Finite Group Databasebeta

← Group #11785833

Character table — Group #11785833

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444444444448888888899991212121212121212121212121212121218181818242424242424242424242424242424243672727272
order1222444423366666612121212121212126666121212122222444444448888888844441212121212121212242424242424242424444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1ii−i−i
χ6111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−i−i−iiiii1−i−iii
χ7111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-1-1-11111iiii−i−i−i−i1−i−iii
χ8111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-1-1-11111−i−i−i−iiiii1ii−i−i
χ91111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1-11-11-1
χ101111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-111-1-11-11
χ111111-1-111-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-11111-1-111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11-11
χ121111-1-111-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-11-11-1
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i−i−iii111111-1-1-1-111ii−i−i−i−iii-1i−i−ii
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111−i−iiiii−i−i111111-1-1-1-111−i−iiiii−i−i-1−iii−i
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii1111-1-11111-1-1ii−i−i−i−iii-1−iii−i
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i1111-1-11111-1-1−i−iiiii−i−i-1i−i−ii
χ17222222222222222222222222222222222-2-2-2-20000000000000000-2-2-2-20000000000000000-20000
χ18222222-2-2-2222222222222-2-2-2-2-2-2-2-222-2-222220000000000000000-2-2220000000000000000-20000
χ192222-2-222-222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-20000000000000000-2-222000000000000000020000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-2000000000000000020000
χ2122-2-22i−2i000222-2-2-22-22i2i−2i−2i000000002i−2i002-22-200000000i2−i22−2i2−i22−2002i−2i00000000i2−i22−2i2−i22−200000
χ2222-2-22i−2i000222-2-2-22-22i2i−2i−2i000000002i−2i002-22-200000000−i2i2−22−i2i2−22002i−2i00000000−i2i2−22−i2i2−2200000
χ2322-2-22i−2i000222-2-2-22-22i2i−2i−2i000000002i−2i00-22-22000000002−2−i2i2−22i2−i200−2i2i000000002−2−i2i2−22i2−i200000
χ2422-2-22i−2i000222-2-2-22-22i2i−2i−2i000000002i−2i00-22-2200000000−22i2−i22−2−i2i200−2i2i00000000−22i2−i22−2−i2i200000
χ2522-2-2−2i2i000222-2-2-22-2−2i−2i2i2i00000000−2i2i002-22-200000000i2−i2−22i2−i2−2200−2i2i00000000i2−i2−22i2−i2−2200000
χ2622-2-2−2i2i000222-2-2-22-2−2i−2i2i2i00000000−2i2i002-22-200000000−i2i22−2−i2i22−200−2i2i00000000−i2i22−2−i2i22−200000
χ2722-2-2−2i2i000222-2-2-22-2−2i−2i2i2i00000000−2i2i00-22-22000000002−2i2−i2−22−i2i2002i−2i000000002−2i2−i2−22−i2i200000
χ2822-2-2−2i2i000222-2-2-22-2−2i−2i2i2i00000000−2i2i00-22-2200000000−22−i2i22−2i2−i2002i−2i00000000−22−i2i22−2i2−i200000
χ292-2-22002-2022-2-222-2-2000022-2-20000002-22-2-22002i−2i002i−2i000000002-200002i−2i002i−2i0000000000000
χ302-2-22002-2022-2-222-2-2000022-2-20000002-22-2-2200−2i2i00−2i2i000000002-20000−2i2i00−2i2i0000000000000
χ312-2-22002-2022-2-222-2-2000022-2-20000002-2-222-22i−2i002i−2i0000000000-22002i−2i002i−2i000000000000000
χ322-2-22002-2022-2-222-2-2000022-2-20000002-2-222-2−2i2i00−2i2i0000000000-2200−2i2i00−2i2i000000000000000
χ332-2-2200-22022-2-222-2-20000-2-222000000-222-2-222i−2i00−2i2i0000000000-22002i−2i00−2i2i000000000000000
χ342-2-2200-22022-2-222-2-20000-2-222000000-222-2-22−2i2i002i−2i0000000000-2200−2i2i002i−2i000000000000000
χ352-2-2200-22022-2-222-2-20000-2-222000000-22-222-2002i−2i00−2i2i000000002-200002i−2i00−2i2i0000000000000
χ362-2-2200-22022-2-222-2-20000-2-222000000-22-222-200−2i2i002i−2i000000002-20000−2i2i002i−2i0000000000000
χ374444444441-2111-2-2-2-2-2-2-2111111-2-211-2-200000000000022222222000000000000-1-1-1-1-1-1-1-100000
χ384444444441-2111-2-2-2-2-2-2-2111111-2-211-2-2000000000000-2-2-2-2-2-2-2-20000000000001111111100000
χ39444444444-21-2-2-21111111-2-2-2-2-2-211-2-211000022222222000000000000-1-1-1-1-1-1-1-10000000000000
χ40444444444-21-2-2-21111111-2-2-2-2-2-211-2-2110000-2-2-2-2-2-2-2-2000000000000111111110000000000000
χ41444444-4-4-41-2111-2-2-2-2-2-2-2-1-1-1-1-1-12211220000000000002i2i2i2i−2i−2i−2i−2i000000000000−i−i−i−iiiii00000
χ42444444-4-4-41-2111-2-2-2-2-2-2-2-1-1-1-1-1-1221122000000000000−2i−2i−2i−2i2i2i2i2i000000000000iiii−i−i−i−i00000
χ43444444-4-4-4-21-2-2-21111111222222-1-1-2-2-1-100002222-2-2-2-2000000000000-1-1-1-111110000000000000
χ44444444-4-4-4-21-2-2-21111111222222-1-1-2-2-1-10000-2-2-2-222220000000000001111-1-1-1-10000000000000
χ454444-4-444-41-2111-2-2-222221111-1-122-1-1-2-200000000000022-2-222-2-2000000000000-1-111-1-11100000
χ464444-4-444-41-2111-2-2-222221111-1-122-1-1-2-2000000000000-2-222-2-22200000000000011-1-111-1-100000
χ474444-4-444-4-21-2-2-2111-1-1-1-1-2-2-2-222-1-12211000022-2-222-2-2000000000000-1-111-1-1110000000000000
χ484444-4-444-4-21-2-2-2111-1-1-1-1-2-2-2-222-1-122110000-2-222-2-22200000000000011-1-111-1-10000000000000
χ494444-4-4-4-441-2111-2-2-22222-1-1-1-111-2-2-1-1220000000000002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i00000
χ504444-4-4-4-441-2111-2-2-22222-1-1-1-111-2-2-1-122000000000000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii00000
χ514444-4-4-4-44-21-2-2-2111-1-1-1-12222-2-21122-1-1000022-2-2-2-222000000000000-1-11111-1-10000000000000
χ524444-4-4-4-44-21-2-2-2111-1-1-1-12222-2-21122-1-10000-2-22222-2-200000000000011-1-1-1-1110000000000000
χ5344-4-44i−4i0001-21-1-12-22−2i−2i2i2i3i−3i3i−3i3-300i−i000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ000000000000−ζζζ3−ζ3−ζ3ζ3−ζζ00000
χ5444-4-44i−4i0001-21-1-12-22−2i−2i2i2i3i−3i3i−3i3-300i−i00000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ000000000000ζ−ζ−ζ3ζ3ζ3−ζ3ζ−ζ00000
χ5544-4-44i−4i0001-21-1-12-22−2i−2i2i2i−3i3i−3i3i-3300i−i000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3000000000000−ζ3ζ3−ζζ−ζζζ3−ζ300000
χ5644-4-44i−4i0001-21-1-12-22−2i−2i2i2i−3i3i−3i3i-3300i−i00000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ3000000000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ300000
χ5744-4-4−4i4i0001-21-1-12-222i2i−2i−2i3i−3i3i−3i-3300−ii000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ000000000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ00000
χ5844-4-4−4i4i0001-21-1-12-222i2i−2i−2i3i−3i3i−3i-3300−ii00000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ000000000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ00000
χ5944-4-4−4i4i0001-21-1-12-222i2i−2i−2i−3i3i−3i3i3-300−ii000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3000000000000−ζ3ζ3ζ−ζ−ζζ−ζ3ζ300000
χ6044-4-4−4i4i0001-21-1-12-222i2i−2i−2i−3i3i−3i3i3-300−ii00000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ3000000000000ζ3−ζ3−ζζζ−ζζ3−ζ300000
χ614-44-40000044-44-4-4-44000000000000000044-4-400000000000000000000000000000000000000000
χ624-44-40000044-44-4-4-440000000000000000-4-44400000000000000000000000000000000000000000
χ634-4-44004-40-2122-21-1-13-33-3-2-222003-3001-100002i−2i2i−2i2i−2i2i−2i000000000000−ii−ii−ii−ii0000000000000
χ644-4-44004-40-2122-21-1-13-33-3-2-222003-3001-10000−2i2i−2i2i−2i2i−2i2i000000000000i−ii−ii−ii−i0000000000000
χ654-4-44004-40-2122-21-1-1-33-33-2-22200-33001-100002i−2i−2i2i2i−2i−2i2i000000000000−iii−i−iii−i0000000000000
χ664-4-44004-40-2122-21-1-1-33-33-2-22200-33001-10000−2i2i2i−2i−2i2i2i−2i000000000000i−i−iii−i−ii0000000000000
χ674-4-4400-440-2122-21-1-13-33-322-2-200-3300-1100002i−2i2i−2i−2i2i−2i2i000000000000−ii−iii−ii−i0000000000000
χ684-4-4400-440-2122-21-1-13-33-322-2-200-3300-110000−2i2i−2i2i2i−2i2i−2i000000000000i−ii−i−ii−ii0000000000000
χ694-4-4400-440-2122-21-1-1-33-3322-2-2003-300-1100002i−2i−2i2i−2i2i2i−2i000000000000−iii−ii−i−ii0000000000000
χ704-4-4400-440-2122-21-1-1-33-3322-2-2003-300-110000−2i2i2i−2i2i−2i−2i2i000000000000i−i−ii−iii−i0000000000000
χ7188-8-88i−8i000-42-444-22-22i2i−2i−2i00000000−4i4i00000000000000000000000000000000000000000000000
χ7288-8-8−8i8i000-42-444-22-2−2i−2i2i2i000000004i−4i00000000000000000000000000000000000000000000000
χ738-88-8000002-4-22-244-400006i−6i−6i6i00000000000000000000000000000000000000000000000000000
χ748-88-8000002-4-22-244-40000−6i6i6i−6i00000000000000000000000000000000000000000000000000000
χ758-88-800000-424-44-2-226i−6i−6i6i000000000000000000000000000000000000000000000000000000000
χ768-88-800000-424-44-2-22−6i6i6i−6i000000000000000000000000000000000000000000000000000000000
χ778-8-88008-802-4-2-22-444000022-2-2000000-44000000000000000000000000000000000000000000000
χ788-8-8800-8802-4-2-22-4440000-2-2220000004-4000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.