2-121-2-123-3003-30000003i−3i00−3i3i00ii−2i−2i−i−i2i2i0000000000000000000000000000
χ624-44-4004-4-441-2001-2-123-3003-300-1200−4i4i1-2-121-2-123-3003-3000000−3i3i003i−3i00−i−i2i2iii−2i−2i0000000000000000000000000000
χ634-44-4004-4-441-2001-2-12-3300-3300-12004i−4i1-2-121-2-12-3300-33000000−3i3i003i−3i00ii−2i−2i−i−i2i2i0000000000000000000000000000
χ644-44-4004-4-441-2001-2-12-3300-3300-1200−4i4i1-2-121-2-12-3300-330000003i−3i00−3i3i00−i−i2i2iii−2i−2i0000000000000000000000000000
χ654-44-4004-4-44-2100-212-1003-3003-32-1004i−4i-212-1-212-1003-3003-30000003i−3i00−3i3i−2i−2iii2i2i−i−i0000000000000000000000000000
χ664-44-4004-4-44-2100-212-1003-3003-32-100−4i4i-212-1-212-1003-3003-3000000−3i3i003i−3i2i2i−i−i−2i−2iii0000000000000000000000000000
χ674-44-4004-4-44-2100-212-100-3300-332-1004i−4i-212-1-212-100-3300-33000000−3i3i003i−3i−2i−2iii2i2i−i−i0000000000000000000000000000
χ684-44-4004-4-44-2100-212-100-3300-332-100−4i4i-212-1-212-100-3300-330000003i−3i00−3i3i2i2i−i−i−2i−2iii0000000000000000000000000000
χ694-44-400-222-2440044-4-400000000-4-40000-2-222-2-222000000004-44-4000000000000000000-22-220000000000000000000000
χ704-44-400-222-2440044-4-400000000-4-40000-2-222-2-22200000000-44-440000000000000000002-22-20000000000000000000000
χ714-4-44004-44-41-200-121-23-300-3300-124i−4i001-2-12-121-23-300-33000000ii−2i−2i−i−i2i2i3i−3i00−3i3i000000000000000000000000000000
χ724-4-44004-44-41-200-121-23-300-3300-12−4i4i001-2-12-121-23-300-33000000−i−i2i2iii−2i−2i−3i3i003i−3i000000000000000000000000000000
χ734-4-44004-44-41-200-121-2-33003-300-124i−4i001-2-12-121-2-33003-3000000ii−2i−2i−i−i2i2i−3i3i003i−3i000000000000000000000000000000
χ744-4-44004-44-41-200-121-2-33003-300-12−4i4i001-2-12-121-2-33003-3000000−i−i2i2iii−2i−2i3i−3i00−3i3i000000000000000000000000000000
χ754-4-44004-44-4-21002-1-21003-300-332-14i−4i00-212-12-1-21003-300-330000−2i−2iii2i2i−i−i003i−3i00−3i3i0000000000000000000000000000
χ764-4-44004-44-4-21002-1-21003-300-332-1−4i4i00-212-12-1-21003-300-3300002i2i−i−i−2i−2iii00−3i3i003i−3i0000000000000000000000000000
χ774-4-44004-44-4-21002-1-2100-33003-32-14i−4i00-212-12-1-2100-33003-30000−2i−2iii2i2i−i−i00−3i3i003i−3i0000000000000000000000000000
χ784-4-44004-44-4-21002-1-2100-33003-32-1−4i4i00-212-12-1-2100-33003-300002i2i−i−i−2i−2iii003i−3i00−3i3i0000000000000000000000000000
χ794-4-4400-22-224400-4-44400000000-4-40000-2-22222-2-2000000004i−4i−4i4i000000000000000000−2i2i2i−2i0000000000000000000000
χ804-4-4400-22-224400-4-44400000000-4-40000-2-22222-2-200000000−4i4i4i−4i0000000000000000002i−2i−2i2i0000000000000000000000
χ81888888-4-4-4-42-4-4-42-42-422-4-422-4-42-40000-12-12-12-12-1-122-1-122000000000000000000000000000000000000000000000000
χ82888888-4-4-4-4-42-4-4-42-42-4-422-4-422-4200002-12-12-12-122-1-122-1-1000000000000000000000000000000000000000000000000
χ838888-8-8-4-4-4-42-4442-42-4-2-244-2-2442-40000-12-12-12-1211-2-211-2-2000000000000000000000000000000000000000000000000
χ848888-8-8-4-4-4-4-4244-42-4244-2-244-2-2-4200002-12-12-12-1-2-211-2-211000000000000000000000000000000000000000000000000
χ8588-8-88-8-4-4442-4-44-24-2422-4-4-2-2442-40000-12-121-21-2-1-12211-2-2000000000000000000000000000000000000000000000000
χ8688-8-88-8-4-444-42-444-24-2-4-42244-2-2-4200002-12-1-21-2122-1-1-2-211000000000000000000000000000000000000000000000000
χ8788-8-8-88-4-4442-44-4-24-24-2-24422-4-42-40000-12-121-21-211-2-2-1-122000000000000000000000000000000000000000000000000
χ8888-8-8-88-4-444-424-44-24-244-2-2-4-422-4200002-12-1-21-21-2-21122-1-1000000000000000000000000000000000000000000000000
χ898-88-800-444-42-4002-4-246-6006-600-240000-121-2-121-2-3300-3300000000000000000000000000000000000000000000000000
χ908-88-800-444-42-4002-4-24-6600-6600-240000-121-2-121-23-3003-300000000000000000000000000000000000000000000000000
χ918-88-800-444-4-4200-424-2006-6006-64-200002-1-212-1-2100-3300-33000000000000000000000000000000000000000000000000
χ928-88-800-444-4-4200-424-200-6600-664-200002-1-212-1-21003-3003-3000000000000000000000000000000000000000000000000
χ938-8-8800-44-442-400-242-46-600-6600-240000-121-21-2-12-33003-300000000000000000000000000000000000000000000000000
χ948-8-8800-44-442-400-242-4-66006-600-240000-121-21-2-123-300-3300000000000000000000000000000000000000000000000000
χ958-8-8800-44-44-42004-2-42006-600-664-200002-1-21-212-100-33003-3000000000000000000000000000000000000000000000000
χ968-8-8800-44-44-42004-2-4200-66006-64-200002-1-21-212-1003-300-33000000000000000000000000000000000000000000000000

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