Finite Group Databasebeta

← Group #8935

Character table — Group #8935

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222244444444444444444488888888888888881616
order1222444444444444244444444488888888224488888888888888
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−iii−i−iii−i−i11-1-1i−ii−i11-1-111-1-1i−i
χ101111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−iii−i−i−i−iii-1-111i−i−ii11-1-1-1-111−ii
χ111111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−iiiii−i−i-1-111−iii−i-1-11111-1-1−ii
χ121111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−iii−i−iii11-1-1−ii−ii-1-111-1-111i−i
χ131111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiii−i−iii−i−i11-1-1i−ii−i-1-111-1-111−ii
χ141111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiii−i−i−i−iii-1-111i−i−ii-1-11111-1-1i−i
χ151111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiii−i−iiiii−i−i-1-111−iii−i11-1-1-1-111i−i
χ161111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiii−i−iii−i−iii11-1-1−ii−ii11-1-111-1-1−ii
χ172222222222-2-222-2-2-2-20000000000002222000000-2-20000000000
χ182222222222-2-222-2-2-2-2000000000000-2-2-2-2000000220000000000
χ1922222222-2-222-2-222-2-200000000222200000000-2-2000000000000
χ2022222222-2-222-2-222-2-200000000-2-2-2-20000000022000000000000
χ2122222222-2-2-2-2-2-2-2-22200000000000000002-22-200000000000000
χ2222222222-2-2-2-2-2-2-2-2220000000000000000-22-2200000000000000
χ232222-2-2-2-22222-2-2-2-2-2200000000000000002-2-2200000000000000
χ242222-2-2-2-22222-2-2-2-2-220000000000000000-222-200000000000000
χ252222-2-2-2-222-2-2-2-2222-2000000002i2i−2i−2i00000000−2i2i000000000000
χ262222-2-2-2-222-2-2-2-2222-200000000−2i−2i2i2i000000002i−2i000000000000
χ272222-2-2-2-2-2-22222-2-22-20000000000002i2i−2i−2i000000−2i2i0000000000
χ282222-2-2-2-2-2-22222-2-22-2000000000000−2i−2i2i2i0000002i−2i0000000000
χ2922-2-22i−2i2i−2i002i−2i002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ−2ζ2ζ3−2ζ30000000000002−2i2−i2000000
χ3022-2-22i−2i2i−2i002i−2i002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ2ζ−2ζ32ζ3000000000000−22−i2i2000000
χ3122-2-22i−2i2i−2i002i−2i002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ−2ζ2ζ3−2ζ3000000000000−22−i2i2000000
χ3222-2-22i−2i2i−2i002i−2i002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ2ζ−2ζ32ζ30000000000002−2i2−i2000000
χ3322-2-2−2i2i−2i2i00−2i2i002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ3−2ζ32ζ−2ζ000000000000−22i2−i2000000
χ3422-2-2−2i2i−2i2i00−2i2i002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ32ζ3−2ζ2ζ0000000000002−2−i2i2000000
χ3522-2-2−2i2i−2i2i00−2i2i002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ3−2ζ32ζ−2ζ0000000000002−2−i2i2000000
χ3622-2-2−2i2i−2i2i00−2i2i002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ32ζ3−2ζ2ζ000000000000−22i2−i2000000
χ372-22-22i−2i−2i2i2i−2i002-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002ζ−2ζ2ζ3−2ζ3000000000000i2−i22−200
χ382-22-22i−2i−2i2i2i−2i002-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−2ζ2ζ−2ζ32ζ3000000000000−i2i2−2200
χ392-22-22i−2i−2i2i2i−2i002-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002ζ−2ζ2ζ3−2ζ3000000000000−i2i2−2200
χ402-22-22i−2i−2i2i2i−2i002-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2ζ2ζ−2ζ32ζ3000000000000i2−i22−200
χ412-22-2−2i2i2i−2i−2i2i002-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002ζ3−2ζ32ζ−2ζ000000000000i2−i2−2200
χ422-22-2−2i2i2i−2i−2i2i002-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−2ζ32ζ3−2ζ2ζ000000000000−i2i22−200
χ432-22-2−2i2i2i−2i−2i2i002-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002ζ3−2ζ32ζ−2ζ000000000000−i2i22−200
χ442-22-2−2i2i2i−2i−2i2i002-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−2ζ32ζ3−2ζ2ζ000000000000i2−i2−2200
χ4544-4-44i−4i4i−4i00−4i4i00-44000000000000000000000000000000000000
χ4644-4-4−4i4i−4i4i004i−4i00-44000000000000000000000000000000000000
χ474-44-44i−4i−4i4i−4i4i00-4400000000000000000000000000000000000000
χ484-44-4−4i4i4i−4i4i−4i00-4400000000000000000000000000000000000000
χ494-4-4444-4-400000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ504-4-4444-4-40000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ514-4-44-4-44400000000002-2-222-2-2200000000000000000000000000
χ524-4-44-4-4440000000000-222-2-222-200000000000000000000000000

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