Finite Group Databasebeta

← Group #11776251

Character table — Group #11776251

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444444448888888888999912121212121212121818181824242424242424242424242436363636363636363648484848
order1222444423366666612121212666612121212121244448888888844444444242424242424242448888888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ5111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11-1-11-11-1iiii−i−i−i−i1iiii−i−i−i−i1-11-1
χ6111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11-1-1-11-11iiii−i−i−i−i1−i−i−i−iiiii-11-11
χ7111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11-1-11-11-1−i−i−i−iiiii1−i−i−i−iiiii1-11-1
χ8111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11-1-1-11-11−i−i−i−iiiii1iiii−i−i−i−i-11-11
χ91111-1-111-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-1111-1-111-1-1-1-111
χ101111-1-111-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-11-1-111-1-11111-1-1
χ111111-1-111-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1111-1-111-1-111-1-111
χ121111-1-111-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111111-1-111-1-111-1-1
χ131111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iii-1-1-1-11-1-11ii−i−i−i−iii1ii−i−i−i−iii-111-1
χ141111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111ii−i−i−i−iii-1-1-1-1-111-1ii−i−i−i−iii1−i−iiiii−i−i1-1-11
χ151111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−i-1-1-1-11-1-11−i−iiiii−i−i1−i−iiiii−i−i-111-1
χ161111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111−i−iiiii−i−i-1-1-1-1-111-1−i−iiiii−i−i1ii−i−i−i−iii1-1-11
χ172222222222222222222222222222222-2-2-2-200000000-2-2-2-2000000000000-2000000000000
χ18222222-2-2-222222222-2-2-2-2-2-2-2-22222-2-2222200000000-2-222000000000000-2000000000000
χ192222-2-222-2222222222222-2-2-2-2-2-2-2-22222220000000022-2-2000000000000-2000000000000
χ202222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000002222000000000000-2000000000000
χ2122-2-2002-2022-2-2-22-2222-2-2000000002-22i2i−2i−2i000000002i−2i0000000000000002−2i2−i22−2i2−i20000
χ2222-2-2002-2022-2-2-22-2222-2-2000000002-22i2i−2i−2i000000002i−2i000000000000000−22−i2i2−22−i2i20000
χ2322-2-2002-2022-2-2-22-2222-2-2000000002-2−2i−2i2i2i00000000−2i2i0000000000000002−2−i2i22−2−i2i20000
χ2422-2-2002-2022-2-2-22-2222-2-2000000002-2−2i−2i2i2i00000000−2i2i000000000000000−22i2−i2−22i2−i20000
χ2522-2-200-22022-2-2-22-22-2-22200000000-222i2i−2i−2i00000000−2i2i000000000000000i2−i22−2−i2i2−220000
χ2622-2-200-22022-2-2-22-22-2-22200000000-222i2i−2i−2i00000000−2i2i000000000000000−i2i2−22i2−i22−20000
χ2722-2-200-22022-2-2-22-22-2-22200000000-22−2i−2i2i2i000000002i−2i000000000000000i2−i2−22−i2i22−20000
χ2822-2-200-22022-2-2-22-22-2-22200000000-22−2i−2i2i2i000000002i−2i000000000000000−i2i22−2i2−i2−220000
χ292-2-222i−2i000222-2-2-22-2000000002i−2i2i−2i002i−2i2i−2ii2−i22−2i2−i22−2002-20000i2−i22−2i2−i22−20000000000000
χ302-2-222i−2i000222-2-2-22-2000000002i−2i2i−2i002i−2i2i−2i−i2i2−22−i2i2−22002-20000−i2i2−22−i2i2−220000000000000
χ312-2-222i−2i000222-2-2-22-2000000002i−2i2i−2i00−2i2i−2i2i2−2−i2i2−22i2−i200-2200002−2−i2i2−22i2−i20000000000000
χ322-2-222i−2i000222-2-2-22-2000000002i−2i2i−2i00−2i2i−2i2i−22i2−i22−2−i2i200-220000−22i2−i22−2−i2i20000000000000
χ332-2-22−2i2i000222-2-2-22-200000000−2i2i−2i2i002i−2i2i−2i2−2i2−i2−22−i2i200-2200002−2i2−i2−22−i2i20000000000000
χ342-2-22−2i2i000222-2-2-22-200000000−2i2i−2i2i002i−2i2i−2i−22−i2i22−2i2−i200-220000−22−i2i22−2i2−i20000000000000
χ352-2-22−2i2i000222-2-2-22-200000000−2i2i−2i2i00−2i2i−2i2ii2−i2−22i2−i2−22002-20000i2−i2−22i2−i2−220000000000000
χ362-2-22−2i2i000222-2-2-22-200000000−2i2i−2i2i00−2i2i−2i2i−i2i22−2−i2i22−2002-20000−i2i22−2−i2i22−20000000000000
χ374444444441-211-21-2-2111111-2-211-2-2-2-200002222222200000000-1-1-1-1-1-1-1-10000000000000
χ384444444441-211-21-2-2111111-2-211-2-2-2-20000-2-2-2-2-2-2-2-200000000111111110000000000000
χ39444444444-21-2-21-211-2-2-2-2-2-211-2-211110000000000000000222200000000000000000-1-1-1-1
χ40444444444-21-2-21-211-2-2-2-2-2-211-2-211110000000000000000-2-2-2-2000000000000000001111
χ41444444-4-4-41-211-21-2-2-1-1-1-1-1-12211-2-22200002i2i2i2i−2i−2i−2i−2i00000000−i−i−i−iiiii0000000000000
χ42444444-4-4-41-211-21-2-2-1-1-1-1-1-12211-2-2220000−2i−2i−2i−2i2i2i2i2i00000000iiii−i−i−i−i0000000000000
χ43444444-4-4-4-21-2-21-211222222-1-1-2-211-1-100000000000000002-22-200000000000000000-11-11
χ44444444-4-4-4-21-2-21-211222222-1-1-2-211-1-10000000000000000-22-22000000000000000001-11-1
χ454444-4-444-41-211-21-2-21111-1-122-1-122-2-2000022-2-222-2-200000000-1-111-1-1110000000000000
χ464444-4-444-41-211-21-2-21111-1-122-1-122-2-20000-2-222-2-2220000000011-1-111-1-10000000000000
χ474444-4-444-4-21-2-21-211-2-2-2-222-1-122-1-111000000000000000022-2-20000000000000000011-1-1
χ484444-4-444-4-21-2-21-211-2-2-2-222-1-122-1-1110000000000000000-2-22200000000000000000-1-111
χ494444-4-4-4-441-211-21-2-2-1-1-1-111-2-2-1-1222200002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-441-211-21-2-2-1-1-1-111-2-2-1-122220000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-44-21-2-21-2112222-2-21122-1-1-1-100000000000000002-2-22000000000000000001-1-11
χ524444-4-4-4-44-21-2-21-2112222-2-21122-1-1-1-10000000000000000-222-200000000000000000-111-1
χ534-44-40000044-444-4-4-4000000000000004-4-440000000000000000000000000000000000000
χ544-44-40000044-444-4-4-400000000000000-444-40000000000000000000000000000000000000
χ554-4-444i−4i0001-21-12-1-223i−3i3i−3i3-300i−i−2i2i0000002ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ00000000−ζζζ3−ζ3−ζ3ζ3−ζζ0000000000000
χ564-4-444i−4i0001-21-12-1-223i−3i3i−3i3-300i−i−2i2i000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ00000000ζ−ζ−ζ3ζ3ζ3−ζ3ζ−ζ0000000000000
χ574-4-444i−4i0001-21-12-1-22−3i3i−3i3i-3300i−i−2i2i0000002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ300000000−ζ3ζ3−ζζ−ζζζ3−ζ30000000000000
χ584-4-444i−4i0001-21-12-1-22−3i3i−3i3i-3300i−i−2i2i000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ300000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ30000000000000
χ594-4-44−4i4i0001-21-12-1-223i−3i3i−3i-3300−ii2i−2i0000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ00000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ0000000000000
χ604-4-44−4i4i0001-21-12-1-223i−3i3i−3i-3300−ii2i−2i000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ00000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ0000000000000
χ614-4-44−4i4i0001-21-12-1-22−3i3i−3i3i3-300−ii2i−2i0000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000−ζ3ζ3ζ−ζ−ζζ−ζ3ζ30000000000000
χ624-4-44−4i4i0001-21-12-1-22−3i3i−3i3i3-300−ii2i−2i000000−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000ζ3−ζ3−ζζζ−ζζ3−ζ30000000000000
χ6388-8-8008-802-4-2-2424-422-2-200000000-4400000000000000000000000000000000000000000
χ6488-8-8008-80-4244-2-4-22-4-444000000002-200000000000000000000000000000000000000000
χ6588-8-800-8802-4-2-2424-4-2-222000000004-400000000000000000000000000000000000000000
χ6688-8-800-880-4244-2-4-2244-4-400000000-2200000000000000000000000000000000000000000
χ678-88-8000002-4-22-4-2446i−6i−6i6i000000000000000000000000000000000000000000000000000
χ688-88-8000002-4-22-4-244−6i6i6i−6i000000000000000000000000000000000000000000000000000
χ698-88-800000-424-424-2-20000006-600000000000000000000000000000000000000000000000
χ708-88-800000-424-424-2-2000000-6600000000000000000000000000000000000000000000000
χ718-8-888i−8i000-42-44-242-200000000−4i4i2i−2i0000000000000000000000000000000000000000000
χ728-8-88−8i8i000-42-44-242-2000000004i−4i−2i2i0000000000000000000000000000000000000000000

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