Finite Group Databasebeta

← Group #11774447

Character table — Group #11774447

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444444448888888888999912121212121212121818181824242424242424242424242436363636363636363648484848
order122244442336666661212121266661212121212124444888888884444244424242424242424244888888886121212
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−i11-1-1
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-1-111
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−iiiii11-1-1
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-1-111
χ91111-1-111-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11-1-1111-1-111-1-1-111-1-111-1-11-11-1
χ101111-1-111-1111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-111-111-1-111-1-1-1-1-111-1-111-11-11
χ111111-1-111-1111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-11-1-11-1-111-1-111-1-1-111-1-1111-11-1
χ121111-1-111-1111111111111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-111-1-1-111-1-111-111-1-111-1-1-11-11
χ131111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii111111-1-1ii−i−i−i−iii-1ii−i−i−i−iii1-1-11
χ141111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii1111-1-111ii−i−i−i−iii-1−i−iiiii−i−i-111-1
χ151111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i111111-1-1−i−iiiii−i−i-1−i−iiiii−i−i1-1-11
χ161111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i1111-1-111−i−iiiii−i−i-1ii−i−i−i−iii-111-1
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
χ192222-2-222-2222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000-2-2220000000000002000000000000
χ202222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2222200000000-2-2-2-20000000000002000000000000
χ212-22-2002i−2i0222-2-22-2-22i2i−2i−2i000000002i−2i2i2i−2i−2i000000002-2000000000000000002ζ−2ζ002ζ3−2ζ30000
χ222-22-2002i−2i0222-2-22-2-22i2i−2i−2i000000002i−2i2i2i−2i−2i000000002-200000000000000000−2ζ2ζ00−2ζ32ζ30000
χ232-22-2002i−2i0222-2-22-2-22i2i−2i−2i000000002i−2i−2i−2i2i2i00000000-220000000000000002ζ−2ζ002ζ3−2ζ3000000
χ242-22-2002i−2i0222-2-22-2-22i2i−2i−2i000000002i−2i−2i−2i2i2i00000000-22000000000000000−2ζ2ζ00−2ζ32ζ3000000
χ252-22-200−2i2i0222-2-22-2-2−2i−2i2i2i00000000−2i2i2i2i−2i−2i00000000-220000000000000002ζ3−2ζ3002ζ−2ζ000000
χ262-22-200−2i2i0222-2-22-2-2−2i−2i2i2i00000000−2i2i2i2i−2i−2i00000000-22000000000000000−2ζ32ζ300−2ζ2ζ000000
χ272-22-200−2i2i0222-2-22-2-2−2i−2i2i2i00000000−2i2i−2i−2i2i2i000000002-2000000000000000002ζ3−2ζ3002ζ−2ζ0000
χ282-22-200−2i2i0222-2-22-2-2−2i−2i2i2i00000000−2i2i−2i−2i2i2i000000002-200000000000000000−2ζ32ζ300−2ζ2ζ0000
χ292-2-222i−2i00022-22-2-22-2000000002i−2i2i−2i002-22-2i2−i22−2i2−i22−2002i−2i0000i2−i22−2i2−i22−20000000000000
χ302-2-222i−2i00022-22-2-22-2000000002i−2i2i−2i002-22-2−i2i2−22−i2i2−22002i−2i0000−i2i2−22−i2i2−220000000000000
χ312-2-222i−2i00022-22-2-22-2000000002i−2i2i−2i00-22-222−2−i2i2−22i2−i200−2i2i00002−2−i2i2−22i2−i20000000000000
χ322-2-222i−2i00022-22-2-22-2000000002i−2i2i−2i00-22-22−22i2−i22−2−i2i200−2i2i0000−22i2−i22−2−i2i20000000000000
χ332-2-22−2i2i00022-22-2-22-200000000−2i2i−2i2i002-22-2i2−i2−22i2−i2−2200−2i2i0000i2−i2−22i2−i2−220000000000000
χ342-2-22−2i2i00022-22-2-22-200000000−2i2i−2i2i002-22-2−i2i22−2−i2i22−200−2i2i0000−i2i22−2−i2i22−20000000000000
χ352-2-22−2i2i00022-22-2-22-200000000−2i2i−2i2i00-22-222−2i2−i2−22−i2i2002i−2i00002−2i2−i2−22−i2i20000000000000
χ362-2-22−2i2i00022-22-2-22-200000000−2i2i−2i2i00-22-22−22−i2i22−2i2−i2002i−2i0000−22−i2i22−2i2−i20000000000000
χ374444444441-2111-2-2-2111111-2-211-2-2-2-200002222222200000000-1-1-1-1-1-1-1-10000000000000
χ384444444441-2111-2-2-2111111-2-211-2-2-2-20000-2-2-2-2-2-2-2-200000000111111110000000000000
χ39444444444-21-2-2-2111-2-2-2-2-2-211-2-211110000000000000000222200000000000000000-1-1-1-1
χ40444444444-21-2-2-2111-2-2-2-2-2-211-2-211110000000000000000-2-2-2-2000000000000000001111
χ41444444-4-4-41-2111-2-2-2-1-1-1-1-1-12211-2-22200002i2i2i2i−2i−2i−2i−2i00000000−i−i−i−iiiii0000000000000
χ42444444-4-4-41-2111-2-2-2-1-1-1-1-1-12211-2-2220000−2i−2i−2i−2i2i2i2i2i00000000iiii−i−i−i−i0000000000000
χ43444444-4-4-4-21-2-2-2111222222-1-1-2-211-1-100000000000000002-22-200000000000000000-1-111
χ44444444-4-4-4-21-2-2-2111222222-1-1-2-211-1-10000000000000000-22-220000000000000000011-1-1
χ454444-4-444-41-2111-2-2-21111-1-122-1-122-2-2000022-2-222-2-200000000-1-111-1-1110000000000000
χ464444-4-444-41-2111-2-2-21111-1-122-1-122-2-20000-2-222-2-2220000000011-1-111-1-10000000000000
χ474444-4-444-4-21-2-2-2111-2-2-2-222-1-122-1-11100000000000000002-2-2200000000000000000-11-11
χ484444-4-444-4-21-2-2-2111-2-2-2-222-1-122-1-1110000000000000000-222-2000000000000000001-11-1
χ494444-4-4-4-441-2111-2-2-2-1-1-1-111-2-2-1-1222200002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-441-2111-2-2-2-1-1-1-111-2-2-1-122220000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-44-21-2-2-21112222-2-21122-1-1-1-1000000000000000022-2-200000000000000000-111-1
χ524444-4-4-4-44-21-2-2-21112222-2-21122-1-1-1-10000000000000000-2-222000000000000000001-1-11
χ5344-4-40000044-4-44-4-44000000000000004i−4i−4i4i0000000000000000000000000000000000000
χ5444-4-40000044-4-44-4-4400000000000000−4i4i4i−4i0000000000000000000000000000000000000
χ554-4-444i−4i0001-2-11-12-223i−3i3i−3i3-300i−i−2i2i0000002ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ00000000−ζζζ3−ζ3−ζ3ζ3−ζζ0000000000000
χ564-4-444i−4i0001-2-11-12-223i−3i3i−3i3-300i−i−2i2i000000−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ00000000ζ−ζ−ζ3ζ3ζ3−ζ3ζ−ζ0000000000000
χ574-4-444i−4i0001-2-11-12-22−3i3i−3i3i-3300i−i−2i2i0000002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ300000000−ζ3ζ3−ζζ−ζζζ3−ζ30000000000000
χ584-4-444i−4i0001-2-11-12-22−3i3i−3i3i-3300i−i−2i2i000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ300000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ30000000000000
χ594-4-44−4i4i0001-2-11-12-223i−3i3i−3i-3300−ii2i−2i0000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ00000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ0000000000000
χ604-4-44−4i4i0001-2-11-12-223i−3i3i−3i-3300−ii2i−2i000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ00000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ0000000000000
χ614-4-44−4i4i0001-2-11-12-22−3i3i−3i3i3-300−ii2i−2i0000002ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000−ζ3ζ3ζ−ζ−ζζ−ζ3ζ30000000000000
χ624-4-44−4i4i0001-2-11-12-22−3i3i−3i3i3-300−ii2i−2i000000−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000ζ3−ζ3−ζζζ−ζζ3−ζ30000000000000
χ6388-8-8000002-4-2-2244-46-6-66000000000000000000000000000000000000000000000000000
χ6488-8-8000002-4-2-2244-4-666-6000000000000000000000000000000000000000000000000000
χ6588-8-800000-4244-4-2-220000006-600000000000000000000000000000000000000000000000
χ6688-8-800000-4244-4-2-22000000-6600000000000000000000000000000000000000000000000
χ678-88-8008i−8i02-42-2-2-4442i2i−2i−2i00000000−4i4i00000000000000000000000000000000000000000
χ688-88-8008i−8i0-42-4442-2-2−4i−4i4i4i000000002i−2i00000000000000000000000000000000000000000
χ698-88-800−8i8i02-42-2-2-444−2i−2i2i2i000000004i−4i00000000000000000000000000000000000000000
χ708-88-800−8i8i0-42-4442-2-24i4i−4i−4i00000000−2i2i00000000000000000000000000000000000000000
χ718-8-888i−8i000-424-44-22-200000000−4i4i2i−2i0000000000000000000000000000000000000000000
χ728-8-88−8i8i000-424-44-22-2000000004i−4i−2i2i0000000000000000000000000000000000000000000

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