Finite Group Databasebeta

← Group #8437

Character table — Group #8437

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222244444444444444444488888888888888881616
order1222444422444444444444444488888888222444444444888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-111
χ511111111111111111-1-1-1-11111111111111-1-1-1-111-1-11111-1-1-1-1-1-1
χ611111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ711111111111111111-1-1-1-1-1-1-1-1111111111-111-1-1-111-1-1-1-1-1-1-1-111
χ811111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1
χ91111-1-1-1-1-1-11111-1-1111-1-111-1-1-1iiii−i−i−i−i111-11-1-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-1-1-11111-1-1111-1-111-1-1-1−i−i−i−iiiii111-11-1-1-1−i−iii−i−iii−ii
χ111111-1-1-1-1-1-11111-1-1111-1-1-1-111-1iiii−i−i−i−i1-1-1-1-1111−i−iiiii−i−i−ii
χ121111-1-1-1-1-1-11111-1-1111-1-1-1-111-1−i−i−i−iiiii1-1-1-1-1111ii−i−i−i−iiii−i
χ131111-1-1-1-1-1-11111-1-11-1-11111-1-1-1iiii−i−i−i−i-1-1-111-111ii−i−i−i−iii−ii
χ141111-1-1-1-1-1-11111-1-11-1-11111-1-1-1−i−i−i−iiiii-1-1-111-111−i−iiiii−i−ii−i
χ151111-1-1-1-1-1-11111-1-11-1-111-1-111-1iiii−i−i−i−i-1111-11-1-1−i−iii−i−iiii−i
χ161111-1-1-1-1-1-11111-1-11-1-111-1-111-1−i−i−i−iiiii-1111-11-1-1ii−i−iii−i−i−ii
χ17222222222222-2-2-2-2-222220000-200000000-200-200000000000000
χ18222222222222-2-2-2-2-2-2-2-2-20000-200000000200200000000000000
χ1922222222-2-2-2-22222-200002222-2000000000000-2-2000000000000
χ2022222222-2-2-2-22222-20000-2-2-2-2-200000000000022000000000000
χ2122222222-2-2-2-2-2-2-2-220000000020000000002-20002-20000000000
χ2222222222-2-2-2-2-2-2-2-22000000002000000000-22000-220000000000
χ232222-2-2-2-222-2-222-2-2-2000022-2-22000000000000-22000000000000
χ242222-2-2-2-222-2-222-2-2-20000-2-22220000000000002-2000000000000
χ252222-2-2-2-222-2-2-2-222200000000-20000000002-2000-220000000000
χ262222-2-2-2-222-2-2-2-222200000000-2000000000-220002-20000000000
χ272222-2-2-2-2-2-222-2-222-222-2-20000200000000-200200000000000000
χ282222-2-2-2-2-2-222-2-222-2-2-2220000200000000200-200000000000000
χ2922-2-222-2-2-222-2000002i−2i2i−2i00000i2i2−i2−i2i2i2−i2−i20000000000002−22−200
χ3022-2-222-2-2-222-2000002i−2i2i−2i00000−i2−i2i2i2−i2−i2i2i2000000000000−22−2200
χ3122-2-222-2-2-222-200000−2i2i−2i2i00000i2i2−i2−i2i2i2−i2−i2000000000000−22−2200
χ3222-2-222-2-2-222-200000−2i2i−2i2i00000−i2−i2i2i2−i2−i2i2i20000000000002−22−200
χ3322-2-2-2-2222-22-2000002i−2i−2i2i0000022−2−2−2−222000000000000−i2i2i2−i200
χ3422-2-2-2-2222-22-2000002i−2i−2i2i00000−2−22222−2−2000000000000i2−i2−i2i200
χ3522-2-2-2-2222-22-200000−2i2i2i−2i0000022−2−2−2−222000000000000i2−i2−i2i200
χ3622-2-2-2-2222-22-200000−2i2i2i−2i00000−2−22222−2−2000000000000−i2i2i2−i200
χ372-22-22i−2i2i−2i00002-22i−2i000002-22i−2i01+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i−1−i1−i−1+i000000
χ382-22-22i−2i2i−2i00002-22i−2i000002-22i−2i0−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i1+i−1+i1−i000000
χ392-22-22i−2i2i−2i00002-22i−2i00000-22−2i2i01+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1−i1+i−1+i1−i000000
χ402-22-22i−2i2i−2i00002-22i−2i00000-22−2i2i0−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001+i−1−i1−i−1+i000000
χ412-22-2−2i2i−2i2i00002-2−2i2i000002-2−2i2i01−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i−1+i1+i−1−i000000
χ422-22-2−2i2i−2i2i00002-2−2i2i000002-2−2i2i0−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i1−i−1−i1+i000000
χ432-22-2−2i2i−2i2i00002-2−2i2i00000-222i−2i01−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1+i1−i−1−i1+i000000
χ442-22-2−2i2i−2i2i00002-2−2i2i00000-222i−2i0−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001−i−1+i1+i−1−i000000
χ4544-4-444-4-44-4-440000000000000000000000000000000000000000
χ4644-4-4-4-444-44-440000000000000000000000000000000000000000
χ474-44-44i−4i4i−4i0000-44−4i4i000000000000000000000000000000000000
χ484-44-4−4i4i−4i4i0000-444i−4i000000000000000000000000000000000000
χ494-4-444i−4i−4i4i0000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ504-4-444i−4i−4i4i000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ514-4-44−4i4i4i−4i0000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ524-4-44−4i4i4i−4i000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000

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