Finite Group Databasebeta

← Group #11775908

Character table — Group #11775908

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444448888888888121212121212121216161616161616161818181818182424242424242424242424242424242424242424367272
order1222334444666666346661212121212121212441212121212121212888888881212121212121212224444888824242424242424242424242424242424444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1
χ611111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111
χ711111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111
χ811111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111-1-1
χ9111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1ii−i−iii−i−i11-1-111-1-11111-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i-11-1
χ10111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1ii−i−i−i−iii11-1-111-1-1-1-1-1-111i−i−iiii−i−iii−i−i−i−iii−i−iii1-11
χ11111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1−i−iiiii−i−i11-1-111-1-1-1-1-1-111−iii−i−i−iii−i−iiiii−i−iii−i−i1-11
χ12111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1−i−iii−i−iii11-1-111-1-11111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii-11-1
χ13111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1ii−i−iii−i−i-1-111-1-1111111-1-1−ii−iiii−i−i−i−iiiii−i−i−i−iii-1-11
χ14111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1ii−i−i−i−iii-1-111-1-111-1-1-1-111−iii−iii−i−i−i−iii−i−iiiii−i−i11-1
χ15111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1−i−iiiii−i−i-1-111-1-111-1-1-1-111i−i−ii−i−iiiii−i−iii−i−i−i−iii11-1
χ16111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1−i−iii−i−iii-1-111-1-1111111-1-1i−ii−i−i−iiiii−i−i−i−iiiii−i−i-1-11
χ1722222222-2-22222222-22222222-2-2-2-200-2-2-2-222-2-2000000000000000022-2-22200000000000000000000-200
χ1822222222-2-22222222-22222222-2-2-2-200-2-2-2-222-2-20000000000000000-2-222-2-200000000000000000000200
χ19222222-2-2222222222-2222-2-2-2-2222200-2-2-2-2-2-222000000000000000022-2-2-2-200000000000000000000200
χ20222222-2-2222222222-2222-2-2-2-2222200-2-2-2-2-2-2220000000000000000-2-2222200000000000000000000-200
χ2122222-122222-122-1-1-12-1-1-122-1-122-1-1222-1-1-1-1-1-1-1000022222-12-1-1-1-1-1000000002200000000-1-1-1-1-1-1-1-1000
χ2222222-122222-122-1-1-12-1-1-122-1-122-1-1222-1-1-1-1-1-1-10000-2-2-2-22-12-1-1-1-1-100000000-2-20000000011111111000
χ2322222-122222-122-1-1-12-1-1-122-1-122-1-1-2-22-1-1-1-1-1-1-100002222-21-21111100000000-2-200000000-1-1-1-11111000
χ2422222-122222-122-1-1-12-1-1-122-1-122-1-1-2-22-1-1-1-1-1-1-10000-2-2-2-2-21-2111110000000022000000001111-1-1-1-1000
χ2522222-1-2-2-2-22-122-1-1-12-1-1-1-2-211-2-2112-22-1-1-1111100002i2i−2i−2i2-1-21-1-111000000002i−2i00000000−i−iii−i−iii000
χ2622222-1-2-2-2-22-122-1-1-12-1-1-1-2-211-2-2112-22-1-1-111110000−2i−2i2i2i2-1-21-1-11100000000−2i2i00000000ii−i−iii−i−i000
χ2722222-1-2-2-2-22-122-1-1-12-1-1-1-2-211-2-211-222-1-1-1111100002i2i−2i−2i-212-111-1-100000000−2i2i00000000−i−iiiii−i−i000
χ2822222-1-2-2-2-22-122-1-1-12-1-1-1-2-211-2-211-222-1-1-111110000−2i−2i2i2i-212-111-1-1000000002i−2i00000000ii−i−i−i−iii000
χ292222-122222-12-1-122-12-1-1-1-1-122-1-12222-12-1-1-1-1-1-122220000-12-12-1-1-1-10000002200-1-1-1-1-1-1-1-100000000000
χ302222-122222-12-1-122-12-1-1-1-1-122-1-12222-12-1-1-1-1-1-1-2-2-2-20000-12-12-1-1-1-1000000-2-2001111111100000000000
χ312222-122222-12-1-122-12-1-1-1-1-122-1-122-2-2-12-1-1-1-1-1-1222200001-21-21111000000-2-200-1-1-1-1111100000000000
χ322222-122222-12-1-122-12-1-1-1-1-122-1-122-2-2-12-1-1-1-1-1-1-2-2-2-200001-21-2111100000022001111-1-1-1-100000000000
χ332222-12-2-2-2-2-12-1-122-12-1-1-111-2-211-2-22-2-12-1-111112i2i−2i−2i0000-121-2-1-1110000002i−2i00−i−iii−i−iii00000000000
χ342222-12-2-2-2-2-12-1-122-12-1-1-111-2-211-2-22-2-12-1-11111−2i−2i2i2i0000-121-2-1-111000000−2i2i00ii−i−iii−i−i00000000000
χ352222-12-2-2-2-2-12-1-122-12-1-1-111-2-211-2-2-22-12-1-111112i2i−2i−2i00001-2-1211-1-1000000−2i2i00−i−iiiii−i−i00000000000
χ362222-12-2-2-2-2-12-1-122-12-1-1-111-2-211-2-2-22-12-1-11111−2i−2i2i2i00001-2-1211-1-10000002i−2i00ii−i−i−i−iii00000000000
χ372-22-222002i−2i-2-22-22-220-22-200002i−2i2i−2i000000002i−2i1+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000002i−2i2-200001+i−1−i1−i−1+i00001−i−1+i1+i−1−i0000000
χ382-22-222002i−2i-2-22-22-220-22-200002i−2i2i−2i000000002i−2i1+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000−2i2i-2200001+i−1−i1−i−1+i0000−1+i1−i−1−i1+i0000000
χ392-22-222002i−2i-2-22-22-220-22-200002i−2i2i−2i000000002i−2i−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000−2i2i-220000−1−i1+i−1+i1−i00001−i−1+i1+i−1−i0000000
χ402-22-222002i−2i-2-22-22-220-22-200002i−2i2i−2i000000002i−2i−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000002i−2i2-20000−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i0000000
χ412-22-22200−2i2i-2-22-22-220-22-20000−2i2i−2i2i00000000−2i2i1−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000−2i2i2-200001−i−1+i1+i−1−i00001+i−1−i1−i−1+i0000000
χ422-22-22200−2i2i-2-22-22-220-22-20000−2i2i−2i2i00000000−2i2i1−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000002i−2i-2200001−i−1+i1+i−1−i0000−1−i1+i−1+i1−i0000000
χ432-22-22200−2i2i-2-22-22-220-22-20000−2i2i−2i2i00000000−2i2i−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000002i−2i-220000−1+i1−i−1−i1+i00001+i−1−i1−i−1+i0000000
χ442-22-22200−2i2i-2-22-22-220-22-20000−2i2i−2i2i00000000−2i2i−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000−2i2i2-20000−1+i1−i−1−i1+i0000−1−i1+i−1+i1−i0000000
χ4544444-244-4-44-244-2-2-2-4-2-2-244-2-2-4-42200-4222-2-222000000000000000000000000000000000000000000000
χ4644444-2-4-4444-244-2-2-2-4-2-2-2-4-42244-2-200-422222-2-2000000000000000000000000000000000000000000000
χ474444-2444-4-4-24-2-244-2-4-2-2-2-2-24422-4-4002-422-2-222000000000000000000000000000000000000000000000
χ484444-24-4-444-24-2-244-2-4-2-2-222-4-4-2-244002-42222-2-2000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-244-2-211111100000000-2-2-2-2111100000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-4-4-2-2111111000000002222-1-1-1-100000000000000000000000000000
χ514444-2-244-4-4-2-2-2-2-2-21-4111-2-2-2-222220022-1-111-1-10000000000003-33-300000000000000000000000000000
χ524444-2-244-4-4-2-2-2-2-2-21-4111-2-2-2-222220022-1-111-1-1000000000000-33-3300000000000000000000000000000
χ534444-2-2-4-444-2-2-2-2-2-21-41112222-2-2-2-20022-1-1-1-1110000000000003-3-3300000000000000000000000000000
χ544444-2-2-4-444-2-2-2-2-2-21-41112222-2-2-2-20022-1-1-1-111000000000000-333-300000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-214111222222224-4-2-211-1-1-1-100000000-2-22211-1-100000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-21411122222222-44-2-211-1-1-1-10000000022-2-2-1-11100000000000000000000000000000
χ5744-4-444000044-4-4-4-4404-4-400000000000000000000000000000000004-4000000000000000000000000000
χ5844-4-444000044-4-4-4-4404-4-40000000000000000000000000000000000-44000000000000000000000000000
χ594-44-44-2004i−4i-424-4-22-202-2200004i−4i−2i2i00000000−2i2i00002−2i−2+2i2+2i−2−2i00000000000000000000000000−1+i1−i−1−i1+i0000000
χ604-44-44-2004i−4i-424-4-22-202-2200004i−4i−2i2i00000000−2i2i0000−2+2i2−2i−2−2i2+2i000000000000000000000000001−i−1+i1+i−1−i0000000
χ614-44-44-200−4i4i-424-4-22-202-220000−4i4i2i−2i000000002i−2i00002+2i−2−2i2−2i−2+2i00000000000000000000000000−1−i1+i−1+i1−i0000000
χ624-44-44-200−4i4i-424-4-22-202-220000−4i4i2i−2i000000002i−2i0000−2−2i2+2i−2+2i2−2i000000000000000000000000001+i−1−i1−i−1+i0000000
χ634-44-4-24004i−4i2-4-224-4-202-220000−2i2i4i−4i00000000−2i2i2+2i−2−2i2−2i−2+2i0000000000000000000000−1−i1+i−1+i1−i000000000000000
χ644-44-4-24004i−4i2-4-224-4-202-220000−2i2i4i−4i00000000−2i2i−2−2i2+2i−2+2i2−2i00000000000000000000001+i−1−i1−i−1+i000000000000000
χ654-44-4-2400−4i4i2-4-224-4-202-2200002i−2i−4i4i000000002i−2i2−2i−2+2i2+2i−2−2i0000000000000000000000−1+i1−i−1−i1+i000000000000000
χ664-44-4-2400−4i4i2-4-224-4-202-2200002i−2i−4i4i000000002i−2i−2+2i2−2i−2−2i2+2i00000000000000000000001−i−1+i1+i−1−i000000000000000
χ674-4-44444i−4i00-4-4-44-4440-4-444i−4i4i−4i00000000004i−4i00000000000000000000000000000000000000000000000
χ684-4-4444−4i4i00-4-4-44-4440-4-44−4i4i−4i4i0000000000−4i4i00000000000000000000000000000000000000000000000
χ694-4-444-24i−4i00-42-442-2-2022-24i−4i−2i2i0000000000−2i2i0000000000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000
χ704-4-444-24i−4i00-42-442-2-2022-24i−4i−2i2i0000000000−2i2i0000000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000
χ714-4-444-2−4i4i00-42-442-2-2022-2−4i4i2i−2i00000000002i−2i0000000000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000
χ724-4-444-2−4i4i00-42-442-2-2022-2−4i4i2i−2i00000000002i−2i0000000000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000
χ734-4-44-244i−4i002-42-2-44-2022-2−2i2i4i−4i0000000000−2i2i00000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000
χ744-4-44-244i−4i002-42-2-44-2022-2−2i2i4i−4i0000000000−2i2i00000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000
χ754-4-44-24−4i4i002-42-2-44-2022-22i−2i−4i4i00000000002i−2i00000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000
χ764-4-44-24−4i4i002-42-2-44-2022-22i−2i−4i4i00000000002i−2i00000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000
χ7788-8-88-400008-4-8-844-40-444000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-480000-4844-8-8-40-444000000000000000000000000000000000000000000000000000000000000000
χ7988-8-8-4-40000-4-44444202-2-20000000000006-60000000000000000000000000000000000000000000000000
χ8088-8-8-4-40000-4-44444202-2-2000000000000-660000000000000000000000000000000000000000000000000
χ818-88-8-4-4008i−8i44-44-4420-22-20000−4i4i−4i4i000000002i−2i000000000000000000000000000000000000000000000
χ828-88-8-4-400−8i8i44-44-4420-22-200004i−4i4i−4i00000000−2i2i000000000000000000000000000000000000000000000
χ838-8-88-4-48i−8i00444-44-420-2-22−4i4i−4i4i00000000002i−2i00000000000000000000000000000000000000000000000
χ848-8-88-4-4−8i8i00444-44-420-2-224i−4i4i−4i0000000000−2i2i00000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.