Finite Group Databasebeta

← Group #7296

Character table — Group #7296

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
χ2922-2-222-2-22-2002-20022−2−222−2−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3022-2-222-2-22-2002-20022−2−222−2−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3122-2-222-2-22-2002-200−2−222−2−22200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3222-2-222-2-22-2002-200−2−222−2−22200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3322-2-222-2-2-2200-220022−2−222−2−200−22−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3422-2-222-2-2-2200-220022−2−222−2−200−22−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3522-2-222-2-2-2200-2200−2−222−2−222002−22−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3622-2-222-2-2-2200-2200−2−222−2−222002−22−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3722-2-2-2-2222-200-220022−2−2−2−222002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3822-2-2-2-2222-200-220022−2−2−2−222002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3922-2-2-2-2222-200-2200−2−22222−2−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4022-2-2-2-2222-200-2200−2−22222−2−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4122-2-2-2-222-22002-20022−2−2−2−22200−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ4222-2-2-2-222-22002-20022−2−2−2−22200−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4322-2-2-2-222-22002-200−2−22222−2−2002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4422-2-2-2-222-22002-200−2−22222−2−2002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ452-22-22i−2i2i−2i002i−2i002-22i−2i2i−2i2-22-200000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ462-22-22i−2i2i−2i002i−2i002-22i−2i2i−2i2-22-20000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ472-22-22i−2i2i−2i002i−2i002-2−2i2i−2i2i-22-2200000000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ482-22-22i−2i2i−2i002i−2i002-2−2i2i−2i2i-22-220000000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ492-22-2−2i2i−2i2i00−2i2i002-22i−2i2i−2i-22-2200000000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ502-22-2−2i2i−2i2i00−2i2i002-22i−2i2i−2i-22-220000000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ512-22-2−2i2i−2i2i00−2i2i002-2−2i2i−2i2i2-22-200000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ522-22-2−2i2i−2i2i00−2i2i002-2−2i2i−2i2i2-22-20000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ534-44-44i−4i4i−4i00−4i4i00-44000000000000000000000000000000000000000000
χ544-44-4−4i4i−4i4i004i−4i00-44000000000000000000000000000000000000000000
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 16 (ζ16 = 1); i = ζ4.