Finite Group Databasebeta

← Group #8903

Character table — Group #8903

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222244444444444444444488888888888888881616
order1222444422444444444444888888888888244444888888888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111-1-1-1-11111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ711111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-1-1-1-1-111-1-111-111-1-11ii−i−i1111-1-1-1-11-1ii−i−ii−iii−i−i11-1-1i−i
χ101111-1-1-1-1-1-111-1-111-111-1-11ii−i−i-1-1-1-111111-1−i−iiii−iii−i−i-1-111−ii
χ111111-1-1-1-1-1-111-1-111-111-1-11−i−iii1111-1-1-1-11-1−i−iii−ii−i−iii11-1-1−ii
χ121111-1-1-1-1-1-111-1-111-111-1-11−i−iii-1-1-1-111111-1ii−i−i−ii−i−iii-1-111i−i
χ131111-1-1-1-1-1-111-1-111-1-1-1111ii−i−i1111-1-1-1-1-11ii−i−ii−i−i−iii-1-111−ii
χ141111-1-1-1-1-1-111-1-111-1-1-1111ii−i−i-1-1-1-11111-11−i−iiii−i−i−iii11-1-1i−i
χ151111-1-1-1-1-1-111-1-111-1-1-1111−i−iii1111-1-1-1-1-11−i−iii−iiii−i−i-1-111i−i
χ161111-1-1-1-1-1-111-1-111-1-1-1111−i−iii-1-1-1-11111-11ii−i−i−iiii−i−i11-1-1−ii
χ17222222222222-2-2-2-2-22222-2000000000000-2-20000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2000000000000220000000000000000
χ1922222222-2-2-2-22222-20000-2222200000000000000-2-20000000000
χ2022222222-2-2-2-22222-20000-2-2-2-2-200000000000000220000000000
χ2122222222-2-2-2-2-2-2-2-2200002000000000000000000002-22-2000000
χ2222222222-2-2-2-2-2-2-2-220000200000000000000000000-22-22000000
χ232222-2-2-2-222-2-222-2-2-200002000000000000000000002i−2i−2i2i000000
χ242222-2-2-2-222-2-222-2-2-20000200000000000000000000−2i2i2i−2i000000
χ252222-2-2-2-222-2-2-2-22220000-22i2i−2i−2i00000000000000−2i2i0000000000
χ262222-2-2-2-222-2-2-2-22220000-2−2i−2i2i2i000000000000002i−2i0000000000
χ272222-2-2-2-2-2-22222-2-2222-2-2-2000000000000-220000000000000000
χ282222-2-2-2-2-2-22222-2-22-2-222-20000000000002-20000000000000000
χ2922-2-222-2-2-222-2000002i−2i2i−2i0000022−2−222−2−2000000000000i2−i2i2−i200
χ3022-2-222-2-2-222-2000002i−2i2i−2i00000−2−222−2−222000000000000−i2i2−i2i200
χ3122-2-222-2-2-222-200000−2i2i−2i2i0000022−2−222−2−2000000000000−i2i2−i2i200
χ3222-2-222-2-2-222-200000−2i2i−2i2i00000−2−222−2−222000000000000i2−i2i2−i200
χ3322-2-2-2-2222-22-2000002i−2i−2i2i0000022−2−2−2−222000000000000i2−i2−i2i200
χ3422-2-2-2-2222-22-2000002i−2i−2i2i00000−2−22222−2−2000000000000−i2i2i2−i200
χ3522-2-2-2-2222-22-200000−2i2i2i−2i0000022−2−2−2−222000000000000−i2i2i2−i200
χ3622-2-2-2-2222-22-200000−2i2i2i−2i00000−2−22222−2−2000000000000i2−i2−i2i200
χ372-22-22i−2i2i−2i00002i−2i2-20000002ζ−2ζ2ζ3−2ζ3i2−i2i2−i22−22−2001−i−1+i1+i−1−i000000000000
χ382-22-22i−2i2i−2i00002i−2i2-20000002ζ−2ζ2ζ3−2ζ3−i2i2−i2i2−22−2200−1+i1−i−1−i1+i000000000000
χ392-22-22i−2i2i−2i00002i−2i2-2000000−2ζ2ζ−2ζ32ζ3i2−i2i2−i22−22−200−1+i1−i−1−i1+i000000000000
χ402-22-22i−2i2i−2i00002i−2i2-2000000−2ζ2ζ−2ζ32ζ3−i2i2−i2i2−22−22001−i−1+i1+i−1−i000000000000
χ412-22-2−2i2i−2i2i0000−2i2i2-20000002ζ3−2ζ32ζ−2ζi2−i2i2−i2−22−22001+i−1−i1−i−1+i000000000000
χ422-22-2−2i2i−2i2i0000−2i2i2-20000002ζ3−2ζ32ζ−2ζ−i2i2−i2i22−22−200−1−i1+i−1+i1−i000000000000
χ432-22-2−2i2i−2i2i0000−2i2i2-2000000−2ζ32ζ3−2ζ2ζi2−i2i2−i2−22−2200−1−i1+i−1+i1−i000000000000
χ442-22-2−2i2i−2i2i0000−2i2i2-2000000−2ζ32ζ3−2ζ2ζ−i2i2−i2i22−22−2001+i−1−i1−i−1+i000000000000
χ4544-4-444-4-44-4-440000000000000000000000000000000000000000
χ4644-4-4-4-444-44-440000000000000000000000000000000000000000
χ474-44-44i−4i4i−4i0000−4i4i-44000000000000000000000000000000000000
χ484-44-4−4i4i−4i4i00004i−4i-44000000000000000000000000000000000000
χ494-4-444i−4i−4i4i0000000000000000002i−2i−2i2i2-2-22000000000000000000
χ504-4-444i−4i−4i4i000000000000000000−2i2i2i−2i-222-2000000000000000000
χ514-4-44−4i4i4i−4i0000000000000000002i−2i−2i2i-222-2000000000000000000
χ524-4-44−4i4i4i−4i000000000000000000−2i2i2i−2i2-2-22000000000000000000

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