Finite Group Databasebeta

← Group #9053

Character table — Group #9053

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222244444444444444444488888888888888881616
order1222444422444444448888888888888888224444448888888824
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ91111-1-1-1-1-1-11111-1-1-11ii−i−iii−i−i1111-1-1-1-111-1-1ii−i−ii−ii−iii−i−i1-1
χ101111-1-1-1-1-1-11111-1-1-11ii−i−iii−i−i-1-1-1-1111111-1-1−i−iiii−ii−i−i−iii-11
χ111111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iii1111-1-1-1-1-1-111ii−i−i−iii−i−i−iii-11
χ121111-1-1-1-1-1-11111-1-1-11ii−i−i−i−iii-1-1-1-11111-1-111−i−iii−iii−iii−i−i1-1
χ131111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−i1111-1-1-1-1-1-111−i−iiii−i−iiii−i−i-11
χ141111-1-1-1-1-1-11111-1-1-11−i−iiiii−i−i-1-1-1-11111-1-111ii−i−ii−i−ii−i−iii1-1
χ151111-1-1-1-1-1-11111-1-1-11−i−iii−i−iii1111-1-1-1-111-1-1−i−iii−ii−ii−i−iii1-1
χ161111-1-1-1-1-1-11111-1-1-11−i−iii−i−iii-1-1-1-1111111-1-1ii−i−i−ii−iiii−i−i-11
χ172222222222-2-222-2-2-2-2000022220000000000000000-2-200000000
χ182222222222-2-222-2-2-2-20000-2-2-2-200000000000000002200000000
χ1922222222-2-222-2-222-2-222220000000000000000000000-2-2000000
χ2022222222-2-222-2-222-2-2-2-2-2-2000000000000000000000022000000
χ2122222222-2-2-2-2-2-2-2-22200000000000000002-22-200000000000000
χ2222222222-2-2-2-2-2-2-2-2220000000000000000-22-2200000000000000
χ232222-2-2-2-22222-2-2-2-22-22i2i−2i−2i0000000000000000000000−2i2i000000
χ242222-2-2-2-22222-2-2-2-22-2−2i−2i2i2i00000000000000000000002i−2i000000
χ252222-2-2-2-222-2-2-2-222-2200000000000000002-2-2200000000000000
χ262222-2-2-2-222-2-2-2-222-220000000000000000-222-200000000000000
χ272222-2-2-2-2-2-2-2-222222-200002i2i−2i−2i0000000000000000−2i2i00000000
χ282222-2-2-2-2-2-2-2-222222-20000−2i−2i2i2i00000000000000002i−2i00000000
χ2922-2-22i−2i2i−2i002-2002i−2i002ζ−2ζ2ζ3−2ζ3000022−2−2i2i2−i2−i200001+i−1−i1−i−1+i0000000000
χ3022-2-22i−2i2i−2i002-2002i−2i002ζ−2ζ2ζ3−2ζ30000−2−222−i2−i2i2i20000−1−i1+i−1+i1−i0000000000
χ3122-2-22i−2i2i−2i002-2002i−2i00−2ζ2ζ−2ζ32ζ3000022−2−2i2i2−i2−i20000−1−i1+i−1+i1−i0000000000
χ3222-2-22i−2i2i−2i002-2002i−2i00−2ζ2ζ−2ζ32ζ30000−2−222−i2−i2i2i200001+i−1−i1−i−1+i0000000000
χ3322-2-2−2i2i−2i2i002-200−2i2i002ζ3−2ζ32ζ−2ζ000022−2−2−i2−i2i2i20000−1+i1−i−1−i1+i0000000000
χ3422-2-2−2i2i−2i2i002-200−2i2i002ζ3−2ζ32ζ−2ζ0000−2−222i2i2−i2−i200001−i−1+i1+i−1−i0000000000
χ3522-2-2−2i2i−2i2i002-200−2i2i00−2ζ32ζ3−2ζ2ζ000022−2−2−i2−i2i2i200001−i−1+i1+i−1−i0000000000
χ3622-2-2−2i2i−2i2i002-200−2i2i00−2ζ32ζ3−2ζ2ζ0000−2−222i2i2−i2−i20000−1+i1−i−1−i1+i0000000000
χ372-2-2222-2-22-2002-2000000002i−2i2i−2i2−22−22−22−2000000000000i2−i2i2−i200
χ382-2-2222-2-22-2002-2000000002i−2i2i−2i−22−22−22−22000000000000−i2i2−i2i200
χ392-2-2222-2-22-2002-200000000−2i2i−2i2i2−22−22−22−2000000000000−i2i2−i2i200
χ402-2-2222-2-22-2002-200000000−2i2i−2i2i−22−22−22−22000000000000i2−i2i2−i200
χ412-2-22-2-222-22002-2000000002-2-222−22−2−22−220000000000002−2−2200
χ422-2-22-2-222-22002-2000000002-2-22−22−222−22−2000000000000−222−200
χ432-2-22-2-222-22002-200000000-222-22−22−2−22−22000000000000−222−200
χ442-2-22-2-222-22002-200000000-222-2−22−222−22−20000000000002−2−2200
χ4544-4-44i−4i4i−4i00-4400−4i4i000000000000000000000000000000000000
χ4644-4-4−4i4i−4i4i00-44004i−4i000000000000000000000000000000000000
χ474-44-44i−4i−4i4i0000000000000000002-2-222i−2i−2i2i000000000000000000
χ484-44-44i−4i−4i4i000000000000000000-222-2−2i2i2i−2i000000000000000000
χ494-44-4−4i4i4i−4i0000000000000000002-2-22−2i2i2i−2i000000000000000000
χ504-44-4−4i4i4i−4i000000000000000000-222-22i−2i−2i2i000000000000000000
χ514-4-4444-4-4-4400-4400000000000000000000000000000000000000
χ524-4-44-4-4444-400-4400000000000000000000000000000000000000

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