Finite Group Databasebeta

← Group #9213

Character table — Group #9213

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11111111222222224444444444888888888888888816161616
order1222444444444444248888888824448888888888882488
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
χ91111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-1i−i
χ101111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i-11−ii
χ111111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-11−ii
χ121111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−i-1-111-1-111−i−iii−i−iii1-1i−i
χ131111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-1−ii
χ141111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii-11i−i
χ151111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-11i−i
χ161111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i1-1−ii
χ172222222222-2-2-2-222-2-222-2-222-2-200000000000000000000
χ182222222222-2-2-2-222-2-2-2-222-2-22200000000000000000000
χ1922222222-2-22222-2-2-2-2000000002-2-220000000000000000
χ2022222222-2-22222-2-2-2-200000000-222-20000000000000000
χ2122222222-2-2-2-2-2-2-2-222000000000000000000002i−2i2i−2i0000
χ2222222222-2-2-2-2-2-2-2-22200000000000000000000−2i2i−2i2i0000
χ232222-2-2-2-222-2-222-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000000000
χ242222-2-2-2-222-2-222-2-22-2−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ252222-2-2-2-2-2-222-2-2222-2000000002-22-20000000000000000
χ262222-2-2-2-2-2-222-2-2222-200000000-22-220000000000000000
χ272222-2-2-2-2-2-2-2-22222-22000000000000000000002-2-220000
χ282222-2-2-2-2-2-2-2-22222-2200000000000000000000-222-20000
χ2922-2-22i−2i2i−2i2-200002i−2i00002ζ3−2ζ3002ζ−2ζ00002−2i2−i21−i−1+i1+i−1−i00000000
χ3022-2-22i−2i2i−2i2-200002i−2i00002ζ3−2ζ3002ζ−2ζ0000−22−i2i2−1+i1−i−1−i1+i00000000
χ3122-2-22i−2i2i−2i2-200002i−2i0000−2ζ32ζ300−2ζ2ζ00002−2i2−i2−1+i1−i−1−i1+i00000000
χ3222-2-22i−2i2i−2i2-200002i−2i0000−2ζ32ζ300−2ζ2ζ0000−22−i2i21−i−1+i1+i−1−i00000000
χ3322-2-2−2i2i−2i2i2-20000−2i2i00002ζ−2ζ002ζ3−2ζ300002−2−i2i2−1−i1+i−1+i1−i00000000
χ3422-2-2−2i2i−2i2i2-20000−2i2i00002ζ−2ζ002ζ3−2ζ30000−22i2−i21+i−1−i1−i−1+i00000000
χ3522-2-2−2i2i−2i2i2-20000−2i2i0000−2ζ2ζ00−2ζ32ζ300002−2−i2i21+i−1−i1−i−1+i00000000
χ3622-2-2−2i2i−2i2i2-20000−2i2i0000−2ζ2ζ00−2ζ32ζ30000−22i2−i2−1−i1+i−1+i1−i00000000
χ3744-4-44i−4i4i−4i-440000−4i4i000000000000000000000000000000
χ3844-4-4−4i4i−4i4i-4400004i−4i000000000000000000000000000000
χ394-44-44i−4i−4i4i004-44i−4i00000000000000000000000000000000
χ404-44-44i−4i−4i4i00-44−4i4i00000000000000000000000000000000
χ414-44-4−4i4i4i−4i004-4−4i4i00000000000000000000000000000000
χ424-44-4−4i4i4i−4i00-444i−4i00000000000000000000000000000000
χ434-4-4444-4-400000000002i2−2i2002i2−2i20000000000000000000000
χ444-4-4444-4-40000000000−2i22i200−2i22i20000000000000000000000
χ454-4-44-4-444000000000022−2200−22220000000000000000000000
χ464-4-44-4-4440000000000−22220022−220000000000000000000000

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