Finite Group Databasebeta

← Group #9749

Character table — Group #9749

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order1222444422444444888888884444444444888888888888888888884444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
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
χ71111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1-11-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii-11-11
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i-11-11
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii1-11-1
χ131111-1-1-1-1-1-11111-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i−i−iii1-1-11
χ141111-1-1-1-1-1-11111-1-1-1-1-1-111111-1iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i-111-1
χ151111-1-1-1-1-1-11111-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii-111-1
χ161111-1-1-1-1-1-11111-1-1-1-1-1-111111-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iiiii−i−i1-1-11
χ172222222222-2-222-2-222222222-2-20000000000000000-2-2-2-2000000000000
χ182222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222000000000000
χ1922222222-2-222-2-22200000000-2-20000000022-2-222-2-20000000000000000
χ2022222222-2-222-2-22200000000-2-200000000-2-222-2-2220000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000222i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-20000000022−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ232222-2-2-2-22222-2-2-2-200000000-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ242222-2-2-2-22222-2-2-2-200000000-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ252222-2-2-2-222-2-2-2-222000000002-222-2-2-2-222000000000000000000000000
χ262222-2-2-2-222-2-2-2-222000000002-2-2-22222-2-2000000000000000000000000
χ272222-2-2-2-2-2-2-2-222222222-2-2-2-2-220000000000000000-2-222000000000000
χ282222-2-2-2-2-2-2-2-22222-2-2-2-22222-22000000000000000022-2-2000000000000
χ2922-2-222-2-22-2002-20022-2-222-2-200000000000000000000002−22−22−22−20000
χ3022-2-222-2-22-2002-20022-2-222-2-20000000000000000000000−22−22−22−220000
χ3122-2-222-2-22-2002-200-2-222-2-22200000000000000000000002−22−2−22−220000
χ3222-2-222-2-22-2002-200-2-222-2-2220000000000000000000000−22−222−22−20000
χ3322-2-2-2-222-22002-20022-2-2-2-2220000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ3422-2-2-2-222-22002-20022-2-2-2-2220000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ3522-2-2-2-222-22002-200-2-22222-2-20000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ3622-2-2-2-222-22002-200-2-22222-2-20000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ372-22-22i−2i2i−2i002-2002i−2ii2−i2i2−i22−22−2001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ3−2ζ3002ζ−2ζi2−i22−2000000000000
χ382-22-22i−2i2i−2i002-2002i−2ii2−i2i2−i22−22−200−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ32ζ300−2ζ2ζi2−i22−2000000000000
χ392-22-22i−2i2i−2i002-2002i−2i−i2i2−i2i2−22−22001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ32ζ300−2ζ2ζ−i2i2−22000000000000
χ402-22-22i−2i2i−2i002-2002i−2i−i2i2−i2i2−22−2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ3−2ζ3002ζ−2ζ−i2i2−22000000000000
χ412-22-22i−2i2i−2i00-2200−2i2ii2−i2i2−i22−22−2001−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300−i2i2−22000000000000
χ422-22-22i−2i2i−2i00-2200−2i2ii2−i2i2−i22−22−200−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300−i2i2−22000000000000
χ432-22-22i−2i2i−2i00-2200−2i2i−i2i2−i2i2−22−22001−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300i2−i22−2000000000000
χ442-22-22i−2i2i−2i00-2200−2i2i−i2i2−i2i2−22−2200−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300i2−i22−2000000000000
χ452-22-2−2i2i−2i2i002-200−2i2ii2−i2i2−i2−22−22001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ−2ζ002ζ3−2ζ3i2−i2−22000000000000
χ462-22-2−2i2i−2i2i002-200−2i2ii2−i2i2−i2−22−2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ2ζ00−2ζ32ζ3i2−i2−22000000000000
χ472-22-2−2i2i−2i2i002-200−2i2i−i2i2−i2i22−22−2001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ2ζ00−2ζ32ζ3−i2i22−2000000000000
χ482-22-2−2i2i−2i2i002-200−2i2i−i2i2−i2i22−22−200−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ−2ζ002ζ3−2ζ3−i2i22−2000000000000
χ492-22-2−2i2i−2i2i00-22002i−2ii2−i2i2−i2−22−22001+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00−i2i22−2000000000000
χ502-22-2−2i2i−2i2i00-22002i−2ii2−i2i2−i2−22−2200−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00−i2i22−2000000000000
χ512-22-2−2i2i−2i2i00-22002i−2i−i2i2−i2i22−22−2001+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00i2−i2−22000000000000
χ522-22-2−2i2i−2i2i00-22002i−2i−i2i2−i2i22−22−200−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00i2−i2−22000000000000
χ5344-4-444-4-4-4400-4400000000000000000000000000000000000000000000
χ5444-4-4-4-4444-400-4400000000000000000000000000000000000000000000
χ554-4-444i−4i−4i4i000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000
χ564-4-444i−4i−4i4i00000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000
χ574-4-44−4i4i4i−4i000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000
χ584-4-44−4i4i4i−4i00000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000

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