Finite Group Databasebeta

← Group #11897575

Character table — Group #11897575

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222244444444444444444888888888888888888888888121212122424242424242424242424242424363636363636363648484848
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242422224444446666121212124444888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-111-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-1111111-1-1-1-111-1-1
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111111-1-1111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-11-11111-1-1-1-11-11-111-1-11-11-1
χ10111111-1-1111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-11-1111-1-1-1-111-11-11-1-1111-1-11
χ11111111-1-1111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-11-1-1-11111-1-1-11-11-1-111-111-1
χ12111111-1-1111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-111111-11-111-1-1-11-11
χ13111111-1-1111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1-1-111111-1-1-1-1-11-1111-1-1-11-11
χ14111111-1-1111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-111-111-1-1-1-1111-11-1-1-111-111-1
χ15111111-1-1111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-11-1-11-1-11111-1-11-11-1-1-1111-1-11
χ16111111-1-1111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-1-1-1-1-11111-11-1111-1-11-11-1
χ1722222222-2-22222222-2222-2-22222-2-2-2-2-2-200-2-222-2-2000000000000000000000000000000000022-2-200000000
χ1822222222-2-22222222-2222-2-22222-2-2-2-2-2-200-2-222-2-20000000000000000000000000000000000-2-22200000000
χ19222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000000000000000000002-2-2200000000
χ20222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000000000000000000000-222-200000000
χ2122222-1222222-1-1-12-12-1-1-12-1-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200222000-1-100-1-10000000000-1-100
χ2222222-1222222-1-1-12-12-1-1-12-1-1-122-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2-200011001100000000001100
χ2322222-1222222-1-1-12-12-1-1-12-1-1-122-1-12-1-1-1-2-22-1-1-1-1-1-2-2111111-2-21111112200-2-22000-1-100-1-100000000001100
χ2422222-1222222-1-1-12-12-1-1-12-1-1-122-1-12-1-1-1-2-22-1-1-1-1-1-2-2111111-2-2111111-2-20022-20001100110000000000-1-100
χ2522222-1-2-22222-1-1-12-1-2-1-1-12-111-2-2-1-12-1-1-12-2-21111122-1-1-1-1-1-1-2-211111122002-2-2000-1-100110000000000-1100
χ2622222-1-2-22222-1-1-12-1-2-1-1-12-111-2-2-1-12-1-1-12-2-21111122-1-1-1-1-1-1-2-2111111-2-200-2220001100-1-100000000001-100
χ2722222-1-2-22222-1-1-12-1-2-1-1-12-111-2-2-1-12-1-1-1-22-211111-2-211111122-1-1-1-1-1-12200-22-2000-1-1001100000000001-100
χ2822222-1-2-22222-1-1-12-1-2-1-1-12-111-2-2-1-12-1-1-1-22-211111-2-211111122-1-1-1-1-1-1-2-2002-220001100-1-10000000000-1100
χ292222-122222-1-1222-1-12-1-1-1-1222-1-1-1-1-12-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1002200022200-1-100-1-10000000000-1-1
χ302222-122222-1-1222-1-12-1-1-1-1222-1-1-1-1-12-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-2000-2-2-200110011000000000011
χ312222-122222-1-1222-1-12-1-1-1-1222-1-1-1-1-12-1-1-2-2-12-1-1-1-111-2-2111111-2-2111100220002-2-200-1-100-1-1000000000011
χ322222-122222-1-1222-1-12-1-1-1-1222-1-1-1-1-12-1-1-2-2-12-1-1-1-111-2-2111111-2-2111100-2-2000-222001100110000000000-1-1
χ332222-12-2-222-1-1222-1-1-2-1-1-1-12-2-211-1-1-12-1-12-21-21111-1-122-1-1-1-111-2-211110022000-22-200-1-100110000000000-11
χ342222-12-2-222-1-1222-1-1-2-1-1-1-12-2-211-1-1-12-1-12-21-21111-1-122-1-1-1-111-2-2111100-2-20002-22001100-1-100000000001-1
χ352222-12-2-222-1-1222-1-1-2-1-1-1-12-2-211-1-1-12-1-1-221-2111111-2-21111-1-122-1-1-1-10022000-2-2200-1-1001100000000001-1
χ362222-12-2-222-1-1222-1-1-2-1-1-1-12-2-211-1-1-12-1-1-221-2111111-2-21111-1-122-1-1-1-100-2-200022-2001100-1-10000000000-11
χ3722-2-222002-22-22-2-2-2202-2-222000022-2-2-2-20000000000000000000000002-22-20000002-22-2000000002-2000000
χ3822-2-222002-22-22-2-2-2202-2-222000022-2-2-2-20000000000000000000000002-2-220000002-2-2200000000-22000000
χ3922-2-222002-22-22-2-2-2202-2-222000022-2-2-2-2000000000000000000000000-222-2000000-222-200000000-22000000
χ4022-2-222002-22-22-2-2-2202-2-222000022-2-2-2-2000000000000000000000000-22-22000000-22-22000000002-2000000
χ4144444-244-4-444-2-2-24-2-4-2-2-2-42-2-24422-422200-42-2-2220000000000000000000000000000000000000000000000
χ4244444-2-4-4-4-444-2-2-24-24-2-2-2-4222-4-422-4222004-222-2-20000000000000000000000000000000000000000000000
χ434444-2444-4-4-2-2444-2-2-4-2-2-22-444-2-2222-422002-4-2-2220000000000000000000000000000000000000000000000
χ444444-24-4-4-4-4-2-2444-2-24-2-2-22-4-4-422222-42200-2422-2-20000000000000000000000000000000000000000000000
χ454444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-211-2-21144-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000000
χ464444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-211-2-211-4-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000000
χ474444-2-244-4-4-2-2-2-2-2-21-411122-2-2-2-2-1-122-1-1002211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ484444-2-244-4-4-2-2-2-2-2-21-411122-2-2-2-2-1-122-1-1002211-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ494444-2-2-4-444-2-2-2-2-2-21-4111-2-2222211-2-2114-422-1-1-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000
χ504444-2-2-4-444-2-2-2-2-2-21-4111-2-2222211-2-211-4422-1-1-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000
χ514444-2-2-4-4-4-4-2-2-2-2-2-214111222222-1-122-1-100-2-2-1-11100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ524444-2-2-4-4-4-4-2-2-2-2-2-214111222222-1-122-1-100-2-2-1-1110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ5344-4-44400-444-44-4-4-4404-4-4-4-40000-4-44444000000000000000000000000000000000000000000000000000000
χ5444-4-44-2004-44-4-222-4-20-2224-20000-2-2-42220000000000000000000000004-400000000-22000000000000000000
χ5544-4-44-2004-44-4-222-4-20-2224-20000-2-2-4222000000000000000000000000-44000000002-2000000000000000000
χ5644-4-44-200-444-4-222-4-20-222-420000224-2-2-20000000000000000000000000000000000000023−2300000000000000
χ5744-4-44-200-444-4-222-4-20-222-420000224-2-2-200000000000000000000000000000000000000−232300000000000000
χ5844-4-4-24004-4-224-4-42-20-222-240000-2-22-422000000000000000000000000004-400000000-220000000000000000
χ5944-4-4-24004-4-224-4-42-20-222-240000-2-22-42200000000000000000000000000-44000000002-20000000000000000
χ6044-4-4-2400-44-224-4-42-20-2222-4000022-24-2-2000000000000000000000000000000000000000023−23000000000000
χ6144-4-4-2400-44-224-4-42-20-2222-4000022-24-2-20000000000000000000000000000000000000000−2323000000000000
χ624-44-4440000-44-4-44-440-44-4000000000000000000000000000000000000000000000000000000000000−2i22i20000
χ634-44-4440000-44-4-44-440-44-40000000000000000000000000000000000000000000000000000000000002i2−2i20000
χ644-4-44444-400-4-4-44-4440-4-44004-44-400000000004-4000000000000000000000000000000000000000000000000
χ654-4-4444-4400-4-4-44-4440-4-4400-44-440000000000-44000000000000000000000000000000000000000000000000
χ664-4-444-24-400-4-42-224-2022-200-224-40000000000-2200006−66−66−6006−66−66−6000000000000000000000000000000
χ674-4-444-24-400-4-42-224-2022-200-224-40000000000-220000−66−66−6600−66−66−66000000000000000000000000000000
χ684-4-444-2-4400-4-42-224-2022-2002-2-4400000000002-200006−66−66−600−66−66−66000000000000000000000000000000
χ694-4-444-2-4400-4-42-224-2022-2002-2-4400000000002-20000−66−66−66006−66−66−6000000000000000000000000000000
χ704-4-44-244-40022-44-4-2-2022-2004-4-220000000000-2200i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ714-4-44-244-40022-44-4-2-2022-2004-4-220000000000-2200−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ724-4-44-24-440022-44-4-2-2022-200-442-200000000002-200i6−i600i6−i6−i6i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ734-4-44-24-440022-44-4-2-2022-200-442-200000000002-200−i6i600−i6i6i6−i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ744-4-44-2-24-400222-22-210-1-1100-22-223i−3i003i−3i00001-13i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ754-4-44-2-24-400222-22-210-1-1100-22-223i−3i003i−3i00001-13i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ764-4-44-2-24-400222-22-210-1-1100-22-22−3i3i00−3i3i00001-1−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ774-4-44-2-24-400222-22-210-1-1100-22-22−3i3i00−3i3i00001-1−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ784-4-44-2-2-4400222-22-210-1-11002-22-23i−3i003i−3i0000-11−3i3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ794-4-44-2-2-4400222-22-210-1-11002-22-23i−3i003i−3i0000-11−3i3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ804-4-44-2-2-4400222-22-210-1-11002-22-2−3i3i00−3i3i0000-113i−3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ814-4-44-2-2-4400222-22-210-1-11002-22-2−3i3i00−3i3i0000-113i−3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ8288-8-8-4-4008-8-44-4444202-2-2-4-400002244-2-2000000000000000000000000000000000000000000000000000000
χ8388-8-8-4-400-88-44-4444202-2-2440000-2-2-4-422000000000000000000000000000000000000000000000000000000
χ848-88-88-40000-8844-4-8-404-44000000000000000000000000000000000000000000000000000000000000000000
χ858-88-8-4800004-4-8-884-404-44000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-4-400004-444-4420-22-20000006i−6i00−6i6i000000000000000000000000000000000000000000000000000000
χ878-88-8-4-400004-444-4420-22-2000000−6i6i006i−6i000000000000000000000000000000000000000000000000000000

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