Finite Group Databasebeta

← Group #9591

Character table — Group #9591

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11111111222222224444444444888888888888888816161616
order1222444422444444448888888844448888888888884488
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-1111-1-111-1iiii−i−i−i−iii−i−ii−ii−i11-1-111-1-11-1i−i
χ101111-1-1-1-1-1-1111-1-111-1iiii−i−i−i−iii−i−i−ii−ii-1-11111-1-1-11−ii
χ111111-1-1-1-1-1-1111-1-111-1iiii−i−i−i−i−i−iiii−ii−i11-1-1-1-111-11−ii
χ121111-1-1-1-1-1-1111-1-111-1iiii−i−i−i−i−i−iii−ii−ii-1-111-1-1111-1i−i
χ131111-1-1-1-1-1-1111-1-111-1−i−i−i−iiiiiii−i−ii−ii−i-1-111-1-1111-1−ii
χ141111-1-1-1-1-1-1111-1-111-1−i−i−i−iiiiiii−i−i−ii−ii11-1-1-1-111-11i−i
χ151111-1-1-1-1-1-1111-1-111-1−i−i−i−iiiii−i−iiii−ii−i-1-11111-1-1-11i−i
χ161111-1-1-1-1-1-1111-1-111-1−i−i−i−iiiii−i−iii−ii−ii11-1-111-1-11-1−ii
χ1722222222222-2-2-2-22-2-200000000000022-2-2000000000000
χ1822222222222-2-2-2-22-2-2000000000000-2-222000000000000
χ1922222222-2-2-22222-2-2-222-2-222-2-200000000000000000000
χ2022222222-2-2-22222-2-2-2-2-222-2-22200000000000000000000
χ2122222222-2-2-2-2-2-2-2-22200000000000000002i−2i2i−2i00000000
χ2222222222-2-2-2-2-2-2-2-2220000000000000000−2i2i−2i2i00000000
χ232222-2-2-2-222-222-2-2-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ242222-2-2-2-222-222-2-2-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ252222-2-2-2-222-2-2-222-22-200000000000000002i−2i−2i2i00000000
χ262222-2-2-2-222-2-2-222-22-20000000000000000−2i2i2i−2i00000000
χ272222-2-2-2-2-2-22-2-2222-220000000000002i−2i−2i2i000000000000
χ282222-2-2-2-2-2-22-2-2222-22000000000000−2i2i2i−2i000000000000
χ292-22-22i−2i2i−2i0002-22i−2i000002ζ3−2ζ3002ζ−2ζ1+i−1−i1−i−1+i00000000i2−i22−20000
χ302-22-22i−2i2i−2i0002-22i−2i000002ζ3−2ζ3002ζ−2ζ−1−i1+i−1+i1−i00000000−i2i2−220000
χ312-22-22i−2i2i−2i0002-22i−2i00000−2ζ32ζ300−2ζ2ζ1+i−1−i1−i−1+i00000000−i2i2−220000
χ322-22-22i−2i2i−2i0002-22i−2i00000−2ζ32ζ300−2ζ2ζ−1−i1+i−1+i1−i00000000i2−i22−20000
χ332-22-2−2i2i−2i2i0002-2−2i2i000002ζ−2ζ002ζ3−2ζ31−i−1+i1+i−1−i00000000i2−i2−220000
χ342-22-2−2i2i−2i2i0002-2−2i2i000002ζ−2ζ002ζ3−2ζ3−1+i1−i−1−i1+i00000000−i2i22−20000
χ352-22-2−2i2i−2i2i0002-2−2i2i00000−2ζ2ζ00−2ζ32ζ31−i−1+i1+i−1−i00000000−i2i22−20000
χ362-22-2−2i2i−2i2i0002-2−2i2i00000−2ζ2ζ00−2ζ32ζ3−1+i1−i−1−i1+i00000000i2−i2−220000
χ3744-4-444-4-44-4-400004000000000000000000000000000000
χ3844-4-444-4-4-4440000-4000000000000000000000000000000
χ3944-4-4-4-4444-440000-4000000000000000000000000000000
χ4044-4-4-4-444-44-400004000000000000000000000000000000
χ414-44-44i−4i4i−4i000-44−4i4i0000000000000000000000000000000
χ424-44-4−4i4i−4i4i000-444i−4i0000000000000000000000000000000
χ434-4-444i−4i−4i4i00000000002−2i−2+2i002+2i−2−2i0000000000000000000000
χ444-4-444i−4i−4i4i0000000000−2+2i2−2i00−2−2i2+2i0000000000000000000000
χ454-4-44−4i4i4i−4i00000000002+2i−2−2i002−2i−2+2i0000000000000000000000
χ464-4-44−4i4i4i−4i0000000000−2−2i2+2i00−2+2i2−2i0000000000000000000000

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