Finite Group Databasebeta

← Group #11868732

Character table — Group #11868732

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424444444442244444444121212121212121241212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1
χ91111111-1-111111111-1111-1-111-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-11-111-1-111-1-1-11-11-11-1
χ101111111-1-111111111-1111-1-111-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-11-11
χ111111111-1-111111111-1111-1-111-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-1-11111-1-11-111-1-11
χ121111111-1-111111111-1111-1-111-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11-1-111-1-111-1-11-111-1
χ131111111-1-111111111-1111-1-111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-11-1111-1-111-1-1-1-11-11-11
χ141111111-1-111111111-1111-1-111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-111-111-1-1-1-1111-111-11-1
χ151111111-1-111111111-1111-1-111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1-11-1-11111-1-111-1-111-1
χ161111111-1-111111111-1111-1-111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11-11-1-1-111-1-111-11-11-1-11
χ17222222-222-22222222-222222-2-222-2-2-2-2-2-200-2-222-2-200000000000000000000000022-2-222000000000000-2000000
χ18222222-222-22222222-222222-2-222-2-2-2-2-2-200-2-222-2-2000000000000000000000000-2-222-2-20000000000002000000
χ19222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000000000022-2-2-2-20000000000002000000
χ20222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000000000-2-22222000000000000-2000000
χ2122222-1222222-1-1-12-12-1-1-1222-1-1-1-1-12-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1220022000000002200-1-1-1-100000-1-10000
χ2222222-1222222-1-1-12-12-1-1-1222-1-1-1-1-12-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-200000000-2-200111100000110000
χ2322222-1222222-1-1-12-12-1-1-1222-1-1-1-1-12-1-1-1-2-2-12-1-1-1-1-2-2111111-2-211111122002200000000-2-200-1-1-1-100000110000
χ2422222-1222222-1-1-12-12-1-1-1222-1-1-1-1-12-1-1-1-2-2-12-1-1-1-1-2-2111111-2-2111111-2-200-2-2000000002200111100000-1-10000
χ2522222-12-2-2222-1-1-12-1-2-1-1-1-2-22-111-1-12-1-1-12-21-2111122-1-1-1-1-1-1-2-21111112200-2-2000000002-200-1-11100000-110000
χ2622222-12-2-2222-1-1-12-1-2-1-1-1-2-22-111-1-12-1-1-12-21-2111122-1-1-1-1-1-1-2-2111111-2-2002200000000-220011-1-1000001-10000
χ2722222-12-2-2222-1-1-12-1-2-1-1-1-2-22-111-1-12-1-1-1-221-21111-2-211111122-1-1-1-1-1-12200-2-200000000-2200-1-111000001-10000
χ2822222-12-2-2222-1-1-12-1-2-1-1-1-2-22-111-1-12-1-1-1-221-21111-2-211111122-1-1-1-1-1-1-2-20022000000002-20011-1-100000-110000
χ292222-122222-1-1222-1-12-1-1-1-1-1-1222-1-1-12-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10022002200000000220000-1-1-1-1000-1-100
χ302222-122222-1-1222-1-12-1-1-1-1-1-1222-1-1-12-1-1222-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-200-2-200000000-2-2000011110001100
χ312222-122222-1-1222-1-12-1-1-1-1-1-1222-1-1-12-1-1-2-22-1-1-1-1-111-2-2111111-2-211110022002200000000-2-20000-1-1-1-10001100
χ322222-122222-1-1222-1-12-1-1-1-1-1-1222-1-1-12-1-1-2-22-1-1-1-1-111-2-2111111-2-2111100-2-200-2-2000000002200001111000-1-100
χ332222-122-2-22-1-1222-1-1-2-1-1-111-12-2-2-1-1-12-1-12-2-211111-1-122-1-1-1-111-2-21111002200-2-2000000002-20000-1-111000-1100
χ342222-122-2-22-1-1222-1-1-2-1-1-111-12-2-2-1-1-12-1-12-2-211111-1-122-1-1-1-111-2-2111100-2-2002200000000-22000011-1-10001-100
χ352222-122-2-22-1-1222-1-1-2-1-1-111-12-2-2-1-1-12-1-1-22-21111111-2-21111-1-122-1-1-1-1002200-2-200000000-220000-1-1110001-100
χ362222-122-2-22-1-1222-1-1-2-1-1-111-12-2-2-1-1-12-1-1-22-21111111-2-21111-1-122-1-1-1-100-2-20022000000002-2000011-1-1000-1100
χ3722-2-222200-2-222-2-2-2202-2-200220022-2-2-2-20000000000000000000000002-22-200002-22-20000002-2002-2000000000
χ3822-2-222200-2-222-2-2-2202-2-200220022-2-2-2-20000000000000000000000002-2-220000-22-220000002-200-22000000000
χ3922-2-222200-2-222-2-2-2202-2-200220022-2-2-2-2000000000000000000000000-222-20000-22-22000000-22002-2000000000
χ4022-2-222200-2-222-2-2-2202-2-200220022-2-2-2-2000000000000000000000000-22-2200002-22-2000000-2200-22000000000
χ4122-2-222-2002-222-2-2-2202-2-200-2-200-2-2222200000000000000000000000000002i−2i2i−2i2-2-22000000002i−2i002i−2i0000000
χ4222-2-222-2002-222-2-2-2202-2-200-2-200-2-2222200000000000000000000000000002i−2i−2i2i-222-2000000002i−2i00−2i2i0000000
χ4322-2-222-2002-222-2-2-2202-2-200-2-200-2-222220000000000000000000000000000−2i2i2i−2i-222-200000000−2i2i002i−2i0000000
χ4422-2-222-2002-222-2-2-2202-2-200-2-200-2-222220000000000000000000000000000−2i2i−2i2i2-2-2200000000−2i2i00−2i2i0000000
χ4544444-2-444-444-2-2-24-2-4-2-2-244-42-2-222-4222002-4-2-2220000000000000000000000000000000000000000000000000
χ4644444-2-4-4-4-444-2-2-24-24-2-2-2-4-4-422222-422200-2422-2-20000000000000000000000000000000000000000000000000
χ474444-24-444-4-2-2444-2-2-4-2-2-2-2-22-444222-42200-42-2-2220000000000000000000000000000000000000000000000000
χ484444-24-4-4-4-4-2-2444-2-24-2-2-2222-4-4-4222-422004-222-2-20000000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-211-2-21144-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-211-2-211-4-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ514444-2-24-4-44-2-2-2-2-2-21-411122-2-22211-2-2114-422-1-1-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ524444-2-24-4-44-2-2-2-2-2-21-411122-2-22211-2-211-4422-1-1-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ534444-2-2-444-4-2-2-2-2-2-21-4111-2-222-2-2-1-122-1-1002211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ544444-2-2-444-4-2-2-2-2-2-21-4111-2-222-2-2-1-122-1-1002211-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-214111222222-1-122-1-100-2-2-1-11100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-214111222222-1-122-1-100-2-2-1-1110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ5744-4-44-2400-4-44-222-4-20-222004-200-2-2-42220000000000000000000000004-40000000000000000-220000000000000
χ5844-4-44-2400-4-44-222-4-20-222004-200-2-2-4222000000000000000000000000-4400000000000000002-20000000000000
χ5944-4-44-2-4004-44-222-4-20-22200-4200224-2-2-200000000000000000000000000004i−4i00000000000000−2i2i00000000000
χ6044-4-44-2-4004-44-222-4-20-22200-4200224-2-2-20000000000000000000000000000−4i4i000000000000002i−2i00000000000
χ6144-4-4-24400-42-24-4-42-20-22200-2400-2-22-422000000000000000000000000004-4000000000000000000-22000000000
χ6244-4-4-24400-42-24-4-42-20-22200-2400-2-22-42200000000000000000000000000-440000000000000000002-2000000000
χ6344-4-4-24-40042-24-4-42-20-222002-40022-24-2-20000000000000000000000000000004i−4i0000000000000000−2i2i0000000
χ6444-4-4-24-40042-24-4-42-20-222002-40022-24-2-2000000000000000000000000000000−4i4i00000000000000002i−2i0000000
χ654-44-44404-404-4-4-44-440-44-44-4004-400000000004-4000000000000000000000000000000000000000000000000000
χ664-44-4440-4404-4-4-44-440-44-4-4400-440000000000-44000000000000000000000000000000000000000000000000000
χ674-44-44-204-404-422-2-4-202-224-400-220000000000-2200006−66−66−6006−66−66−6000000000000000000000000000000000
χ684-44-44-204-404-422-2-4-202-224-400-220000000000-220000−66−66−6600−66−66−66000000000000000000000000000000000
χ694-44-44-20-4404-422-2-4-202-22-44002-200000000002-200006−66−66−600−66−66−66000000000000000000000000000000000
χ704-44-44-20-4404-422-2-4-202-22-44002-200000000002-20000−66−66−66006−66−66−6000000000000000000000000000000000
χ714-44-4-2404-40-22-4-442-202-22-22004-40000000000-2200i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000000000000
χ724-44-4-2404-40-22-4-442-202-22-22004-40000000000-2200−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000000000000
χ734-44-4-240-440-22-4-442-202-222-200-4400000000002-200i6−i600i6−i6−i6i6−i6i600−i6i6i6−i6000000000000000000000000000000000
χ744-44-4-240-440-22-4-442-202-222-200-4400000000002-200−i6i600−i6i6i6−i6i6−i600i6−i6−i6i6000000000000000000000000000000000
χ754-44-4-2-204-40-2222-2210-11-1-2200-223i−3i003i−3i00001-13i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ764-44-4-2-204-40-2222-2210-11-1-2200-223i−3i003i−3i00001-13i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ774-44-4-2-204-40-2222-2210-11-1-2200-22−3i3i00−3i3i00001-1−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ784-44-4-2-204-40-2222-2210-11-1-2200-22−3i3i00−3i3i00001-1−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ794-44-4-2-20-440-2222-2210-11-12-2002-23i−3i003i−3i0000-11−3i3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ804-44-4-2-20-440-2222-2210-11-12-2002-23i−3i003i−3i0000-11−3i3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ814-44-4-2-20-440-2222-2210-11-12-2002-2−3i3i00−3i3i0000-113i−3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ824-44-4-2-20-440-2222-2210-11-12-2002-2−3i3i00−3i3i0000-113i−3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ834-4-44440000-4-4-44-4440-4-440000000000000000000000000000000000000000000000004i−4i0000000000000000000
χ844-4-44440000-4-4-44-4440-4-44000000000000000000000000000000000000000000000000−4i4i0000000000000000000
χ8588-8-8-4-4800-84-4-4444202-2-200-4-4002244-2-2000000000000000000000000000000000000000000000000000000000
χ8688-8-8-4-4-80084-4-4444202-2-2004400-2-2-4-422000000000000000000000000000000000000000000000000000000000
χ878-8-888-40000-8-84-448-4044-4000000000000000000000000000000000000000000000000000000000000000000000
χ888-8-88-48000044-88-8-4-4044-4000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-40000444-44-420-2-220000006i−6i00−6i6i000000000000000000000000000000000000000000000000000000000
χ908-8-88-4-40000444-44-420-2-22000000−6i6i006i−6i000000000000000000000000000000000000000000000000000000000

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