Finite Group Databasebeta

← Group #8991

Character table — Group #8991

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222244444444444444444488888888888888881616
order1222444422444444224444888888888888244444888888888824
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111-1-11-1-11111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ71111111111111111-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-1-1-1-1-1-1-11111111-1-1-1ii−i−iiiii−i−i−i−i-11ii−i−ii−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-1-1-11111111-1-1-1ii−i−i−i−i−i−iiiii-11−i−iiii−iii−i−i-1-111-11
χ111111-1-1-1-1-1-1-1-11111111-1-1-1−i−iiiiiii−i−i−i−i-11ii−i−i−ii−i−iii-1-111-11
χ121111-1-1-1-1-1-1-1-11111111-1-1-1−i−iii−i−i−i−iiiii-11−i−iii−ii−i−iii11-1-11-1
χ131111-1-1-1-1-1-1-1-11111-1-1111-1ii−i−iiiii−i−i−i−i1-1−i−iiii−i−i−iii11-1-1-11
χ141111-1-1-1-1-1-1-1-11111-1-1111-1ii−i−i−i−i−i−iiiii1-1ii−i−ii−i−i−iii-1-1111-1
χ151111-1-1-1-1-1-1-1-11111-1-1111-1−i−iiiiiii−i−i−i−i1-1−i−iii−iiii−i−i-1-1111-1
χ161111-1-1-1-1-1-1-1-11111-1-1111-1−i−iii−i−i−i−iiiii1-1ii−i−i−iiii−i−i11-1-1-11
χ172222222222-2-222-2-200-200-2222200000000000000-2-20000000000
χ182222222222-2-222-2-200-200-2-2-2-2-200000000000000220000000000
χ1922222222-2-222-2-22222-222-2000000000000-2-20000000000000000
χ2022222222-2-222-2-222-2-2-2-2-2-2000000000000220000000000000000
χ2122222222-2-2-2-2-2-2-2-2002002000000000000000000002-22-2000000
χ2222222222-2-2-2-2-2-2-2-200200200000000000000000000-22-22000000
χ232222-2-2-2-22222-2-2-2-200200-2000000000000000000002i−2i−2i2i000000
χ242222-2-2-2-22222-2-2-2-200200-200000000000000000000−2i2i2i−2i000000
χ252222-2-2-2-222-2-2-2-22222-2-2-220000000000002-20000000000000000
χ262222-2-2-2-222-2-2-2-222-2-2-2222000000000000-220000000000000000
χ272222-2-2-2-2-2-22222-2-200-20022i2i−2i−2i00000000000000−2i2i0000000000
χ282222-2-2-2-2-2-22222-2-200-2002−2i−2i2i2i000000000000002i−2i0000000000
χ2922-2-22i−2i2i−2i002i−2i002-22-202i−2i000001+i1+i−1−i−1−i1−i1−i−1+i−1+i001+i−1−i1−i−1+i000000000000
χ3022-2-22i−2i2i−2i002i−2i002-22-202i−2i00000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−1−i1+i−1+i1−i000000000000
χ3122-2-22i−2i2i−2i002i−2i002-2-220−2i2i000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00−1−i1+i−1+i1−i000000000000
χ3222-2-22i−2i2i−2i002i−2i002-2-220−2i2i00000−1−i−1−i1+i1+i−1+i−1+i1−i1−i001+i−1−i1−i−1+i000000000000
χ3322-2-2−2i2i−2i2i00−2i2i002-22-20−2i2i000001−i1−i−1+i−1+i1+i1+i−1−i−1−i001−i−1+i1+i−1−i000000000000
χ3422-2-2−2i2i−2i2i00−2i2i002-22-20−2i2i00000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−1+i1−i−1−i1+i000000000000
χ3522-2-2−2i2i−2i2i00−2i2i002-2-2202i−2i000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−1+i1−i−1−i1+i000000000000
χ3622-2-2−2i2i−2i2i00−2i2i002-2-2202i−2i00000−1+i−1+i1−i1−i−1−i−1−i1+i1+i001−i−1+i1+i−1−i000000000000
χ372-2-2222-2-22-2002-2000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000000000002−22−200
χ382-2-2222-2-22-2002-2000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000−22−2200
χ392-2-2222-2-22-2002-200000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000−22−2200
χ402-2-2222-2-22-2002-200000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000000000002−22−200
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−4i00−4i4i00-44000000000000000000000000000000000000
χ4644-4-4−4i4i−4i4i004i−4i00-44000000000000000000000000000000000000
χ474-44-44i−4i−4i4i0000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ484-44-44i−4i−4i4i000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ494-44-4−4i4i4i−4i0000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ504-44-4−4i4i4i−4i000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
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.