Finite Group Databasebeta

← Group #7299

Character table — Group #7299

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order12224444224444448888888844888816161616161616161616161616161616444444448888
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ101111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ111111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ121111-1-1-1-111-1-1-1-1111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ131111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−iii−i
χ141111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−i−ii
χ151111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−ii
χ161111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−i
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222-2-222-2-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ192222222222-2-222-2-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ2022222222-2-222-2-22222222222-2-2-2-2-2-20000000000000000000000000000
χ2122222222-2-2-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2222222222-2-2-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ232222-2-2-2-22222-2-2-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ242222-2-2-2-22222-2-2-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ252222-2-2-2-222-2-2-2-222-2-2-2-222222-2-2-2220000000000000000000000000000
χ262222-2-2-2-2-2-22222-2-2000000002-2000022−2−2−2−222−2−22222−2−2000000000000
χ272222-2-2-2-2-2-22222-2-2000000002-20000−2−22222−2−222−2−2−2−222000000000000
χ282222-2-2-2-2-2-2-2-222222222-2-2-2-2-22-2-2220000000000000000000000000000
χ2922-2-22i2i−2i−2i002i−2i002-22i2i−2i−2i22-2-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ3022-2-22i2i−2i−2i002i−2i002-22i2i−2i−2i22-2-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ3122-2-22i2i−2i−2i002i−2i002-2−2i−2i2i2i-2-22200000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ3222-2-22i2i−2i−2i002i−2i002-2−2i−2i2i2i-2-2220000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ3322-2-2−2i−2i2i2i00−2i2i002-22i2i−2i−2i-2-22200000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ3422-2-2−2i−2i2i2i00−2i2i002-22i2i−2i−2i-2-2220000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ3522-2-2−2i−2i2i2i00−2i2i002-2−2i−2i2i2i22-2-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ3622-2-2−2i−2i2i2i00−2i2i002-2−2i−2i2i2i22-2-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ372-22-22i−2i2i−2i2-2002i−2i002−22−2i2−i2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ382-22-22i−2i2i−2i2-2002i−2i002−22−2i2−i2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ392-22-22i−2i2i−2i2-2002i−2i00−22−22−i2i2−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ402-22-22i−2i2i−2i2-2002i−2i00−22−22−i2i2−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ412-22-22i−2i2i−2i-2200−2i2i002−22−2i2−i2i2−i200−22−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ422-22-22i−2i2i−2i-2200−2i2i002−22−2i2−i2i2−i200−22−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ432-22-22i−2i2i−2i-2200−2i2i00−22−22−i2i2−i2i2002−2i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ442-22-22i−2i2i−2i-2200−2i2i00−22−22−i2i2−i2i2002−2i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ452-22-2−2i2i−2i2i2-200−2i2i002−22−2−i2i2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ462-22-2−2i2i−2i2i2-200−2i2i002−22−2−i2i2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ472-22-2−2i2i−2i2i2-200−2i2i00−22−22i2−i2i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ482-22-2−2i2i−2i2i2-200−2i2i00−22−22i2−i2i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ492-22-2−2i2i−2i2i-22002i−2i002−22−2−i2i2−i2i200−22i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ502-22-2−2i2i−2i2i-22002i−2i002−22−2−i2i2−i2i200−22i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ512-22-2−2i2i−2i2i-22002i−2i00−22−22i2−i2i2−i2002−2−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ522-22-2−2i2i−2i2i-22002i−2i00−22−22i2−i2i2−i2002−2−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ5344-4-44i4i−4i−4i00−4i4i00-44000000000000000000000000000000000000000000
χ5444-4-4−4i−4i4i4i004i−4i00-44000000000000000000000000000000000000000000
χ554-4-444-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ564-4-444-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ574-4-44-444-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ584-4-44-444-400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.