Finite Group Databasebeta

← Group #136107

Character table — Group #136107

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12224444224444444444444424888888888888888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-1-1-111-1-1111-1i−ii−ii−ii−ii−ii−iii−i−i11-1-111-1-1
χ101111-1-1-1-111-1-111-1-1-1-111-1-1111-1i−ii−i−ii−ii−ii−iiii−i−i-1-111-1-111
χ111111-1-1-1-111-1-111-1-1-1-111-1-1111-1−ii−iii−ii−ii−ii−i−i−iii-1-111-1-111
χ121111-1-1-1-111-1-111-1-1-1-111-1-1111-1−ii−ii−ii−ii−ii−ii−i−iii11-1-111-1-1
χ131111-1-1-1-111-1-111-1-1-1-1-1-11111-11i−ii−ii−i−iii−i−ii−i−iii11-1-1-1-111
χ141111-1-1-1-111-1-111-1-1-1-1-1-11111-11i−ii−i−iii−i−iii−i−i−iii-1-11111-1-1
χ151111-1-1-1-111-1-111-1-1-1-1-1-11111-11−ii−iii−i−iii−i−iiii−i−i-1-11111-1-1
χ161111-1-1-1-111-1-111-1-1-1-1-1-11111-11−ii−ii−iii−i−iii−iii−i−i11-1-1-1-111
χ172222222222222222-2-22222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-22-200002-2000000002200-2-2000000000000
χ20222222222222-2-2-2-22-200002-200000000-2-20022000000000000
χ21222222222222-2-2-2-2-220000-220000002200-2-200000000000000
χ22222222222222-2-2-2-2-220000-22000000-2-2002200000000000000
χ232222-2-2-2-222-2-222-2-22222-2-2-2-2-22000000000000000000000000
χ242222-2-2-2-222-2-222-2-222-2-222-2-22-2000000000000000000000000
χ252222-2-2-2-222-2-2-2-2222-20000-220000002i−2i00−2i2i00000000000000
χ262222-2-2-2-222-2-2-2-2222-20000-22000000−2i2i002i−2i00000000000000
χ272222-2-2-2-222-2-2-2-222-2200002-2000000002i−2i00−2i2i000000000000
χ282222-2-2-2-222-2-2-2-222-2200002-200000000−2i2i002i−2i000000000000
χ2922-2-22i−2i2i−2i2-22i−2i2-22i−2i002i−2i2-2000000000000000000002−2i2−i2i2−i22−2
χ3022-2-22i−2i2i−2i2-22i−2i2-22i−2i002i−2i2-200000000000000000000−22−i2i2−i2i2−22
χ3122-2-22i−2i2i−2i2-22i−2i2-22i−2i00−2i2i-22000000000000000000002−2i2−i2−i2i2−22
χ3222-2-22i−2i2i−2i2-22i−2i2-22i−2i00−2i2i-2200000000000000000000−22−i2i2i2−i22−2
χ3322-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002i−2i-22000000000000000000002−2−i2i2i2−i2−22
χ3422-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002i−2i-2200000000000000000000−22i2−i2−i2i22−2
χ3522-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i00−2i2i2-2000000000000000000002−2−i2i2−i2i22−2
χ3622-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i00−2i2i2-200000000000000000000−22i2−i2i2−i2−22
χ3744444444-4-4-4-40000000000000022-2-200000000000000000000
χ3844444444-4-4-4-400000000000000-2-22200000000000000000000
χ394444-4-4-4-4-4-444000000000000002i−2i−2i2i00000000000000000000
χ404444-4-4-4-4-4-44400000000000000−2i2i2i−2i00000000000000000000
χ4144-4-44i−4i4i−4i4-44i−4i-44−4i4i0000000000000000000000000000000000
χ4244-4-44i−4i4i−4i-44−4i4i000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4344-4-44i−4i4i−4i-44−4i4i00000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4444-4-4−4i4i−4i4i4-4−4i4i-444i−4i0000000000000000000000000000000000
χ4544-4-4−4i4i−4i4i-444i−4i000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4644-4-4−4i4i−4i4i-444i−4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ478-88-888-8-8000000000000000000000000000000000000000000
χ488-88-8-8-888000000000000000000000000000000000000000000
χ498-8-888i−8i−8i8i000000000000000000000000000000000000000000
χ508-8-88−8i8i8i−8i000000000000000000000000000000000000000000

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