Finite Group Databasebeta

← Group #9587

Character table — Group #9587

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11111111222222224444444444888888888888888816161616
order1222444444444444248888888888888888888888884488
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−ii−ii−i11-1-1ii−i−i11-1-11-1i−i
χ101111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−ii−ii−i11-1-1−i−iii-1-111-11−ii
χ111111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−i−ii−ii-1-111ii−i−i11-1-1-11−ii
χ121111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−i−ii−ii-1-111−i−iii-1-1111-1i−i
χ131111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiiii−ii−i-1-111ii−i−i-1-1111-1−ii
χ141111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiiii−ii−i-1-111−i−iii11-1-1-11i−i
χ151111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii−ii−ii11-1-1ii−i−i-1-111-11i−i
χ161111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii−ii−ii11-1-1−i−iii11-1-11-1−ii
χ172222222222-2-222-2-2-2-20000000022-2-20000000000000000
χ182222222222-2-222-2-2-2-200000000-2-2220000000000000000
χ1922222222-2-222-2-222-2-222-2-222-2-200000000000000000000
χ2022222222-2-222-2-222-2-2-2-222-2-22200000000000000000000
χ2122222222-2-2-2-2-2-2-2-2220000000000002i−2i2i−2i000000000000
χ2222222222-2-2-2-2-2-2-2-222000000000000−2i2i−2i2i000000000000
χ232222-2-2-2-222-2-2-2-2222-2000000002i−2i−2i2i0000000000000000
χ242222-2-2-2-222-2-2-2-2222-200000000−2i2i2i−2i0000000000000000
χ252222-2-2-2-2-2-22222-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ262222-2-2-2-2-2-22222-2-22-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ272222-2-2-2-2-2-2-2-22222-220000000000002i−2i−2i2i000000000000
χ282222-2-2-2-2-2-2-2-22222-22000000000000−2i2i2i−2i000000000000
χ292-22-22i−2i2i−2i002-2002i−2i00002ζ3−2ζ3002ζ−2ζ000000001+i−1−i1−i−1+ii2−i22−20000
χ302-22-22i−2i2i−2i002-2002i−2i00002ζ3−2ζ3002ζ−2ζ00000000−1−i1+i−1+i1−i−i2i2−220000
χ312-22-22i−2i2i−2i002-2002i−2i0000−2ζ32ζ300−2ζ2ζ000000001+i−1−i1−i−1+i−i2i2−220000
χ322-22-22i−2i2i−2i002-2002i−2i0000−2ζ32ζ300−2ζ2ζ00000000−1−i1+i−1+i1−ii2−i22−20000
χ332-22-2−2i2i−2i2i002-200−2i2i00002ζ−2ζ002ζ3−2ζ3000000001−i−1+i1+i−1−ii2−i2−220000
χ342-22-2−2i2i−2i2i002-200−2i2i00002ζ−2ζ002ζ3−2ζ300000000−1+i1−i−1−i1+i−i2i22−20000
χ352-22-2−2i2i−2i2i002-200−2i2i0000−2ζ2ζ00−2ζ32ζ3000000001−i−1+i1+i−1−i−i2i22−20000
χ362-22-2−2i2i−2i2i002-200−2i2i0000−2ζ2ζ00−2ζ32ζ300000000−1+i1−i−1−i1+ii2−i2−220000
χ3744-4-444-4-4000000000022−220022−220000000000000000000000
χ3844-4-444-4-40000000000−222200−22220000000000000000000000
χ3944-4-4-4-44400000000002i2−2i200−2i22i20000000000000000000000
χ4044-4-4-4-4440000000000−2i22i2002i2−2i20000000000000000000000
χ414-44-44i−4i4i−4i00-4400−4i4i000000000000000000000000000000
χ424-44-4−4i4i−4i4i00-44004i−4i000000000000000000000000000000
χ434-4-444i−4i−4i4i4-4004i−4i00000000000000000000000000000000
χ444-4-444i−4i−4i4i-4400−4i4i00000000000000000000000000000000
χ454-4-44−4i4i4i−4i4-400−4i4i00000000000000000000000000000000
χ464-4-44−4i4i4i−4i-44004i−4i00000000000000000000000000000000

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