Finite Group Databasebeta

← Group #11264

Character table — Group #11264

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111111122222222222244444444888888888888888888888888
order1222444422222244444488888888444488888888888888888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91-1-1111-1-111-1-1-1111-11-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−i
χ101-1-1111-1-111-1-1-1111-11-1-1iiii−i−i−i−i11-1-1-1-111−i−iii−i−iii-1-111ii−i−i
χ111-1-1111-1-111-1-1-1111-11-1-1iiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i-1-111−i−iii
χ121-1-1111-1-111-1-1-1111-11-1-1iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11-1-1−i−iii
χ131-1-1111-1-111-1-1-1111-11-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii
χ141-1-1111-1-111-1-1-1111-11-1-1−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i-1-111−i−iii
χ151-1-1111-1-111-1-1-1111-11-1-1−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii-1-111ii−i−i
χ161-1-1111-1-111-1-1-1111-11-1-1−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11-1-1ii−i−i
χ17222222222-22-2-2-22-2-2-22-20000000000000000000000002i−2i2i−2i0000
χ18222222222-22-2-2-22-2-2-22-2000000000000000000000000−2i2i−2i2i0000
χ1922222222-22-22-2-2-2-222-2-2000000000000000000002i−2i2i−2i00000000
χ2022222222-22-22-2-2-2-222-2-200000000000000000000−2i2i−2i2i00000000
χ2122222222-2-2-2-222-22-2-2-2200000000000000000000000000002-22-2
χ2222222222-2-2-2-222-22-2-2-220000000000000000000000000000-22-22
χ232222-2-2-2-2222222-2-2-2-2-2-2000000002-22-200000000000000000000
χ242222-2-2-2-2222222-2-2-2-2-2-200000000-22-2200000000000000000000
χ252222-2-2-2-22-22-2-2-2-2222-220000000000002i−2i2i−2i0000000000000000
χ262222-2-2-2-22-22-2-2-2-2222-22000000000000−2i2i−2i2i0000000000000000
χ272222-2-2-2-2-22-22-2-222-2-22200000000000000002i−2i2i−2i000000000000
χ282222-2-2-2-2-22-22-2-222-2-2220000000000000000−2i2i−2i2i000000000000
χ292222-2-2-2-2-2-2-2-2222-2222-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ302222-2-2-2-2-2-2-2-2222-2222-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312-2-2222-2-22-2-222-22-22-2-220000000000000000000000002i−2i−2i2i0000
χ322-2-2222-2-22-2-222-22-22-2-22000000000000000000000000−2i2i2i−2i0000
χ332-2-2222-2-2-222-22-2-2-2-2222000000000000000000002-2-2200000000
χ342-2-2222-2-2-222-22-2-2-2-222200000000000000000000-222-200000000
χ352-2-2222-2-2-2-222-22-222-22-200000000000000000000000000002i−2i−2i2i
χ362-2-2222-2-2-2-222-22-222-22-20000000000000000000000000000−2i2i2i−2i
χ372-2-22-2-22222-2-2-22-2-22-222000000002-2-2200000000000000000000
χ382-2-22-2-22222-2-2-22-2-22-22200000000-222-200000000000000000000
χ392-2-22-2-2222-2-222-2-22-222-20000000000002i−2i−2i2i0000000000000000
χ402-2-22-2-2222-2-222-2-22-222-2000000000000−2i2i2i−2i0000000000000000
χ412-2-22-2-222-222-22-2222-2-2-200000000000000002-2-22000000000000
χ422-2-22-2-222-222-22-2222-2-2-20000000000000000-222-2000000000000
χ432-2-22-2-222-2-222-222-2-22-2222-2-2-2-222000000000000000000000000
χ442-2-22-2-222-2-222-222-2-22-22-2-22222-2-2000000000000000000000000
χ4544-4-44i−4i4i−4i0000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ4644-4-44i−4i4i−4i000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ4744-4-4−4i4i−4i4i0000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ4844-4-4−4i4i−4i4i000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ494-44-44i−4i−4i4i0000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000000000
χ504-44-44i−4i−4i4i000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000000000
χ514-44-4−4i4i4i−4i0000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000000000
χ524-44-4−4i4i4i−4i000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000000000

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