Finite Group Databasebeta

← Group #136281

Character table — Group #136281

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224444444444444488888888888844888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111-111-1-11-1ii−i−iii−i−iii−i−i1-1ii−i−ii−i11-1-1ii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-1111-111-1-11-1ii−i−iii−i−iii−i−i1-1−i−iiii−i-1-111−i−iii-1-111
χ111111-1-1-1-111-1-1-1-1111-111-1-11-1−i−iii−i−iii−i−iii1-1ii−i−i−ii-1-111ii−i−i-1-111
χ121111-1-1-1-111-1-1-1-1111-111-1-11-1−i−iii−i−iii−i−iii1-1−i−iii−ii11-1-1−i−iii11-1-1
χ131111-1-1-1-111-1-1-1-1111-1-1-1111-1ii−i−i−i−iiiii−i−i-11ii−i−i−ii11-1-1−i−iii-1-111
χ141111-1-1-1-111-1-1-1-1111-1-1-1111-1ii−i−i−i−iiiii−i−i-11−i−iii−ii-1-111ii−i−i11-1-1
χ151111-1-1-1-111-1-1-1-1111-1-1-1111-1−i−iiiii−i−i−i−iii-11ii−i−ii−i-1-111−i−iii11-1-1
χ161111-1-1-1-111-1-1-1-1111-1-1-1111-1−i−iiiii−i−i−i−iii-11−i−iiii−i11-1-1ii−i−i-1-111
χ172222222222222222-2-20000-2-222220000-2-2-2-200000000000000000000
χ182222222222222222-2-20000-2-2-2-2-2-20000222200000000000000000000
χ19222222222222-2-2-2-22-22222-22000000000000-2-2000000000000000000
χ20222222222222-2-2-2-22-2-2-2-2-2-2200000000000022000000000000000000
χ21222222222222-2-2-2-2-2200002-2000022220000000000-2-2000000000000
χ22222222222222-2-2-2-2-2200002-20000-2-2-2-2000000000022000000000000
χ232222-2-2-2-222-2-222-2-22222-2-2-2-2000000000000-22000000000000000000
χ242222-2-2-2-222-2-222-2-222-2-222-2-20000000000002-2000000000000000000
χ252222-2-2-2-222-2-222-2-2-2-200002200002i2i−2i−2i0000000000−2i2i000000000000
χ262222-2-2-2-222-2-222-2-2-2-20000220000−2i−2i2i2i00000000002i−2i000000000000
χ272222-2-2-2-222-2-2-2-222-220000-222i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ282222-2-2-2-222-2-2-2-222-220000-22−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ292-22-22i2i−2i−2i2-22i−2i2i−2i2-2000000002ζ−2ζ2ζ3−2ζ3000000000000000000001+i−1−i1−i−1+i2−2i2−i2
χ302-22-22i2i−2i−2i2-22i−2i2i−2i2-2000000002ζ−2ζ2ζ3−2ζ300000000000000000000−1−i1+i−1+i1−i−22−i2i2
χ312-22-22i2i−2i−2i2-22i−2i2i−2i2-200000000−2ζ2ζ−2ζ32ζ3000000000000000000001+i−1−i1−i−1+i−22−i2i2
χ322-22-22i2i−2i−2i2-22i−2i2i−2i2-200000000−2ζ2ζ−2ζ32ζ300000000000000000000−1−i1+i−1+i1−i2−2i2−i2
χ332-22-2−2i−2i2i2i2-2−2i2i−2i2i2-2000000002ζ3−2ζ32ζ−2ζ000000000000000000001−i−1+i1+i−1−i−22i2−i2
χ342-22-2−2i−2i2i2i2-2−2i2i−2i2i2-2000000002ζ3−2ζ32ζ−2ζ00000000000000000000−1+i1−i−1−i1+i2−2−i2i2
χ352-22-2−2i−2i2i2i2-2−2i2i−2i2i2-200000000−2ζ32ζ3−2ζ2ζ000000000000000000001−i−1+i1+i−1−i2−2−i2i2
χ362-22-2−2i−2i2i2i2-2−2i2i−2i2i2-200000000−2ζ32ζ3−2ζ2ζ00000000000000000000−1+i1−i−1−i1+i−22i2−i2
χ3744444444-4-4-4-4000000000000000000000000002-22-200000000000000
χ3844444444-4-4-4-400000000000000000000000000-22-2200000000000000
χ394444-4-4-4-4-4-444000000000000000000000000002i−2i−2i2i00000000000000
χ404444-4-4-4-4-4-44400000000000000000000000000−2i2i2i−2i00000000000000
χ414-44-44i4i−4i−4i4-44i−4i−4i4i-440000000000000000000000000000000000000000
χ424-44-44i4i−4i−4i-44−4i4i000000000000000000000000000000002-22i−2i00000000
χ434-44-44i4i−4i−4i-44−4i4i00000000000000000000000000000000-22−2i2i00000000
χ444-44-4−4i−4i4i4i4-4−4i4i4i−4i-440000000000000000000000000000000000000000
χ454-44-4−4i−4i4i4i-444i−4i000000000000000000000000000000002-2−2i2i00000000
χ464-44-4−4i−4i4i4i-444i−4i00000000000000000000000000000000-222i−2i00000000
χ474-4-444i−4i4i−4i00000000002i−2i2-20000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000
χ484-4-444i−4i4i−4i00000000002i−2i2-2000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ300000000000000000000
χ494-4-444i−4i4i−4i0000000000−2i2i-220000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000000000000000
χ504-4-444i−4i4i−4i0000000000−2i2i-22000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ300000000000000000000
χ514-4-44−4i4i−4i4i00000000002i−2i-220000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000
χ524-4-44−4i4i−4i4i00000000002i−2i-22000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ00000000000000000000
χ534-4-44−4i4i−4i4i0000000000−2i2i2-20000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ00000000000000000000
χ544-4-44−4i4i−4i4i0000000000−2i2i2-2000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ00000000000000000000
χ5588-8-88-8-88000000000000000000000000000000000000000000000000
χ5688-8-8-888-8000000000000000000000000000000000000000000000000

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