Finite Group Databasebeta

← Group #9211

Character table — Group #9211

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222444444444444888888882224444444888888888888888888882488
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-11111-1-11-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-11111-1-11-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-1-111111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1-1-111111ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-11111-1-11-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-11111-1-11-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-1-111111−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1-1-111111−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ172222222222-2-2-2-22222222222-2000000-200-2-2-2-200000000000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-2-2-2-2000000-200222200000000000000000000
χ1922222222-2-22222-2-200000000-222-2-2-2-2-222000000000000000000000000
χ2022222222-2-22222-2-200000000-2-2-22222-2-2-2000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000200000020000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-2-2-2-2-2-2-2-20000000020000002000000−2i−2i2i2i−2i−2i2i2i000000000000
χ232222-2-2-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i2000000-200−2i−2i2i2i00000000000000000000
χ242222-2-2-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2000000-2002i2i−2i−2i00000000000000000000
χ252222-2-2-2-2-2-222-2-22200000000222-2-222-2-2-2000000000000000000000000
χ262222-2-2-2-2-2-222-2-222000000002-2-222-2-2-222000000000000000000000000
χ272222-2-2-2-2-2-2-2-2222200000000-2000000200000022-2-2-2-222000000000000
χ282222-2-2-2-2-2-2-2-2222200000000-20000002000000-2-22222-2-2000000000000
χ2922-2-22i−2i2i−2i002-22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0002i−2i2-20001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3022-2-22i−2i2i−2i002-22i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i000−2i2i-220001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3122-2-22i−2i2i−2i002-22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0002i−2i2-2000−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3222-2-22i−2i2i−2i002-22i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−2i2i-22000−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3322-2-22i−2i2i−2i00-22−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i02-2000002i−2i−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ3422-2-22i−2i2i−2i00-22−2i2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0-2200000−2i2i−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ3522-2-22i−2i2i−2i00-22−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i02-2000002i−2i1+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ3622-2-22i−2i2i−2i00-22−2i2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0-2200000−2i2i1+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ3722-2-2−2i2i−2i2i002-2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0002i−2i-220001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3822-2-2−2i2i−2i2i002-2−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000−2i2i2-20001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3922-2-2−2i2i−2i2i002-2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0002i−2i-22000−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ4022-2-2−2i2i−2i2i002-2−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−2i2i2-2000−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ4122-2-2−2i2i−2i2i00-222i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i02-200000−2i2i−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ4222-2-2−2i2i−2i2i00-222i−2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0-22000002i−2i−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ4322-2-2−2i2i−2i2i00-222i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i02-200000−2i2i1−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ4422-2-2−2i2i−2i2i00-222i−2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0-22000002i−2i1−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ452-22-22i−2i−2i2i2-200002i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000002−2i2−i21−i−1+i1+i−1−i0000
χ462-22-22i−2i−2i2i2-200002i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000−22−i2i2−1+i1−i−1−i1+i0000
χ472-22-22i−2i−2i2i2-200002i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000002−2i2−i2−1+i1−i−1−i1+i0000
χ482-22-22i−2i−2i2i2-200002i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000−22−i2i21−i−1+i1+i−1−i0000
χ492-22-2−2i2i2i−2i2-20000−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000002−2−i2i2−1−i1+i−1+i1−i0000
χ502-22-2−2i2i2i−2i2-20000−2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000−22i2−i21+i−1−i1−i−1+i0000
χ512-22-2−2i2i2i−2i2-20000−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000002−2−i2i21+i−1−i1−i−1+i0000
χ522-22-2−2i2i2i−2i2-20000−2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000−22i2−i2−1−i1+i−1+i1−i0000
χ534-44-44i−4i−4i4i-440000−4i4i000000000000000000000000000000000000000000
χ544-44-4−4i4i4i−4i-4400004i−4i000000000000000000000000000000000000000000
χ554-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ564-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ574-4-44-4-4440000000022−22−2222−222222−220000000000000000000000000000000000
χ584-4-44-4-44400000000−222222−2222−22−22220000000000000000000000000000000000

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