Finite Group Databasebeta

← Group #11776302

Character table — Group #11776302

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424888888882244444444242424242424242441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1
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
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-111
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
χ9111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1111-1-11-11-1ii−i−iii−i−i-11-11-1i−i
χ10111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-1-1-1-1111-1-11ii−i−i−i−iii11-1-11−ii
χ11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i-1-1-1-111-111-1−i−iiiii−i−i1-111-1−ii
χ12111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii1111-1-1-11-11−i−iii−i−iii-1-11-11i−i
χ13111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i1111-1-1-11-11ii−i−iii−i−i-1-11-11−ii
χ14111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii-1-1-1-111-111-1ii−i−i−i−iii1-111-1i−i
χ15111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-1-1-1-1111-1-11−i−iiiii−i−i11-1-11i−i
χ16111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1111-1-11-11-1−i−iii−i−iii-11-11-1−ii
χ172222222-2-222222222-2222-2-222222222-2-200-2-2-2-2-2-200000000000000000000000022-2-222000000000000-2000000
χ182222222-2-222222222-2222-2-222222222-2-200-2-2-2-2-2-2000000000000000000000000-2-222-2-20000000000002000000
χ19222222-222-22222222-222222-2-2-2-2-2-2-2-22200-2-2-2-22200000000000000000000000022-2-2-2-20000000000002000000
χ20222222-222-22222222-222222-2-2-2-2-2-2-2-22200-2-2-2-222000000000000000000000000-2-22222000000000000-2000000
χ2122222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000222200000000220000-1-1-1-1000-1-100
χ2222222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-200000000-2-2000011110001100
χ2322222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-1-2-22-1-1-1-1-1-2-2111111-2-21111110000222200000000-2-20000-1-1-1-10001100
χ2422222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-1-2-22-1-1-1-1-1-2-2111111-2-21111110000-2-2-2-2000000002200001111000-1-100
χ2522222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-212i−2i2-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00002i2i−2i−2i000000002-20000−i−iii000-1100
χ2622222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-212i−2i2-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii0000−2i−2i2i2i00000000-220000ii−i−i0001-100
χ2722222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-21−2i2i2-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00002i2i−2i−2i00000000-220000−i−iii0001-100
χ2822222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-21−2i2i2-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000−2i−2i2i2i000000002-20000ii−i−i000-1100
χ292222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-1222-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1222200000000002200-1-1-1-100000-1-10000
χ302222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-1222-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-20000000000-2-200111100000110000
χ312222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-12-2-2-12-1-1-1-111-2-2111111-2-2111122220000000000-2-200-1-1-1-100000110000
χ322222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-12-2-2-12-1-1-1-111-2-2111111-2-21111-2-2-2-200000000002200111100000-1-10000
χ332222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-22i−2i-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii2i2i−2i−2i00000000002-200−i−iii00000-110000
χ342222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-22i−2i-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii−2i−2i2i2i0000000000-2200ii−i−i000001-10000
χ352222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-2−2i2i-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i2i2i−2i−2i0000000000-2200−i−iii000001-10000
χ362222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-2−2i2i-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i−2i−2i2i2i00000000002-200ii−i−i00000-110000
χ372-2-2222200-2-2-2-2-222202-2-2002222-2-2-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i22-2002-20000−i2i2−i2i2−i2i2−i2i20000000
χ382-2-2222200-2-2-2-2-222202-2-2002222-2-2-2-200000000000000000000000000−i2i2−i2i2i2−i2i2−i2-2200-220000−i2i2−i2i2i2−i2i2−i20000000
χ392-2-2222200-2-2-2-2-222202-2-2002222-2-2-2-200000000000000000000000000i2−i2i2−i2−i2i2−i2i2-2200-220000i2−i2i2−i2−i2i2−i2i20000000
χ402-2-2222200-2-2-2-2-222202-2-2002222-2-2-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i22-2002-20000i2−i2i2−i2i2−i2i2−i20000000
χ412-2-2222-2002-2-2-2-222202-2-200-2-2-2-22222000000000000000000000000002−2−222−2−222-200-2200002−2−222−2−220000000
χ422-2-2222-2002-2-2-2-222202-2-200-2-2-2-22222000000000000000000000000002−2−22−222−2-22002-200002−2−22−222−20000000
χ432-2-2222-2002-2-2-2-222202-2-200-2-2-2-2222200000000000000000000000000−222−22−2−22-22002-20000−222−22−2−220000000
χ442-2-2222-2002-2-2-2-222202-2-200-2-2-2-2222200000000000000000000000000−222−2−222−22-200-220000−222−2−222−20000000
χ4544444-24-4-4444-2-24-2-2-4-2-2-2-424-2-2-24-2-2-2-4200-4222220000000000000000000000000000000000000000000000000
χ4644444-2-444-444-2-24-2-2-4-2-2-24-2-4222-42224-200-4222-2-20000000000000000000000000000000000000000000000000
χ474444-244-4-44-2-244-24-2-4-2-2-22-4-24-2-2-24-2-22-4002-422220000000000000000000000000000000000000000000000000
χ484444-24-444-4-2-244-24-2-4-2-2-2-242-4222-422-24002-422-2-20000000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-214111-2-2-2-211-2-211-2-244-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-214111-2-2-2-211-2-211-2-2-4-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ514444-2-24-4-44-2-2-2-2-2-21-411122-2-211-2-211220022-1-1-1-1000033-3-3000033-3-3000000000000000000000000000000000
χ524444-2-24-4-44-2-2-2-2-2-21-411122-2-211-2-211220022-1-1-1-10000-3-3330000-3-333000000000000000000000000000000000
χ534444-2-2-444-4-2-2-2-2-2-21-4111-2-222-1-122-1-1-2-20022-1-11100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ544444-2-2-444-4-2-2-2-2-2-21-4111-2-222-1-122-1-1-2-20022-1-1110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-2141112222-1-122-1-1224i−4i-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-2141112222-1-122-1-122−4i4i-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000000
χ5744-4-44400004-44-4-4-440-44-400000000000000000000000000000000000000000000004-4000000000000000000000
χ5844-4-44400004-44-4-4-440-44-40000000000000000000000000000000000000000000000-44000000000000000000000
χ594-44-44404-40-44-44-4-440-4-444-400000000-440000004-40000000000000000000000000000000000000000000000000
χ604-44-4440-440-44-44-4-440-4-44-44000000004-4000000-440000000000000000000000000000000000000000000000000
χ614-44-44-204-40-442-2-42-2022-24200000000-4-2000000-22006−66−66−6006−66−66−6000000000000000000000000000000000
χ624-44-44-204-40-442-2-42-2022-24200000000-4-2000000-2200−66−66−6600−66−66−66000000000000000000000000000000000
χ634-44-44-20-440-442-2-42-2022-2-4-200000000420000002-200i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ644-44-44-20-440-442-2-42-2022-2-4-200000000420000002-200−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ654-44-4-2404-402-2-442-4-2022-2-2-40000000024000000-22i6−i600i6−i6−i6i6i6−i600−i6i6i6−i6000000000000000000000000000000000
χ664-44-4-2404-402-2-442-4-2022-2-2-40000000024000000-22−i6i600−i6i6i6−i6−i6i600i6−i6−i6i6000000000000000000000000000000000
χ674-44-4-240-4402-2-442-4-2022-22400000000-2-40000002-26−6006−6−66−66006−6−66000000000000000000000000000000000
χ684-44-4-240-4402-2-442-4-2022-22400000000-2-40000002-2−6600−666−66−600−666−6000000000000000000000000000000000
χ694-44-4-2-204-402-22-22210-1-11-22003i−3i003i−3i2-200003i−3i1-1i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ704-44-4-2-204-402-22-22210-1-11-22003i−3i003i−3i2-200003i−3i1-1−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ714-44-4-2-204-402-22-22210-1-11-2200−3i3i00−3i3i2-20000−3i3i1-1i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ724-44-4-2-204-402-22-22210-1-11-2200−3i3i00−3i3i2-20000−3i3i1-1−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ734-44-4-2-20-4402-22-22210-1-112-2003i−3i003i−3i-220000−3i3i-116−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ744-44-4-2-20-4402-22-22210-1-112-2003i−3i003i−3i-220000−3i3i-11−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ754-44-4-2-20-4402-22-22210-1-112-200−3i3i00−3i3i-2200003i−3i-116−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ764-44-4-2-20-4402-22-22210-1-112-200−3i3i00−3i3i-2200003i−3i-11−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ774-4-444-2400-4-4-4224-2-20-222004-2-2-2-4222000000000000000000000000000000−2i22i2−2i22i200000000000000i2−i2i2−i20000000
χ784-4-444-2400-4-4-4224-2-20-222004-2-2-2-42220000000000000000000000000000002i2−2i22i2−2i200000000000000−i2i2−i2i20000000
χ794-4-444-2-4004-4-4224-2-20-22200-42224-2-2-200000000000000000000000000000022−22−222200000000000000−222−20000000
χ804-4-444-2-4004-4-4224-2-20-22200-42224-2-2-2000000000000000000000000000000−222222−22000000000000002−2−220000000
χ814-4-44-24400-422-4-4-24-20-22200-24-2-22-42200000000000000000000000000−2i22i2−2i22i200000000000000i2−i2i2−i200000000000
χ824-4-44-24400-422-4-4-24-20-22200-24-2-22-422000000000000000000000000002i2−2i22i2−2i200000000000000−i2i2−i2i200000000000
χ834-4-44-24-400422-4-4-24-20-222002-422-24-2-20000000000000000000000000022−22−222200000000000000−222−200000000000
χ844-4-44-24-400422-4-4-24-20-222002-422-24-2-200000000000000000000000000−222222−22000000000000002−2−2200000000000
χ8588-8-88-400008-8-44-84-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-480000-448-84-8-404-44000000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-40000-44-444420-22-200006i−6i00−6i6i00000000000000000000000000000000000000000000000000000000000
χ8888-8-8-4-40000-44-444420-22-20000−6i6i006i−6i00000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-4800-84444-4-4202-2-200-4-42244-2-200000000000000000000000000000000000000000000000000000000000
χ908-8-88-4-4-80084444-4-4202-2-20044-2-2-4-42200000000000000000000000000000000000000000000000000000000000

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