Finite Group Databasebeta

← Group #11775187

Character table — Group #11775187

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order1222223344666666346666666121212121212121266881212121224242424242424242424242424242424444444444444444444121212121212121241212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-11-11-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-11-11-1-1-1-11111-1-11-11-1-1
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
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
χ611111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-11-1111
χ711111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-11111-11-11-111
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
χ91111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-11-1-11ii−i−iii−i−i-1-111-1i−i
χ101111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-1-1-1-11111-1-1ii−i−i−i−iii1-1-111−ii
χ111111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i-1-1-1-111-1-111−i−iiiii−i−i111-1-1−ii
χ121111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii1111-1-1-111-1−i−iii−i−iii-11-1-11i−i
χ131111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i1111-1-1-111-1ii−i−iii−i−i-11-1-11−ii
χ141111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii-1-1-1-111-1-111ii−i−i−i−iii111-1-1i−i
χ151111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-1-1-1-11111-1-1−i−iiiii−i−i1-1-111i−i
χ161111-1-111-1-111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1111-1-11-1-11−i−iii−i−iii-1-111-1−ii
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
χ192222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000222200000002020000-1-1-1-100-10-100
χ202222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000-20-2000011110010100
χ212222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-2111111000022220000000-20-20000-1-1-1-10010100
χ222222222-1222-12-12-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-21111110000-2-2-2-200000002020000111100-10-100
χ23222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1222200000000002020-1-1-1-100000-10-1000
χ24222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-20000000000-20-20111100000101000
χ25222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-2111122220000000000-20-20-1-1-1-100000101000
χ26222222-1222-12-12-12-12-12-1-1-1-12-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-21111-2-2-2-200000000002020111100000-10-1000
χ272222-2-222222222222-2-2-2222-2-222222222-2-200-2-2-2-200000000000000000000000022-2-222000000000000-2000000
χ282222-2-222222222222-2-2-2222-2-222222222-2-200-2-2-2-2000000000000000000000000-2-222-2-20000000000002000000
χ292222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-2111111112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii00002i2i−2i−2i0000000-2020000−i−iii00-10100
χ302222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-2111111112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000−2i−2i2i2i000000020-20000ii−i−i0010-100
χ312222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-211111111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i00002i2i−2i−2i000000020-20000−i−iii0010-100
χ322222-2-22-1-2-22-12-12-1-12-21-1-1-1-21-2-211111111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000−2i−2i2i2i0000000-2020000ii−i−i00-10100
χ332222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-21111112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii2i2i−2i−2i000000000020-20−i−iii0000010-1000
χ342222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-21111112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii−2i−2i2i2i0000000000-2020ii−i−i00000-101000
χ352222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-2111111−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i2i2i−2i−2i0000000000-2020−i−iii00000-101000
χ362222-2-2-12-2-2-12-12-12-121-2-1-1-11-211-2-2111111−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i−2i−2i2i2i000000000020-20ii−i−i0000010-1000
χ372-2-2200222i−2i-2-222-2-220002-2-2002i−2i2i−2i2i2i−2i−2i0000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i2i−2i002-200001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000
χ382-2-2200222i−2i-2-222-2-220002-2-2002i−2i2i−2i2i2i−2i−2i0000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i−2i2i00-2200001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000
χ392-2-2200222i−2i-2-222-2-220002-2-2002i−2i2i−2i2i2i−2i−2i000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i−2i2i00-220000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000
χ402-2-2200222i−2i-2-222-2-220002-2-2002i−2i2i−2i2i2i−2i−2i000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i2i−2i002-20000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000
χ412-2-220022−2i2i-2-222-2-220002-2-200−2i2i−2i2i−2i−2i2i2i0000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i−2i2i002-200001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000
χ422-2-220022−2i2i-2-222-2-220002-2-200−2i2i−2i2i−2i−2i2i2i0000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i2i−2i00-2200001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000
χ432-2-220022−2i2i-2-222-2-220002-2-200−2i2i−2i2i−2i−2i2i2i000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i2i−2i00-220000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000
χ442-2-220022−2i2i-2-222-2-220002-2-200−2i2i−2i2i−2i−2i2i2i000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i−2i2i002-20000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000
χ454444444-2-4-44-24-24-2-2-44-2-2-2-24-2-4-4222222-2-200-42220000000000000000000000000000000000000000000000000
χ46444444-24-4-4-24-24-24-2-4-24-2-2-2-2422-4-42222-2-2002-4220000000000000000000000000000000000000000000000000
χ47444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-211111144-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ48444444-2-244-2-2-2-2-2-214-2-2111-2-2-2-2-2-2111111-4-4-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ49444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222-1-1-1-1110022-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ50444444-2-2-4-4-2-2-2-2-2-21-4-2-2111-2-22222-1-1-1-1110022-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ514444-4-44-2444-24-24-2-2-4-42-2-2-2-4244-2-2-2-2-2-22200-42220000000000000000000000000000000000000000000000000
χ524444-4-4-2444-24-24-24-2-42-4-2-2-22-4-2-244-2-2-2-222002-4220000000000000000000000000000000000000000000000000
χ534444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-21111-1-10022-1-1000033-3-30000-3-333000000000000000000000000000000000
χ544444-4-4-2-244-2-2-2-2-2-21-42211122-2-2-2-21111-1-10022-1-10000-3-333000033-3-3000000000000000000000000000000000
χ554444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-1-1-1-1-1-14i−4i-2-211−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000000
χ564444-4-4-2-2-4-4-2-2-2-2-2-21422111222222-1-1-1-1-1-1−4i4i-2-2112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000000
χ5744-4-4004400-4-4-4-4444000-4-44000000000000000000000000000000000000000000004i−4i000000000000000000000
χ5844-4-4004400-4-4-4-4444000-4-4400000000000000000000000000000000000000000000−4i4i000000000000000000000
χ594-44-44-4440044-4-4-4-4404-4-44-4-44000000004-40000000000000000000000000000000000000000000000000000000
χ604-44-44-44-2004-2-42-42-20422-22-4-200000000-22000000006−66−66−6006−66−66−6000000000000000000000000000000000
χ614-44-44-44-2004-2-42-42-20422-22-4-200000000-2200000000−66−66−6600−66−66−66000000000000000000000000000000000
χ624-44-44-4-2400-242-42-4-20-2-42-222400000000-22000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000000000000
χ634-44-44-4-2400-242-42-4-20-2-42-222400000000-22000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000000000000
χ644-44-44-4-2-200-2-2222210-22-11-12-200003i−3i3i−3i1-100003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ654-44-44-4-2-200-2-2222210-22-11-12-200003i−3i3i−3i1-100003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ664-44-44-4-2-200-2-2222210-22-11-12-20000−3i3i−3i3i1-10000−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ674-44-44-4-2-200-2-2222210-22-11-12-20000−3i3i−3i3i1-10000−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ684-44-4-44440044-4-4-4-440-44-44-44-400000000-440000000000000000000000000000000000000000000000000000000
χ694-44-4-444-2004-2-42-42-20-4-22-2242000000002-200000000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ704-44-4-444-2004-2-42-42-20-4-22-2242000000002-200000000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ714-44-4-44-2400-242-42-4-20242-22-2-4000000002-20000006−6006−6−66−6600−666−6000000000000000000000000000000000
χ724-44-4-44-2400-242-42-4-20242-22-2-4000000002-2000000−6600−666−66−6006−6−66000000000000000000000000000000000
χ734-44-4-44-2-200-2-22222102-2-11-1-2200003i−3i3i−3i-110000−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ744-44-4-44-2-200-2-22222102-2-11-1-2200003i−3i3i−3i-110000−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ754-44-4-44-2-200-2-22222102-2-11-1-220000−3i3i−3i3i-1100003i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ764-44-4-44-2-200-2-22222102-2-11-1-220000−3i3i−3i3i-1100003i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ774-4-44004-24i−4i-424-2-42-2000-222004i−4i−2i2i−2i−2i2i2i00000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000−1−i1+i−1+i1−i0000000
χ784-4-44004-24i−4i-424-2-42-2000-222004i−4i−2i2i−2i−2i2i2i0000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000001+i−1−i1−i−1+i0000000
χ794-4-44004-2−4i4i-424-2-42-2000-22200−4i4i2i−2i2i2i−2i−2i00000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000−1+i1−i−1−i1+i0000000
χ804-4-44004-2−4i4i-424-2-42-2000-22200−4i4i2i−2i2i2i−2i−2i0000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000001−i−1+i1+i−1−i0000000
χ814-4-4400-244i−4i2-4-242-4-2000-22200−2i2i4i−4i−2i−2i2i2i0000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000−1+i1−i−1−i1+i00000000000
χ824-4-4400-244i−4i2-4-242-4-2000-22200−2i2i4i−4i−2i−2i2i2i000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000001−i−1+i1+i−1−i00000000000
χ834-4-4400-24−4i4i2-4-242-4-2000-222002i−2i−4i4i2i2i−2i−2i0000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000−1−i1+i−1+i1−i00000000000
χ844-4-4400-24−4i4i2-4-242-4-2000-222002i−2i−4i4i2i2i−2i−2i000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000001+i−1−i1−i−1+i00000000000
χ8588-8-8008-400-84-848-4-400044-40000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-48004-84-8-48-400044-40000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-4-4004444-4-42000-2-220000006-6-66000000000000000000000000000000000000000000000000000000000
χ8888-8-800-4-4004444-4-42000-2-22000000-666-6000000000000000000000000000000000000000000000000000000000
χ898-8-8800-4-48i−8i44-4-44420002-2-200−4i4i−4i4i2i2i−2i−2i000000000000000000000000000000000000000000000000000000000
χ908-8-8800-4-4−8i8i44-4-44420002-2-2004i−4i4i−4i−2i−2i2i2i000000000000000000000000000000000000000000000000000000000

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