Finite Group Databasebeta

← Group #136106

Character table — Group #136106

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111122224444888888881616161616161616161616161616161616161616161616161616
order12224444224444444444444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-1-1-111-1-1111-1i−ii−iii−i−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−i−iiii−ii−i−i−iii-1-111-1-111
χ111111-1-1-1-111-1-111-1-1-1-111-1-1111-1−ii−iiii−i−i−ii−iiii−i−i-1-111-1-111
χ121111-1-1-1-111-1-111-1-1-1-111-1-1111-1−ii−ii−i−iii−ii−ii−i−iii11-1-111-1-1
χ131111-1-1-1-111-1-111-1-1-1-1-1-11111-11i−i−iiii−i−ii−i−ii−i−iii11-1-1-1-111
χ141111-1-1-1-111-1-111-1-1-1-1-1-11111-11i−i−ii−i−iiii−i−iiii−i−i-1-11111-1-1
χ151111-1-1-1-111-1-111-1-1-1-1-1-11111-11−iii−iii−i−i−iii−i−i−iii-1-11111-1-1
χ161111-1-1-1-111-1-111-1-1-1-1-1-11111-11−iii−i−i−iii−iii−iii−i−i11-1-1-1-111
χ172222222222222222-2-22222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-22-200002-2000022000000-2-2000000000000
χ20222222222222-2-2-2-22-200002-20000-2-200000022000000000000
χ21222222222222-2-2-2-2-220000-220022000000-2-200000000000000
χ22222222222222-2-2-2-2-220000-2200-2-20000002200000000000000
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
χ252222-2-2-2-222-2-2-2-2222-20000-22002i−2i000000−2i2i00000000000000
χ262222-2-2-2-222-2-2-2-2222-20000-2200−2i2i0000002i−2i00000000000000
χ272222-2-2-2-222-2-2-2-222-2200002-200002i−2i000000−2i2i000000000000
χ282222-2-2-2-222-2-2-2-222-2200002-20000−2i2i0000002i−2i000000000000
χ292-22-22i2i−2i−2i2-22i−2i2-22i−2i002-22i−2i000000000000000000002−2i2−i22−2i2−i2
χ302-22-22i2i−2i−2i2-22i−2i2-22i−2i002-22i−2i00000000000000000000−22−i2i2−22−i2i2
χ312-22-22i2i−2i−2i2-22i−2i2-22i−2i00-22−2i2i000000000000000000002−2i2−i2−22−i2i2
χ322-22-22i2i−2i−2i2-22i−2i2-22i−2i00-22−2i2i00000000000000000000−22−i2i22−2i2−i2
χ332-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i002-2−2i2i000000000000000000002−2−i2i22−2−i2i2
χ342-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i002-2−2i2i00000000000000000000−22i2−i2−22i2−i2
χ352-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i00-222i−2i000000000000000000002−2−i2i2−22i2−i2
χ362-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i00-222i−2i00000000000000000000−22i2−i22−2−i2i2
χ3744444444-4-4-4-40000000000000000002-22-20000000000000000
χ3844444444-4-4-4-4000000000000000000-22-220000000000000000
χ394444-4-4-4-4-4-4440000000000000000002i−2i−2i2i0000000000000000
χ404444-4-4-4-4-4-444000000000000000000−2i2i2i−2i0000000000000000
χ414-44-44i4i−4i−4i4-44i−4i-44−4i4i0000000000000000000000000000000000
χ424-44-44i4i−4i−4i-44−4i4i000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ434-44-44i4i−4i−4i-44−4i4i00000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ444-44-4−4i−4i4i4i4-4−4i4i-444i−4i0000000000000000000000000000000000
χ454-44-4−4i−4i4i4i-444i−4i000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ464-44-4−4i−4i4i4i-444i−4i00000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4788-8-88-88-8000000000000000000000000000000000000000000
χ4888-8-8-88-88000000000000000000000000000000000000000000
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.