Finite Group Databasebeta

← Group #11864136

Character table — Group #11864136

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order1222223344666666346666666121212121212121266881212121224242424242424242424242424242424222244442244442244666612121212266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-11-11-1-1-1-11111-11-1-11-1-1
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
χ511111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-11-1-1111
χ711111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-11111-1-111-111
χ811111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1
χ91111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-111-1-111-1-1-111-1-11-1
χ101111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-1111-11-11-11
χ111111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-1-11111-1-111-11-1-11
χ121111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1-1111-1
χ131111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-111-1-1-1-1-111-11
χ141111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-111-111-1-1-1-11111-11-11-1
χ151111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1111-1-11-1-11111-1-11-11-111-1
χ161111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-111-1-1-1-111-1-111-111-1-1-11
χ1722222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-200000000000000000000000022-2-2-2-20000000000002000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-2000000000000000000000000-2-22222000000000000-2000000
χ192222222-1222-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1222200000000002020-1-1-1-1000000-1-1000
χ202222222-1222-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-20000000000-20-20111100000011000
χ212222222-1222-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-1-2-2111111-2-211111122220000000000-20-20-1-1-1-100000011000
χ222222222-1222-1-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-1-2-2111111-2-2111111-2-2-2-2000000000020201111000000-1-1000
χ23222222-1222-122-12-1-12-1-122-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000222200000002020000-1-1-1-10-100-100
χ24222222-1222-122-12-1-12-1-122-1-1-122-1-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-2-2-20000000-20-2000011110100100
χ25222222-1222-122-12-1-12-1-122-1-1-122-1-1-1-1-1-1-1-1-2-22-1-1-111-2-2111111-2-21111000022220000000-20-20000-1-1-1-10100100
χ26222222-1222-122-12-1-12-1-122-1-1-122-1-1-1-1-1-1-1-1-2-22-1-1-111-2-2111111-2-211110000-2-2-2-20000000202000011110-100-100
χ272222-2-222-2-222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-200222200000000000000000000000022-2-222000000000000-2000000
χ282222-2-222-2-222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2002222000000000000000000000000-2-222-2-20000000000002000000
χ292222-2-22-1222-1-12-12-1-2-2-211-1-1-1-1-122-1-1-1-1112-21-21122-1-1-1-1-1-1-2-211111122-2-2000000000020-20-1-111000000-11000
χ302222-2-22-1222-1-12-12-1-2-2-211-1-1-1-1-122-1-1-1-1112-21-21122-1-1-1-1-1-1-2-2111111-2-2220000000000-202011-1-10000001-1000
χ312222-2-22-1222-1-12-12-1-2-2-211-1-1-1-1-122-1-1-1-111-221-211-2-211111122-1-1-1-1-1-122-2-20000000000-2020-1-1110000001-1000
χ322222-2-22-1222-1-12-12-1-2-2-211-1-1-1-1-122-1-1-1-111-221-211-2-211111122-1-1-1-1-1-1-2-222000000000020-2011-1-1000000-11000
χ332222-2-2-1222-122-12-1-1-211-2-2-1-1-122-1-1-1-1-1-1112-2-2111-1-122-1-1-1-111-2-21111000022-2-2000000020-20000-1-1110-100100
χ342222-2-2-1222-122-12-1-1-211-2-2-1-1-122-1-1-1-1-1-1112-2-2111-1-122-1-1-1-111-2-211110000-2-2220000000-202000011-1-10100-100
χ352222-2-2-1222-122-12-1-1-211-2-2-1-1-122-1-1-1-1-1-111-22-211111-2-21111-1-122-1-1-1-1000022-2-20000000-2020000-1-1110100-100
χ362222-2-2-1222-122-12-1-1-211-2-2-1-1-122-1-1-1-1-1-111-22-211111-2-21111-1-122-1-1-1-10000-2-222000000020-2000011-1-10-100100
χ372-2-2200222-2-2-22-2-22200000-2-222-22-222-2-20000000000000000000000002-2002-2002-22-20000002-2002-2000000000
χ382-2-2200222-2-2-22-2-22200000-2-222-22-222-2-20000000000000000000000002-200-2200-22-220000002-200-22000000000
χ392-2-2200222-2-2-22-2-22200000-2-222-22-222-2-2000000000000000000000000-22002-200-22-22000000-22002-2000000000
χ402-2-2200222-2-2-22-2-22200000-2-222-22-222-2-2000000000000000000000000-2200-22002-22-2000000-2200-22000000000
χ412-2-220022-22-2-22-2-22200000-2-22-22-22-2-222000000000000000000000000002-2002-22-2-22000000002-2002-20000000
χ422-2-220022-22-2-22-2-22200000-2-22-22-22-2-222000000000000000000000000002-200-22-222-2000000002-200-220000000
χ432-2-220022-22-2-22-2-22200000-2-22-22-22-2-22200000000000000000000000000-22002-2-222-200000000-22002-20000000
χ442-2-220022-22-2-22-2-22200000-2-22-22-22-2-22200000000000000000000000000-2200-222-2-2200000000-2200-220000000
χ454444444-2-4-44-2-24-24-2-444-2-2-2-2-222-4-42222-2-2002-4220000000000000000000000000000000000000000000000000
χ46444444-24-4-4-244-24-2-2-4-2-244-2-2-2-4-4222222-2-200-42220000000000000000000000000000000000000000000000000
χ47444444-2-244-2-2-2-2-2-214-2-2-2-2111-2-2-2-211111144-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ48444444-2-244-2-2-2-2-2-214-2-2-2-2111-2-2-2-2111111-4-4-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2-21112222-1-1-1-1110022-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ50444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2-21112222-1-1-1-1110022-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ514444-4-44-2-4-44-2-24-24-24-4-422-2-2-222-4-422222200-24-2-20000000000000000000000000000000000000000000000000
χ524444-4-4-24-4-4-244-24-2-2422-4-4-2-2-2-4-422222222004-2-2-20000000000000000000000000000000000000000000000000
χ534444-4-4-2-244-2-2-2-2-2-21-42222111-2-2-2-21111-1-14-422-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ544444-4-4-2-244-2-2-2-2-2-21-42222111-2-2-2-21111-1-1-4422-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ554444-4-4-2-2-4-4-2-2-2-2-2-21422221112222-1-1-1-1-1-100-2-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ564444-4-4-2-2-4-4-2-2-2-2-2-21422221112222-1-1-1-1-1-100-2-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ5744-4-400440044-4-4-4-44000004-4-4000000000000000000000000000000000000000000004i−4i0000000000000000000
χ5844-4-400440044-4-4-4-44000004-4-400000000000000000000000000000000000000000000−4i4i0000000000000000000
χ594-44-44-44400-4-4-444-4404-44-4-44-4000000004-40000000000000000000000000000000000000000000000000000000
χ604-44-44-44-200-4224-2-4-204-4-222-2200000000-2200000000i6−i6i6−i6i6−i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ614-44-44-44-200-4224-2-4-204-4-222-2200000000-2200000000−i6i6−i6i6−i6i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ624-44-44-4-24002-4-4-242-20-224-42-2200000000-220000006−6006−6−666−6006−6−66000000000000000000000000000000000
χ634-44-44-4-24002-4-4-242-20-224-42-2200000000-22000000−6600−666−6−6600−666−6000000000000000000000000000000000
χ644-44-44-4-2-200222-2-2210-22-22-11-100003i−3i3i−3i1-100003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ654-44-44-4-2-200222-2-2210-22-22-11-100003i−3i3i−3i1-100003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ664-44-44-4-2-200222-2-2210-22-22-11-10000−3i3i−3i3i1-10000−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ674-44-44-4-2-200222-2-2210-22-22-11-10000−3i3i−3i3i1-10000−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ684-44-4-444400-4-4-444-440-44-44-44-400000000-440000000000000000000000000000000000000000000000000000000
χ694-44-4-444-200-4224-2-4-20-442-22-22000000002-200000000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ704-44-4-444-200-4224-2-4-20-442-22-22000000002-200000000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ714-44-4-44-24002-4-4-242-202-2-442-22000000002-20000006−6006−6−66−6600−666−6000000000000000000000000000000000
χ724-44-4-44-24002-4-4-242-202-2-442-22000000002-2000000−6600−666−66−6006−6−66000000000000000000000000000000000
χ734-44-4-44-2-200222-2-22102-22-2-11-100003i−3i3i−3i-110000−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ744-44-4-44-2-200222-2-22102-22-2-11-100003i−3i3i−3i-110000−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ754-44-4-44-2-200222-2-22102-22-2-11-10000−3i3i−3i3i-1100003i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ764-44-4-44-2-200222-2-22102-22-2-11-10000−3i3i−3i3i-1100003i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ774-4-44004-24-4-42-2-424-20000022-2-224-4-2-2220000000000000000000000004-40000000000000000-220000000000000
χ784-4-44004-24-4-42-2-424-20000022-2-224-4-2-222000000000000000000000000-4400000000000000002-20000000000000
χ794-4-44004-2-44-42-2-424-20000022-22-2-4422-2-2000000000000000000000000004-40000000000000000-2200000000000
χ804-4-44004-2-44-42-2-424-20000022-22-2-4422-2-200000000000000000000000000-4400000000000000002-200000000000
χ814-4-4400-244-42-442-4-2-20000022-24-4-22-2-22200000000000000000000000000004-40000000000000000-22000000000
χ824-4-4400-244-42-442-4-2-20000022-24-4-22-2-2220000000000000000000000000000-4400000000000000002-2000000000
χ834-4-4400-24-442-442-4-2-20000022-2-442-222-2-20000000000000000000000000000004-40000000000000000-220000000
χ844-4-4400-24-442-442-4-2-20000022-2-442-222-2-2000000000000000000000000000000-4400000000000000002-20000000
χ8588-8-8008-4008-44-84-8-400000-44400000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-4800-48-84-84-400000-44400000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-4-400-4-444442000002-2-200006i−6i−6i6i000000000000000000000000000000000000000000000000000000000
χ8888-8-800-4-400-4-444442000002-2-20000−6i6i6i−6i000000000000000000000000000000000000000000000000000000000
χ898-8-8800-4-48-844-444-4200000-2-22-44-4422-2-2000000000000000000000000000000000000000000000000000000000
χ908-8-8800-4-4-8844-444-4200000-2-224-44-4-2-222000000000000000000000000000000000000000000000000000000000

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