Finite Group Databasebeta

← Group #9859

Character table — Group #9859

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222222224444444444444444444444441616161616161616
order1222444422444444444488888888888888888888888844448888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−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
χ1922222222-2-222-2-2-2-222-2-2000000000000000022-2-222-2-200000000
χ2022222222-2-222-2-2-2-222-2-20000000000000000-2-222-2-22200000000
χ2122222222-2-2-2-222-2-2-2-2220000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-222-2-2-2-22200000000-2-222-2-2220000000000000000
χ232222-2-2-2-22222-2-2-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ242222-2-2-2-22222-2-2-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ252222-2-2-2-222-2-222-2-222-2-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ262222-2-2-2-222-2-222-2-222-2-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ272222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222000000000000000000000000
χ282222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-2000000000000000000000000
χ292-22-22i2i−2i−2i00002-200002i−2ii2−i2i2−i22−22−2002ζ3−2ζ3002ζ−2ζ1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ302-22-22i2i−2i−2i00002-200002i−2ii2−i2i2−i22−22−200−2ζ32ζ300−2ζ2ζ−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ312-22-22i2i−2i−2i00002-200002i−2i−i2i2−i2i2−22−22002ζ3−2ζ3002ζ−2ζ−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ322-22-22i2i−2i−2i00002-200002i−2i−i2i2−i2i2−22−2200−2ζ32ζ300−2ζ2ζ1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ332-22-22i2i−2i−2i0000-220000−2i2ii2−i2−i2i22−2−222ζ3−2ζ3002ζ−2ζ001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ342-22-22i2i−2i−2i0000-220000−2i2ii2−i2−i2i22−2−22−2ζ32ζ300−2ζ2ζ00−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ352-22-22i2i−2i−2i0000-220000−2i2i−i2i2i2−i2−222−22ζ3−2ζ3002ζ−2ζ00−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ362-22-22i2i−2i−2i0000-220000−2i2i−i2i2i2−i2−222−2−2ζ32ζ300−2ζ2ζ001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ372-22-2−2i−2i2i2i00002-20000−2i2ii2−i2i2−i2−22−22002ζ−2ζ002ζ3−2ζ31−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ382-22-2−2i−2i2i2i00002-20000−2i2ii2−i2i2−i2−22−2200−2ζ2ζ00−2ζ32ζ3−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ392-22-2−2i−2i2i2i00002-20000−2i2i−i2i2−i2i22−22−2002ζ−2ζ002ζ3−2ζ3−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ402-22-2−2i−2i2i2i00002-20000−2i2i−i2i2−i2i22−22−200−2ζ2ζ00−2ζ32ζ31−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ412-22-2−2i−2i2i2i0000-2200002i−2ii2−i2−i2i2−222−22ζ−2ζ002ζ3−2ζ3001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ422-22-2−2i−2i2i2i0000-2200002i−2ii2−i2−i2i2−222−2−2ζ2ζ00−2ζ32ζ300−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ432-22-2−2i−2i2i2i0000-2200002i−2i−i2i2i2−i22−2−222ζ−2ζ002ζ3−2ζ300−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ442-22-2−2i−2i2i2i0000-2200002i−2i−i2i2i2−i22−2−22−2ζ2ζ00−2ζ32ζ3001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ4544-4-44-44-44-400004-4000000000000000000000000000000000000
χ4644-4-44-44-4-440000-44000000000000000000000000000000000000
χ4744-4-4-44-444-40000-44000000000000000000000000000000000000
χ4844-4-4-44-44-4400004-4000000000000000000000000000000000000
χ494-4-444i−4i−4i4i004-400004i−4i0000000000000000000000000000000000
χ504-4-444i−4i−4i4i00-440000−4i4i0000000000000000000000000000000000
χ514-4-44−4i4i4i−4i004-40000−4i4i0000000000000000000000000000000000
χ524-4-44−4i4i4i−4i00-4400004i−4i0000000000000000000000000000000000

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