Finite Group Databasebeta

← Group #9852

Character table — Group #9852

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222222224444444444444444444444441616161616161616
order1222444422444444444444444444888888888888888822448888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ91111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1i−ii−i
χ101111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−ii−ii
χ111111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1-11i−i−ii
χ121111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-111-1−iii−i
χ131111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−ii−ii
χ141111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111i−ii−i
χ151111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1-11−iii−i
χ161111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-111-1i−i−ii
χ172222222222-2-2-2-222-2-2-2-222-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-222-2-2-2-2-2-222000000000000000022-2-222-2-200000000
χ2022222222-2-222-2-2-2-2-2-2220000000000000000-2-222-2-22200000000
χ2122222222-2-2-2-222-2-222-2-20000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-222-2-222-2-200000000-2-222-2-2220000000000000000
χ232222-2-2-2-2222222-2-2-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ242222-2-2-2-2222222-2-2-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ252222-2-2-2-222-2-2-2-2-2-222220000000022-2-2-2-2220000000000000000
χ262222-2-2-2-222-2-2-2-2-2-2222200000000-2-22222-2-20000000000000000
χ272222-2-2-2-2-2-2-2-22222-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ282222-2-2-2-2-2-2-2-22222-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2922-2-22i2i−2i−2i002-20000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2−22−2i2−i2i2−i2002ζ−2ζ002ζ3−2ζ300000000
χ3022-2-22i2i−2i−2i002-20000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−22−i2i2−i2i200−2ζ2ζ00−2ζ32ζ300000000
χ3122-2-22i2i−2i−2i002-20000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−22−2i2−i2i2−i200−2ζ2ζ00−2ζ32ζ300000000
χ3222-2-22i2i−2i−2i002-20000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−22−i2i2−i2i2002ζ−2ζ002ζ3−2ζ300000000
χ3322-2-22i2i−2i−2i00-22000000−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i2−2−22i2−i2−i2i22ζ−2ζ002ζ3−2ζ30000000000
χ3422-2-22i2i−2i−2i00-22000000−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−222−2−i2i2i2−i2−2ζ2ζ00−2ζ32ζ30000000000
χ3522-2-22i2i−2i−2i00-22000000−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i2−2−22i2−i2−i2i2−2ζ2ζ00−2ζ32ζ30000000000
χ3622-2-22i2i−2i−2i00-22000000−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−222−2−i2i2i2−i22ζ−2ζ002ζ3−2ζ30000000000
χ3722-2-2−2i−2i2i2i002-2000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2−22−2−i2i2−i2i200−2ζ32ζ300−2ζ2ζ00000000
χ3822-2-2−2i−2i2i2i002-2000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−22−22i2−i2i2−i2002ζ3−2ζ3002ζ−2ζ00000000
χ3922-2-2−2i−2i2i2i002-2000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−22−2−i2i2−i2i2002ζ3−2ζ3002ζ−2ζ00000000
χ4022-2-2−2i−2i2i2i002-2000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22−22i2−i2i2−i200−2ζ32ζ300−2ζ2ζ00000000
χ4122-2-2−2i−2i2i2i00-220000002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i2−2−22−i2i2i2−i2−2ζ32ζ300−2ζ2ζ0000000000
χ4222-2-2−2i−2i2i2i00-220000002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−222−2i2−i2−i2i22ζ3−2ζ3002ζ−2ζ0000000000
χ4322-2-2−2i−2i2i2i00-220000002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i2−2−22−i2i2i2−i22ζ3−2ζ3002ζ−2ζ0000000000
χ4422-2-2−2i−2i2i2i00-220000002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−222−2i2−i2−i2i2−2ζ32ζ300−2ζ2ζ0000000000
χ454-44-44i−4i4i−4i00004i−4i004-40000000000000000000000000000000000
χ464-44-44i−4i4i−4i0000−4i4i00-440000000000000000000000000000000000
χ474-44-4−4i4i−4i4i00004i−4i00-440000000000000000000000000000000000
χ484-44-4−4i4i−4i4i0000−4i4i004-40000000000000000000000000000000000
χ494-4-444-4-444-400004-4000000000000000000000000000000000000
χ504-4-444-4-44-440000-44000000000000000000000000000000000000
χ514-4-44-444-44-40000-44000000000000000000000000000000000000
χ524-4-44-444-4-4400004-4000000000000000000000000000000000000

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