Finite Group Databasebeta

← Group #11865855

Character table — Group #11865855

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424222244442244442244666612121212466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1
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
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-111-111-1-111
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
χ91111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-11-11111-1-1-1-1-11-11-11-1
χ101111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-11-1-111-1-11111-1-11-11
χ111111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-111-1-111-1-11-111-1-11
χ121111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11-1-1-1-11111-1-11-111-1
χ131111111-1-111111111-11111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-11-111111-1-1-1-1-1-11-11-11
χ141111111-1-111111111-11111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-111-1-1-111-1-1111-111-11-1
χ151111111-1-111111111-11111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1-1111-1-111-1-111-1-111-1
χ161111111-1-111111111-11111-1-1-1-11111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11-11-1-1-1-1-11111-11-11-1-11
χ17222222-222-22222222-2222-22222-2-2-2-2-2-2-200-2-222-2-200000000000000000000000022-2-222000000000000-2000000
χ18222222-222-22222222-2222-22222-2-2-2-2-2-2-200-2-222-2-2000000000000000000000000-2-222-2-20000000000002000000
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
χ2122222-122222-1-12-12-12-1-1-1-122-1-12-1-1-12-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122002200000000220000-1-1-1-1000-1-10000
χ2222222-122222-1-12-12-12-1-1-1-122-1-12-1-1-12-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-200000000-2-200001111000110000
χ2322222-122222-1-12-12-12-1-1-1-122-1-12-1-1-12-1-1-2-22-1-1-1-1-1-2-2111111-2-211111122002200000000-2-20000-1-1-1-1000110000
χ2422222-122222-1-12-12-12-1-1-1-122-1-12-1-1-12-1-1-2-22-1-1-1-1-1-2-2111111-2-2111111-2-200-2-2000000002200001111000-1-10000
χ2522222-12-2-222-1-12-12-1-2-1-1-1-1-2-2112-1-1-12-1-12-2-21111122-1-1-1-1-1-1-2-21111112200-2-2000000002-20000-1-111000-110000
χ2622222-12-2-222-1-12-12-1-2-1-1-1-1-2-2112-1-1-12-1-12-2-21111122-1-1-1-1-1-1-2-2111111-2-2002200000000-22000011-1-10001-10000
χ2722222-12-2-222-1-12-12-1-2-1-1-1-1-2-2112-1-1-12-1-1-22-211111-2-211111122-1-1-1-1-1-12200-2-200000000-220000-1-1110001-10000
χ2822222-12-2-222-1-12-12-1-2-1-1-1-1-2-2112-1-1-12-1-1-22-211111-2-211111122-1-1-1-1-1-1-2-20022000000002-2000011-1-1000-110000
χ292222-122222-122-12-1-12-1-1-12-1-122-1-1-12-1-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1002200220000000022-1-10000-1-1000-1-100
χ302222-122222-122-12-1-12-1-1-12-1-122-1-1-12-1-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-200-2-200000000-2-2110000110001100
χ312222-122222-122-12-1-12-1-1-12-1-122-1-1-12-1-1-1-2-2-12-1-1-1-111-2-2111111-2-211110022002200000000-2-2-1-10000-1-10001100
χ322222-122222-122-12-1-12-1-1-12-1-122-1-1-12-1-1-1-2-2-12-1-1-1-111-2-2111111-2-2111100-2-200-2-2000000002211000011000-1-100
χ332222-122-2-22-122-12-1-1-2-1-1-1211-2-2-1-1-12-1-1-12-21-21111-1-122-1-1-1-111-2-21111002200-2-2000000002-2-1-1000011000-1100
χ342222-122-2-22-122-12-1-1-2-1-1-1211-2-2-1-1-12-1-1-12-21-21111-1-122-1-1-1-111-2-2111100-2-2002200000000-22110000-1-10001-100
χ352222-122-2-22-122-12-1-1-2-1-1-1211-2-2-1-1-12-1-1-1-221-2111111-2-21111-1-122-1-1-1-1002200-2-200000000-22-1-10000110001-100
χ362222-122-2-22-122-12-1-1-2-1-1-1211-2-2-1-1-12-1-1-1-221-2111111-2-21111-1-122-1-1-1-100-2-20022000000002-2110000-1-1000-1100
χ372-22-222200-2-22-2-2-22202-2-220000222-2-2-2-200000000000000000000000000002i−2i2i−2i2-22-200000000002i−2i2i−2i0000000
χ382-22-222200-2-22-2-2-22202-2-220000222-2-2-2-200000000000000000000000000002i−2i−2i2i-22-2200000000002i−2i−2i2i0000000
χ392-22-222200-2-22-2-2-22202-2-220000222-2-2-2-20000000000000000000000000000−2i2i2i−2i-22-220000000000−2i2i2i−2i0000000
χ402-22-222200-2-22-2-2-22202-2-220000222-2-2-2-20000000000000000000000000000−2i2i−2i2i2-22-20000000000−2i2i−2i2i0000000
χ412-22-222-2002-22-2-2-22202-2-2-20000-2-2-222220000000000000000000000002-22-200002-2-220000002-22-200000000000
χ422-22-222-2002-22-2-2-22202-2-2-20000-2-2-222220000000000000000000000002-2-220000-222-2000000-222-200000000000
χ432-22-222-2002-22-2-2-22202-2-2-20000-2-2-22222000000000000000000000000-222-20000-222-20000002-2-2200000000000
χ442-22-222-2002-22-2-2-22202-2-2-20000-2-2-22222000000000000000000000000-22-2200002-2-22000000-22-2200000000000
χ4544444-2-444-44-2-24-24-2-4-2-2-2244-2-2-4222-42200-42-2-2220000000000000000000000000000000000000000000000000
χ4644444-2-4-4-4-44-2-24-24-24-2-2-22-4-422-4222-422004-222-2-20000000000000000000000000000000000000000000000000
χ474444-24-444-4-244-24-2-2-4-2-2-2-4-2-244222-4222002-4-2-2220000000000000000000000000000000000000000000000000
χ484444-24-4-4-4-4-244-24-2-24-2-2-2-422-4-4222-422200-2422-2-20000000000000000000000000000000000000000000000000
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
χ514444-2-24-4-44-2-2-2-2-2-21-4111-22222-211-2-2114-422-1-1-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ524444-2-24-4-44-2-2-2-2-2-21-4111-22222-211-2-211-4422-1-1-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ534444-2-2-444-4-2-2-2-2-2-21-41112-2-2-2-22-1-122-1-1002211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ544444-2-2-444-4-2-2-2-2-2-21-41112-2-2-2-22-1-122-1-1002211-1-10000−3i−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
χ5744-4-44400004-44-4-4-440-44-40000000000000000000000000000000000000000000000004i−4i0000000000000000000
χ5844-4-44400004-44-4-4-440-44-4000000000000000000000000000000000000000000000000−4i4i0000000000000000000
χ594-44-44-2400-4-4-22-424-20-222-200004-2-22-42200000000000000000000000000004i−4i0000000000000000−2i2i000000000
χ604-44-44-2400-4-4-22-424-20-222-200004-2-22-4220000000000000000000000000000−4i4i00000000000000002i−2i000000000
χ614-44-44-2-4004-4-22-424-20-22220000-422-24-2-20000000000000000000000004-4000000000000000000-2200000000000
χ624-44-44-2-4004-4-22-424-20-22220000-422-24-2-2000000000000000000000000-440000000000000000002-200000000000
χ634-44-4-24400-424-42-4-2-20-22240000-2-2-2-42220000000000000000000000000000004i−4i0000000000000000−2i2i0000000
χ644-44-4-24400-424-42-4-2-20-22240000-2-2-2-4222000000000000000000000000000000−4i4i00000000000000002i−2i0000000
χ654-44-4-24-400424-42-4-2-20-222-400002224-2-2-2000000000000000000000000004-400000000000000-220000000000000
χ664-44-4-24-400424-42-4-2-20-222-400002224-2-2-200000000000000000000000000-44000000000000002-20000000000000
χ674-4-444404-40-4-4-444-440-4-4404-44-4000000000004-4000000000000000000000000000000000000000000000000000
χ684-4-44440-440-4-4-444-440-4-440-44-4400000000000-44000000000000000000000000000000000000000000000000000
χ694-4-444-204-40-4224-2-4-2022-204-4-2200000000000-220000i6−i6i6−i6i6−i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ704-4-444-204-40-4224-2-4-2022-204-4-2200000000000-220000−i6i6−i6i6−i6i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ714-4-444-20-440-4224-2-4-2022-20-442-2000000000002-20000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ724-4-444-20-440-4224-2-4-2022-20-442-2000000000002-20000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ734-4-44-2404-402-4-4-242-2022-20-224-400000000000-22006−6006−6−666−6006−6−66000000000000000000000000000000000
χ744-4-44-2404-402-4-4-242-2022-20-224-400000000000-2200−6600−666−6−6600−666−6000000000000000000000000000000000
χ754-4-44-240-4402-4-4-242-2022-202-2-44000000000002-2006−6006−6−66−6600−666−6000000000000000000000000000000000
χ764-4-44-240-4402-4-4-242-2022-202-2-44000000000002-200−6600−666−66−6006−6−66000000000000000000000000000000000
χ774-4-44-2-204-40222-2-2210-1-110-22-2203i−3i003i−3i00001-13i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ784-4-44-2-204-40222-2-2210-1-110-22-2203i−3i003i−3i00001-13i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ794-4-44-2-204-40222-2-2210-1-110-22-220−3i3i00−3i3i00001-1−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ804-4-44-2-204-40222-2-2210-1-110-22-220−3i3i00−3i3i00001-1−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ814-4-44-2-20-440222-2-2210-1-1102-22-203i−3i003i−3i0000-11−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ824-4-44-2-20-440222-2-2210-1-1102-22-203i−3i003i−3i0000-11−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ834-4-44-2-20-440222-2-2210-1-1102-22-20−3i3i00−3i3i0000-113i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ844-4-44-2-20-440222-2-2210-1-1102-22-20−3i3i00−3i3i0000-113i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ8588-8-88-4000084-4-84-8-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-480000-4-884-84-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40000-44-444420-22-20000006i−6i00−6i6i000000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-44-444420-22-2000000−6i6i006i−6i000000000000000000000000000000000000000000000000000000000
χ898-88-8-4-4800-84-4444-4202-2-2-40000-42244-2-2000000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4-80084-4444-4202-2-2400004-2-2-4-422000000000000000000000000000000000000000000000000000000000

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