Finite Group Databasebeta

← Group #11868769

Character table — Group #11868769

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424444444442244444444121212121212121241212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-11-11-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-11-11-1-111-1-111-1-11-11-1-1
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
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
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-11-1111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-11-1-1-111-1-111-11-11-111
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
χ91111111-1-111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111111-1-1-1-1-11-1-111-1
χ101111111-1-111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-1-1-11
χ111111111-1-111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-11-1-111-11
χ121111111-1-111111111-111111-1-1-1-11111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-11111-1-111-11-1
χ131111111-1-111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-111-11111-1-1-1-1-1-111-1-11
χ141111111-1-111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111-1-1111-1
χ151111111-1-111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11-1
χ161111111-1-111111111-111111-1-1-1-1111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11-1-11-1-1-1-11111-11-1-11-11
χ17222222-222-22222222-2222-2-22222-2-2-2-2-2-200-2-222-2-200000000000000000000000022-2-222000000000000-2000000
χ18222222-222-22222222-2222-2-22222-2-2-2-2-2-200-2-222-2-2000000000000000000000000-2-222-2-20000000000002000000
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
χ2122222-1222222-1-12-1-12-1-1-12-122-1-1-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100220022000000020200-1-100-1-100-10-100
χ2222222-1222222-1-12-1-12-1-1-12-122-1-1-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100-2-200-2-20000000-20-2001100110010100
χ2322222-1222222-1-12-1-12-1-1-12-122-1-1-1-12-1-1-1-2-22-1-1-1-1-1-2-2111111-2-2111111002200220000000-20-200-1-100-1-10010100
χ2422222-1222222-1-12-1-12-1-1-12-122-1-1-1-12-1-1-1-2-22-1-1-1-1-1-2-2111111-2-211111100-2-200-2-200000002020011001100-10-100
χ2522222-12-2-2222-1-12-1-1-2-1-1-12-1-2-211-1-12-1-1-12-2-21111122-1-1-1-1-1-1-2-2111111002200-2-20000000-20200-1-100110010-100
χ2622222-12-2-2222-1-12-1-1-2-1-1-12-1-2-211-1-12-1-1-12-2-21111122-1-1-1-1-1-1-2-211111100-2-20022000000020-2001100-1-100-10100
χ2722222-12-2-2222-1-12-1-1-2-1-1-12-1-2-211-1-12-1-1-1-22-211111-2-211111122-1-1-1-1-1-1002200-2-2000000020-200-1-1001100-10100
χ2822222-12-2-2222-1-12-1-1-2-1-1-12-1-2-211-1-12-1-1-1-22-211111-2-211111122-1-1-1-1-1-100-2-200220000000-202001100-1-10010-100
χ292222-122222-1-122-12-12-1-1-1-12-1-122-1-1-12-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1220022000000002020-1-100-1-1000-10-1000
χ302222-122222-1-122-12-12-1-1-1-12-1-122-1-1-12-1-122-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2-200000000-20-20110011000101000
χ312222-122222-1-122-12-12-1-1-1-12-1-122-1-1-12-1-1-2-2-12-1-1-1-111-2-2111111-2-2111122002200000000-20-20-1-100-1-1000101000
χ322222-122222-1-122-12-12-1-1-1-12-1-122-1-1-12-1-1-2-2-12-1-1-1-111-2-2111111-2-21111-2-200-2-2000000002020110011000-10-1000
χ332222-122-2-22-1-122-12-1-2-1-1-1-1211-2-2-1-1-12-1-12-21-21111-1-122-1-1-1-111-2-211112200-2-20000000020-20-1-10011000-101000
χ342222-122-2-22-1-122-12-1-2-1-1-1-1211-2-2-1-1-12-1-12-21-21111-1-122-1-1-1-111-2-21111-2-2002200000000-20201100-1-100010-1000
χ352222-122-2-22-1-122-12-1-2-1-1-1-1211-2-2-1-1-12-1-1-221-2111111-2-21111-1-122-1-1-1-12200-2-200000000-2020-1-1001100010-1000
χ362222-122-2-22-1-122-12-1-2-1-1-1-1211-2-2-1-1-12-1-1-221-2111111-2-21111-1-122-1-1-1-1-2-200220000000020-201100-1-1000-101000
χ3722-2-222200-22-22-2-2-2202-2-222000022-2-2-2-20000000000000000000000002-22-200002-22-20000002-22-200000000000
χ3822-2-222200-22-22-2-2-2202-2-222000022-2-2-2-20000000000000000000000002-2-220000-22-220000002-2-2200000000000
χ3922-2-222200-22-22-2-2-2202-2-222000022-2-2-2-2000000000000000000000000-222-20000-22-22000000-222-200000000000
χ4022-2-222200-22-22-2-2-2202-2-222000022-2-2-2-2000000000000000000000000-22-2200002-22-2000000-22-2200000000000
χ4122-2-222-20022-22-2-2-2202-2-2-2-20000-2-2222200000000000000000000000000002i−2i2i−2i2-2-2200000000002i−2i2i−2i0000000
χ4222-2-222-20022-22-2-2-2202-2-2-2-20000-2-2222200000000000000000000000000002i−2i−2i2i-222-200000000002i−2i−2i2i0000000
χ4322-2-222-20022-22-2-2-2202-2-2-2-20000-2-222220000000000000000000000000000−2i2i2i−2i-222-20000000000−2i2i2i−2i0000000
χ4422-2-222-20022-22-2-2-2202-2-2-2-20000-2-222220000000000000000000000000000−2i2i−2i2i2-2-220000000000−2i2i−2i2i0000000
χ4544444-2-444-444-2-24-2-2-4-2-2-2-4244-2-222-422200-42-2-2220000000000000000000000000000000000000000000000000
χ4644444-2-4-4-4-444-2-24-2-24-2-2-2-42-4-42222-4222004-222-2-20000000000000000000000000000000000000000000000000
χ474444-24-444-4-2-244-24-2-4-2-2-22-4-2-244222-422002-4-2-2220000000000000000000000000000000000000000000000000
χ484444-24-4-4-4-4-2-244-24-24-2-2-22-422-4-4222-42200-2422-2-20000000000000000000000000000000000000000000000000
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
χ514444-2-24-4-44-2-2-2-2-2-21-4111-2-2222211-2-2114-422-1-1-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ524444-2-24-4-44-2-2-2-2-2-21-4111-2-2222211-2-211-4422-1-1-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ534444-2-2-444-4-2-2-2-2-2-21-411122-2-2-2-2-1-122-1-1002211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ544444-2-2-444-4-2-2-2-2-2-21-411122-2-2-2-2-1-122-1-1002211-1-10000−3i−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
χ5744-4-44-2400-44-4-22-42-20-2224-20000-2-2-4222000000000000000000000000004-40000000000000000-2200000000000
χ5844-4-44-2400-44-4-22-42-20-2224-20000-2-2-422200000000000000000000000000-4400000000000000002-200000000000
χ5944-4-44-2-40044-4-22-42-20-222-420000224-2-2-20000000000000000000000000000004i−4i0000000000000000−2i2i0000000
χ6044-4-44-2-40044-4-22-42-20-222-420000224-2-2-2000000000000000000000000000000−4i4i00000000000000002i−2i0000000
χ6144-4-4-24400-4-224-42-4-20-222-240000-2-22-4220000000000000000000000004-40000000000000000-220000000000000
χ6244-4-4-24400-4-224-42-4-20-222-240000-2-22-422000000000000000000000000-4400000000000000002-20000000000000
χ6344-4-4-24-4004-224-42-4-20-2222-4000022-24-2-200000000000000000000000000004i−4i0000000000000000−2i2i000000000
χ6444-4-4-24-4004-224-42-4-20-2222-4000022-24-2-20000000000000000000000000000−4i4i00000000000000002i−2i000000000
χ654-44-4440000-44-44-4-440-44-40000000000000000000000000000000000000000000000004-40000000000000000000
χ664-44-4440000-44-44-4-440-44-4000000000000000000000000000000000000000000000000-440000000000000000000
χ674-4-444404i−4i0-4-4-4-44440-4-44004i−4i4i−4i00000000004i−4i000000000000000000000000000000000000000000000000000
χ684-4-44440−4i4i0-4-4-4-44440-4-4400−4i4i−4i4i0000000000−4i4i000000000000000000000000000000000000000000000000000
χ694-4-444-204i−4i0-4-4224-2-2022-2004i−4i−2i2i0000000000−2i2i00006−66−66−600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ704-4-444-204i−4i0-4-4224-2-2022-2004i−4i−2i2i0000000000−2i2i0000−66−66−6600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ714-4-444-20−4i4i0-4-4224-2-2022-200−4i4i2i−2i00000000002i−2i00006−66−66−600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ724-4-444-20−4i4i0-4-4224-2-2022-200−4i4i2i−2i00000000002i−2i0000−66−66−6600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ734-4-44-2404i−4i022-4-4-24-2022-200−2i2i4i−4i0000000000−2i2i00i6−i600i6−i6−i6i66−600−666−6000000000000000000000000000000000
χ744-4-44-2404i−4i022-4-4-24-2022-200−2i2i4i−4i0000000000−2i2i00−i6i600−i6i6i6−i6−66006−6−66000000000000000000000000000000000
χ754-4-44-240−4i4i022-4-4-24-2022-2002i−2i−4i4i00000000002i−2i00i6−i600i6−i6−i6i6−66006−6−66000000000000000000000000000000000
χ764-4-44-240−4i4i022-4-4-24-2022-2002i−2i−4i4i00000000002i−2i00−i6i600−i6i6i6−i66−600−666−6000000000000000000000000000000000
χ774-4-44-2-204i−4i02222-2-210-1-1100−2i2i−2i2i3i−3i003i−3i0000i−i3-3i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ784-4-44-2-204i−4i02222-2-210-1-1100−2i2i−2i2i3i−3i003i−3i0000i−i3-3−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ794-4-44-2-204i−4i02222-2-210-1-1100−2i2i−2i2i−3i3i00−3i3i0000i−i-33i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ804-4-44-2-204i−4i02222-2-210-1-1100−2i2i−2i2i−3i3i00−3i3i0000i−i-33−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ814-4-44-2-20−4i4i02222-2-210-1-11002i−2i2i−2i3i−3i003i−3i0000−ii-33i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ824-4-44-2-20−4i4i02222-2-210-1-11002i−2i2i−2i3i−3i003i−3i0000−ii-33−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ834-4-44-2-20−4i4i02222-2-210-1-11002i−2i2i−2i−3i3i00−3i3i0000−ii3-3i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ844-4-44-2-20−4i4i02222-2-210-1-11002i−2i2i−2i−3i3i00−3i3i0000−ii3-3−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ8588-8-8-4-4800-8-44-4444202-2-2-4-400002244-2-2000000000000000000000000000000000000000000000000000000000
χ8688-8-8-4-4-8008-44-4444202-2-2440000-2-2-4-422000000000000000000000000000000000000000000000000000000000
χ878-88-88-40000-884-4-84-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-8-4800004-4-884-8-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8-4-400004-44-44420-22-20000006i−6i00−6i6i000000000000000000000000000000000000000000000000000000000
χ908-88-8-4-400004-44-44420-22-2000000−6i6i006i−6i000000000000000000000000000000000000000000000000000000000

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