Finite Group Databasebeta

← Group #11775880

Character table — Group #11775880

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444448888888888121212121212121216161616161616161818181818182424242424242424242424242424242424242424367272
order122233444466666634666121212121212121224121212121212121288888888666612121212224444888824242424242424242424242424242424424
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
χ9111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-111-1-1-1-111ii−i−iii−i−i1111-1-1-1-111-1-111i−ii−iii−i−iii−i−iii−i−iii−i−i-1-11
χ10111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-111-1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-111-1-1i−i−iiii−i−iii−i−i−i−iii−i−iii11-1
χ11111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-111-1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-111-1-1−iii−i−i−iii−i−iiiii−i−iii−i−i11-1
χ12111111-1-1-1-111111111111-1-1-1-1-1-1-1-11-111-1-1-1-111−i−iii−i−iii1111-1-1-1-111-1-111−ii−ii−i−iii−i−iii−i−iii−i−iii-1-11
χ13111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111ii−i−iii−i−i-1-1-1-1111111-1-111−ii−iiii−i−i−i−iiiii−i−i−i−iii-11-1
χ14111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111ii−i−i−i−iii-1-1-1-11111-1-111-1-1−iii−iii−i−i−i−iii−i−iiiii−i−i1-11
χ15111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111−i−iiiii−i−i-1-1-1-11111-1-111-1-1i−i−ii−i−iiiii−i−iii−i−i−i−iii1-11
χ16111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111−i−iii−i−iii-1-1-1-1111111-1-111i−ii−i−i−iiiii−i−i−i−iiiii−i−i-11-1
χ1722222222-2-22222222-22222222-2-2-2-200-2-222-2-2-2-200000000000000002222-2-200000000000000000000-200
χ1822222222-2-22222222-22222222-2-2-2-200-2-222-2-2-2-20000000000000000-2-2-2-22200000000000000000000200
χ19222222-2-2222222222-2222-2-2-2-2222200-2-2-2-222-2-2000000000000000022-2-2-2-200000000000000000000200
χ20222222-2-2222222222-2222-2-2-2-2222200-2-2-2-222-2-20000000000000000-2-2222200000000000000000000-200
χ2122222-1222222-1-12-1-12-1-1-122-1-122-1-1222-1-1-1-1-1-1-1000022222-1-1-12-1-1-1000000002200000000-1-1-1-1-1-1-1-1000
χ2222222-1222222-1-12-1-12-1-1-122-1-122-1-1222-1-1-1-1-1-1-10000-2-2-2-22-1-1-12-1-1-100000000-2-20000000011111111000
χ2322222-1222222-1-12-1-12-1-1-122-1-122-1-1-2-22-1-1-1-1-1-1-100002222-2111-211100000000-2-200000000-1-1-1-11111000
χ2422222-1222222-1-12-1-12-1-1-122-1-122-1-1-2-22-1-1-1-1-1-1-10000-2-2-2-2-2111-21110000000022000000001111-1-1-1-1000
χ2522222-1-2-2-2-222-1-12-1-12-1-1-1-2-211-2-2112-22-11111-1-100002i2i−2i−2i2-1-1-1-2111000000002i−2i00000000−i−iii−i−iii000
χ2622222-1-2-2-2-222-1-12-1-12-1-1-1-2-211-2-2112-22-11111-1-10000−2i−2i2i2i2-1-1-1-211100000000−2i2i00000000ii−i−iii−i−i000
χ2722222-1-2-2-2-222-1-12-1-12-1-1-1-2-211-2-211-222-11111-1-100002i2i−2i−2i-21112-1-1-100000000−2i2i00000000−i−iiiii−i−i000
χ2822222-1-2-2-2-222-1-12-1-12-1-1-1-2-211-2-211-222-11111-1-10000−2i−2i2i2i-21112-1-1-1000000002i−2i00000000ii−i−i−i−iii000
χ292222-122222-1-122-12-12-1-1-1-1-122-1-12222-12-1-1-1-1-1-122220000-12-1-1-12-1-10000002200-1-1-1-1-1-1-1-100000000000
χ302222-122222-1-122-12-12-1-1-1-1-122-1-12222-12-1-1-1-1-1-1-2-2-2-20000-12-1-1-12-1-1000000-2-2001111111100000000000
χ312222-122222-1-122-12-12-1-1-1-1-122-1-122-2-2-12-1-1-1-1-1-1222200001-2111-211000000-2-200-1-1-1-1111100000000000
χ322222-122222-1-122-12-12-1-1-1-1-122-1-122-2-2-12-1-1-1-1-1-1-2-2-2-200001-2111-21100000022001111-1-1-1-100000000000
χ332222-12-2-2-2-2-1-122-12-12-1-1-111-2-211-2-22-2-121111-1-12i2i−2i−2i0000-12-1-11-2110000002i−2i00−i−iii−i−iii00000000000
χ342222-12-2-2-2-2-1-122-12-12-1-1-111-2-211-2-22-2-121111-1-1−2i−2i2i2i0000-12-1-11-211000000−2i2i00ii−i−iii−i−i00000000000
χ352222-12-2-2-2-2-1-122-12-12-1-1-111-2-211-2-2-22-121111-1-12i2i−2i−2i00001-211-12-1-1000000−2i2i00−i−iiiii−i−i00000000000
χ362222-12-2-2-2-2-1-122-12-12-1-1-111-2-211-2-2-22-121111-1-1−2i−2i2i2i00001-211-12-1-10000002i−2i00ii−i−i−i−iii00000000000
χ3722-2-222002i−2i2-22-2-2-2202-2-200002i−2i2i−2i0000002i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000002-22i−2i00001+i−1−i1−i−1+i00001−i−1+i1+i−1−i0000000
χ3822-2-222002i−2i2-22-2-2-2202-2-200002i−2i2i−2i0000002i−2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000-22−2i2i00001+i−1−i1−i−1+i0000−1+i1−i−1−i1+i0000000
χ3922-2-222002i−2i2-22-2-2-2202-2-200002i−2i2i−2i0000002i−2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000-22−2i2i0000−1−i1+i−1+i1−i00001−i−1+i1+i−1−i0000000
χ4022-2-222002i−2i2-22-2-2-2202-2-200002i−2i2i−2i0000002i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000002-22i−2i0000−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i0000000
χ4122-2-22200−2i2i2-22-2-2-2202-2-20000−2i2i−2i2i000000−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000002-2−2i2i00001−i−1+i1+i−1−i00001+i−1−i1−i−1+i0000000
χ4222-2-22200−2i2i2-22-2-2-2202-2-20000−2i2i−2i2i000000−2i2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000-222i−2i00001−i−1+i1+i−1−i0000−1−i1+i−1+i1−i0000000
χ4322-2-22200−2i2i2-22-2-2-2202-2-20000−2i2i−2i2i000000−2i2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000-222i−2i0000−1+i1−i−1−i1+i00001+i−1−i1−i−1+i0000000
χ4422-2-22200−2i2i2-22-2-2-2202-2-20000−2i2i−2i2i000000−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000002-2−2i2i0000−1+i1−i−1−i1+i0000−1−i1+i−1+i1−i0000000
χ4544444-244-4-444-2-24-2-2-4-2-2-244-2-2-4-42200-42-2-22222000000000000000000000000000000000000000000000
χ4644444-2-4-44444-2-24-2-2-4-2-2-2-4-42244-2-200-4222-2-222000000000000000000000000000000000000000000000
χ474444-2444-4-4-2-244-24-2-4-2-2-2-2-24422-4-4002-4-2-22222000000000000000000000000000000000000000000000
χ484444-24-4-444-2-244-24-2-4-2-2-222-4-4-2-244002-422-2-222000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-244-2-211111100000000-2-211-2-21100000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-4-4-2-21111110000000022-1-122-1-100000000000000000000000000000
χ514444-2-244-4-4-2-2-2-2-2-21-4111-2-2-2-22222002211-1-1-1-100000000003-3003-300000000000000000000000000000
χ524444-2-244-4-4-2-2-2-2-2-21-4111-2-2-2-22222002211-1-1-1-10000000000-3300-3300000000000000000000000000000
χ534444-2-2-4-444-2-2-2-2-2-21-41112222-2-2-2-20022-1-111-1-100000000003-300-3300000000000000000000000000000
χ544444-2-2-4-444-2-2-2-2-2-21-41112222-2-2-2-20022-1-111-1-10000000000-33003-300000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-214111222222224-4-2-2-1-1-1-11100000000-2-21122-1-100000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-21411122222222-44-2-2-1-1-1-1110000000022-1-1-2-21100000000000000000000000000000
χ5744-4-44-2004i−4i4-4-22-42-20-22200004i−4i−2i2i000000−2i2i0000002−2i−2+2i2+2i−2−2i00000000000000000000000000−1+i1−i−1−i1+i0000000
χ5844-4-44-2004i−4i4-4-22-42-20-22200004i−4i−2i2i000000−2i2i000000−2+2i2−2i−2−2i2+2i000000000000000000000000001−i−1+i1+i−1−i0000000
χ5944-4-44-200−4i4i4-4-22-42-20-2220000−4i4i2i−2i0000002i−2i0000002+2i−2−2i2−2i−2+2i00000000000000000000000000−1−i1+i−1+i1−i0000000
χ6044-4-44-200−4i4i4-4-22-42-20-2220000−4i4i2i−2i0000002i−2i000000−2−2i2+2i−2+2i2−2i000000000000000000000000001+i−1−i1−i−1+i0000000
χ6144-4-4-24004i−4i-224-42-4-20-2220000−2i2i4i−4i000000−2i2i002+2i−2−2i2−2i−2+2i0000000000000000000000−1−i1+i−1+i1−i000000000000000
χ6244-4-4-24004i−4i-224-42-4-20-2220000−2i2i4i−4i000000−2i2i00−2−2i2+2i−2+2i2−2i00000000000000000000001+i−1−i1−i−1+i000000000000000
χ6344-4-4-2400−4i4i-224-42-4-20-22200002i−2i−4i4i0000002i−2i002−2i−2+2i2+2i−2−2i0000000000000000000000−1+i1−i−1−i1+i000000000000000
χ6444-4-4-2400−4i4i-224-42-4-20-22200002i−2i−4i4i0000002i−2i00−2+2i2−2i−2−2i2+2i00000000000000000000001−i−1+i1+i−1−i000000000000000
χ654-44-4444i−4i00-44-44-4-440-44-44i−4i4i−4i000000004i−4i0000000000000000000000000000000000000000000000000
χ664-44-444−4i4i00-44-44-4-440-44-4−4i4i−4i4i00000000−4i4i0000000000000000000000000000000000000000000000000
χ674-44-44-24i−4i00-442-2-42-202-224i−4i−2i2i00000000−2i2i000000000000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000
χ684-44-44-24i−4i00-442-2-42-202-224i−4i−2i2i00000000−2i2i000000000000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000
χ694-44-44-2−4i4i00-442-2-42-202-22−4i4i2i−2i000000002i−2i000000000000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000
χ704-44-44-2−4i4i00-442-2-42-202-22−4i4i2i−2i000000002i−2i000000000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000
χ714-44-4-244i−4i002-2-442-4-202-22−2i2i4i−4i00000000−2i2i0000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000
χ724-44-4-244i−4i002-2-442-4-202-22−2i2i4i−4i00000000−2i2i0000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000
χ734-44-4-24−4i4i002-2-442-4-202-222i−2i−4i4i000000002i−2i0000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000
χ744-44-4-24−4i4i002-2-442-4-202-222i−2i−4i4i000000002i−2i0000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000
χ754-4-44440000-4-4-4-44440-4-4400000000000000000000000000000000004-4000000000000000000000000000
χ764-4-44440000-4-4-4-44440-4-440000000000000000000000000000000000-44000000000000000000000000000
χ7788-8-8-4-4008i−8i-44-4444202-2-20000−4i4i−4i4i0000002i−2i00000000000000000000000000000000000000000000000
χ7888-8-8-4-400−8i8i-44-4444202-2-200004i−4i4i−4i000000−2i2i00000000000000000000000000000000000000000000000
χ798-88-8-4-48i−8i004-44-44420-22-2−4i4i−4i4i000000002i−2i0000000000000000000000000000000000000000000000000
χ808-88-8-4-4−8i8i004-44-44420-22-24i−4i4i−4i00000000−2i2i0000000000000000000000000000000000000000000000000
χ818-8-888-40000-8-8448-4-4044-4000000000000000000000000000000000000000000000000000000000000000
χ828-8-88-48000044-8-8-48-4044-4000000000000000000000000000000000000000000000000000000000000000
χ838-8-88-4-400004444-4-420-2-2200000000000000006-6000000000000000000000000000000000000000000000
χ848-8-88-4-400004444-4-420-2-220000000000000000-66000000000000000000000000000000000000000000000

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