Finite Group Databasebeta

← Group #11771114

Character table — Group #11771114

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222444444444444444448888888899991212121212121212121212121212121218181818242424242424242424242424242424243672727272
order1222444423366666612121212121212126666121212124444888888888888888822222424242424242424242424242424242448888
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
χ91111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1ii−i−iii−i−i11-1-111-1-1-1-111ii−i−iii−i−i11-1-111-1-11i−ii−i
χ101111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1ii−i−iii−i−i-1-111-1-111-1-111ii−i−iii−i−i-1-111-1-1111−ii−ii
χ111111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1−i−iii−i−iii11-1-111-1-1-1-111−i−iii−i−iii11-1-111-1-11−ii−ii
χ121111-1-111-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1−i−iii−i−iii-1-111-1-111-1-111−i−iii−i−iii-1-111-1-1111i−ii−i
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii1-111-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii-1-1-1-1−i−iiiii−i−iii−i−i−i−iii11-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i1-111-1
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
χ192222-2-222-222222222-2-2-2-22222-2-2-2-2-2-2222222000000000000000022-2-20000000000000000-20000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022220000000000000000-20000
χ2122-2-2002i−2i02222-2-2-2-200002i2i−2i−2i0000002i−2i2i2i−2i−2ii2−i2i2−i22−22−2000000002-200i2−i2i2−i22−22−20000000000000
χ2222-2-2002i−2i02222-2-2-2-200002i2i−2i−2i0000002i−2i2i2i−2i−2i−i2i2−i2i2−22−22000000002-200−i2i2−i2i2−22−220000000000000
χ2322-2-2002i−2i02222-2-2-2-200002i2i−2i−2i0000002i−2i−2i−2i2i2i2−2−22−i2i2i2−i200000000-22002−2−22−i2i2i2−i20000000000000
χ2422-2-2002i−2i02222-2-2-2-200002i2i−2i−2i0000002i−2i−2i−2i2i2i−222−2i2−i2−i2i200000000-2200−222−2i2−i2−i2i20000000000000
χ2522-2-200−2i2i02222-2-2-2-20000−2i−2i2i2i000000−2i2i2i2i−2i−2i2−2−22i2−i2−i2i200000000-22002−2−22i2−i2−i2i20000000000000
χ2622-2-200−2i2i02222-2-2-2-20000−2i−2i2i2i000000−2i2i2i2i−2i−2i−222−2−i2i2i2−i200000000-2200−222−2−i2i2i2−i20000000000000
χ2722-2-200−2i2i02222-2-2-2-20000−2i−2i2i2i000000−2i2i−2i−2i2i2ii2−i2i2−i2−22−22000000002-200i2−i2i2−i2−22−220000000000000
χ2822-2-200−2i2i02222-2-2-2-20000−2i−2i2i2i000000−2i2i−2i−2i2i2i−i2i2−i2i22−22−2000000002-200−i2i2−i2i22−22−20000000000000
χ292-22-22i−2i00022-2-222-2-22i2i−2i−2i000000002i−2i002i−2i2i−2i00000000i2−i22−2i2−i22−2002-200000000i2−i22−2i2−i22−200000
χ302-22-22i−2i00022-2-222-2-22i2i−2i−2i000000002i−2i002i−2i2i−2i00000000−i2i2−22−i2i2−22002-200000000−i2i2−22−i2i2−2200000
χ312-22-22i−2i00022-2-222-2-22i2i−2i−2i000000002i−2i00−2i2i−2i2i000000002−2−i2i2−22i2−i200-22000000002−2−i2i2−22i2−i200000
χ322-22-22i−2i00022-2-222-2-22i2i−2i−2i000000002i−2i00−2i2i−2i2i00000000−22i2−i22−2−i2i200-2200000000−22i2−i22−2−i2i200000
χ332-22-2−2i2i00022-2-222-2-2−2i−2i2i2i00000000−2i2i002i−2i2i−2i000000002−2i2−i2−22−i2i200-22000000002−2i2−i2−22−i2i200000
χ342-22-2−2i2i00022-2-222-2-2−2i−2i2i2i00000000−2i2i002i−2i2i−2i00000000−22−i2i22−2i2−i200-2200000000−22−i2i22−2i2−i200000
χ352-22-2−2i2i00022-2-222-2-2−2i−2i2i2i00000000−2i2i00−2i2i−2i2i00000000i2−i2−22i2−i2−22002-200000000i2−i2−22i2−i2−2200000
χ362-22-2−2i2i00022-2-222-2-2−2i−2i2i2i00000000−2i2i00−2i2i−2i2i00000000−i2i22−2−i2i22−2002-200000000−i2i22−2−i2i22−200000
χ374444444441-21-21-21-21111-2-2-2-211-2-2-2-211000022222222000000000000-1-1-1-1-1-1-1-10000000000000
χ384444444441-21-21-21-21111-2-2-2-211-2-2-2-2110000-2-2-2-2-2-2-2-2000000000000111111110000000000000
χ39444444444-21-21-21-21-2-2-2-21111-2-21111-2-200000000000022222222000000000000-1-1-1-1-1-1-1-100000
χ40444444444-21-21-21-21-2-2-2-21111-2-21111-2-2000000000000-2-2-2-2-2-2-2-20000000000001111111100000
χ41444444-4-4-41-21-21-21-211112222-1-122-2-2-1-100002222-2-2-2-2000000000000-1-1-1-111110000000000000
χ42444444-4-4-41-21-21-21-211112222-1-122-2-2-1-10000-2-2-2-222220000000000001111-1-1-1-10000000000000
χ43444444-4-4-4-21-21-21-21-2-2-2-2-1-1-1-122-1-111220000000000002i2i2i2i−2i−2i−2i−2i000000000000−i−i−i−iiiii00000
χ44444444-4-4-4-21-21-21-21-2-2-2-2-1-1-1-122-1-11122000000000000−2i−2i−2i−2i2i2i2i2i000000000000iiii−i−i−i−i00000
χ454444-4-444-41-21-21-21-2-1-1-1-1-2-2-2-2-1-122221100002i2i−2i−2i2i2i−2i−2i000000000000−i−iii−i−iii0000000000000
χ464444-4-444-41-21-21-21-2-1-1-1-1-2-2-2-2-1-12222110000−2i−2i2i2i−2i−2i2i2i000000000000ii−i−iii−i−i0000000000000
χ474444-4-444-4-21-21-21-212222111122-1-1-1-1-2-200000000000022-2-222-2-2000000000000-1-111-1-11100000
χ484444-4-444-4-21-21-21-212222111122-1-1-1-1-2-2000000000000-2-222-2-22200000000000011-1-111-1-100000
χ494444-4-4-4-441-21-21-21-2-1-1-1-1222211-2-222-1-100002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-441-21-21-21-2-1-1-1-1222211-2-222-1-10000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-44-21-21-21-212222-1-1-1-1-2-211-1-1220000000000002i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i00000
χ524444-4-4-4-44-21-21-21-212222-1-1-1-1-2-211-1-122000000000000−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii00000
χ5344-4-4004i−4i01-21-2-12-123i−3i3i−3i−2i−2i2i2i3-30000i−i00002ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ000000000000−ζζ−ζ3ζ3ζ3−ζ3−ζζ0000000000000
χ5444-4-4004i−4i01-21-2-12-123i−3i3i−3i−2i−2i2i2i3-30000i−i0000−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ000000000000ζ−ζζ3−ζ3−ζ3ζ3ζ−ζ0000000000000
χ5544-4-4004i−4i01-21-2-12-12−3i3i−3i3i−2i−2i2i2i-330000i−i00002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3000000000000−ζ3ζ3−ζζ−ζζζ3−ζ30000000000000
χ5644-4-4004i−4i01-21-2-12-12−3i3i−3i3i−2i−2i2i2i-330000i−i0000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ3000000000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ30000000000000
χ5744-4-400−4i4i01-21-2-12-123i−3i3i−3i2i2i−2i−2i-330000−ii00002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ000000000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ0000000000000
χ5844-4-400−4i4i01-21-2-12-123i−3i3i−3i2i2i−2i−2i-330000−ii0000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ000000000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ0000000000000
χ5944-4-400−4i4i01-21-2-12-12−3i3i−3i3i2i2i−2i−2i3-30000−ii00002ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3000000000000−ζ3ζ3−ζζζ−ζ−ζ3ζ30000000000000
χ6044-4-400−4i4i01-21-2-12-12−3i3i−3i3i2i2i−2i−2i3-30000−ii0000−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ3000000000000ζ3−ζ3ζ−ζ−ζζζ3−ζ30000000000000
χ614-44-44i−4i000-212-1-212-1−2i−2i2i2i3i−3i3i−3i003-3i−i000000000000002ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ000000000000−ζζζ3−ζ3−ζ3ζ3−ζζ00000
χ624-44-44i−4i000-212-1-212-1−2i−2i2i2i3i−3i3i−3i003-3i−i00000000000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ000000000000ζ−ζ−ζ3ζ3ζ3−ζ3ζ−ζ00000
χ634-44-44i−4i000-212-1-212-1−2i−2i2i2i−3i3i−3i3i00-33i−i000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3000000000000−ζ3ζ3−ζζ−ζζζ3−ζ300000
χ644-44-44i−4i000-212-1-212-1−2i−2i2i2i−3i3i−3i3i00-33i−i00000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ3000000000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ300000
χ654-44-4−4i4i000-212-1-212-12i2i−2i−2i3i−3i3i−3i00-33−ii000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ000000000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ00000
χ664-44-4−4i4i000-212-1-212-12i2i−2i−2i3i−3i3i−3i00-33−ii00000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ000000000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ00000
χ674-44-4−4i4i000-212-1-212-12i2i−2i−2i−3i3i−3i3i003-3−ii000000000000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3000000000000−ζ3ζ3ζ−ζ−ζζ−ζ3ζ300000
χ684-44-4−4i4i000-212-1-212-12i2i−2i−2i−3i3i−3i3i003-3−ii00000000000000−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ3000000000000ζ3−ζ3−ζζζ−ζζ3−ζ300000
χ694-4-440000044-4-4-4-44400000000000000004-4-4400000000000000000000000000000000000000000
χ704-4-440000044-4-4-4-4440000000000000000-444-400000000000000000000000000000000000000000
χ7188-8-8008i−8i0-42-424-24-200002i2i−2i−2i000000−4i4i000000000000000000000000000000000000000000000
χ7288-8-800−8i8i0-42-424-24-20000−2i−2i2i2i0000004i−4i000000000000000000000000000000000000000000000
χ738-88-88i−8i0002-4-242-4-242i2i−2i−2i00000000−4i4i00000000000000000000000000000000000000000000000
χ748-88-8−8i8i0002-4-242-4-24−2i−2i2i2i000000004i−4i00000000000000000000000000000000000000000000000
χ758-8-88000002-4-24-242-46-6-66000000000000000000000000000000000000000000000000000000000
χ768-8-88000002-4-24-242-4-666-6000000000000000000000000000000000000000000000000000000000
χ778-8-8800000-424-24-2-4200006-6-6600000000000000000000000000000000000000000000000000000
χ788-8-8800000-424-24-2-420000-666-600000000000000000000000000000000000000000000000000000

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