Finite Group Databasebeta

← Group #137291

Character table — Group #137291

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224422442444444488888888888822444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-1111111-1-1-1-11111-1111-11-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-1-1111-1-1-11ii−i−iii−i−iii−i−i111-1-1-1i−iii−i−i11-1-1ii−i−i
χ101111-1-1-1-111-1-111-1-1-1111-1-1-11ii−i−iii−i−iii−i−i1-1-11-11i−i−i−iii-1-111−i−iii
χ111111-1-1-1-111-1-111-1-1-1111-1-1-11−i−iii−i−iii−i−iii111-1-1-1−ii−i−iii11-1-1−i−iii
χ121111-1-1-1-111-1-111-1-1-1111-1-1-11−i−iii−i−iii−i−iii1-1-11-11−iiii−i−i-1-111ii−i−i
χ131111-1-1-1-111-1-111-1-1-11-1-111-11ii−i−i−i−iiiii−i−i-111-11-1−iiii−i−i-1-111−i−iii
χ141111-1-1-1-111-1-111-1-1-11-1-111-11ii−i−i−i−iiiii−i−i-1-1-1111−ii−i−iii11-1-1ii−i−i
χ151111-1-1-1-111-1-111-1-1-11-1-111-11−i−iiiii−i−i−i−iii-111-11-1i−i−i−iii-1-111ii−i−i
χ161111-1-1-1-111-1-111-1-1-11-1-111-11−i−iiiii−i−i−i−iii-1-1-1111i−iii−i−i11-1-1−i−iii
χ172222222222222222-2-20000-2-222220000-2-2-2-200000000000000000000
χ182222222222222222-2-20000-2-2-2-2-2-20000222200000000000000000000
χ19222222222222-2-2-2-22-22222-22000000000000-2000-2000000000000000
χ20222222222222-2-2-2-22-2-2-2-2-2-2200000000000020002000000000000000
χ21222222222222-2-2-2-2-2200002-2000022220000000000-2-2000000000000
χ22222222222222-2-2-2-2-2200002-20000-2-2-2-2000000000022000000000000
χ232222-2-2-2-222-2-222-2-22-200002-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ242222-2-2-2-222-2-222-2-22-200002-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ252222-2-2-2-222-2-2-2-222220000-2-200002i2i−2i−2i0000000000−2i2i000000000000
χ262222-2-2-2-222-2-2-2-222220000-2-20000−2i−2i2i2i00000000002i−2i000000000000
χ272222-2-2-2-222-2-2-2-222-2-222-2-222000000000000-20002000000000000000
χ282222-2-2-2-222-2-2-2-222-2-2-2-222220000000000002000-2000000000000000
χ2922-2-22i2i−2i−2i2-22i−2i2-22i−2i00000000000000002ζ3−2ζ32ζ−2ζ0000000000002−2i2−i21−i−1+i1+i−1−i
χ3022-2-22i2i−2i−2i2-22i−2i2-22i−2i00000000000000002ζ3−2ζ32ζ−2ζ000000000000−22−i2i2−1+i1−i−1−i1+i
χ3122-2-22i2i−2i−2i2-22i−2i2-22i−2i0000000000000000−2ζ32ζ3−2ζ2ζ0000000000002−2i2−i2−1+i1−i−1−i1+i
χ3222-2-22i2i−2i−2i2-22i−2i2-22i−2i0000000000000000−2ζ32ζ3−2ζ2ζ000000000000−22−i2i21−i−1+i1+i−1−i
χ3322-2-2−2i−2i2i2i2-2−2i2i2-2−2i2i00000000000000002ζ−2ζ2ζ3−2ζ30000000000002−2−i2i2−1−i1+i−1+i1−i
χ3422-2-2−2i−2i2i2i2-2−2i2i2-2−2i2i00000000000000002ζ−2ζ2ζ3−2ζ3000000000000−22i2−i21+i−1−i1−i−1+i
χ3522-2-2−2i−2i2i2i2-2−2i2i2-2−2i2i0000000000000000−2ζ2ζ−2ζ32ζ30000000000002−2−i2i21+i−1−i1−i−1+i
χ3622-2-2−2i−2i2i2i2-2−2i2i2-2−2i2i0000000000000000−2ζ2ζ−2ζ32ζ3000000000000−22i2−i2−1−i1+i−1+i1−i
χ3744444444-4-4-4-400000000000000000000000002-2-20200000000000000
χ3844444444-4-4-4-40000000000000000000000000-2220-200000000000000
χ394444-4-4-4-4-4-44400000000000000000000000002-220-200000000000000
χ404444-4-4-4-4-4-4440000000000000000000000000-22-20200000000000000
χ4144-4-44i4i−4i−4i4-44i−4i-44−4i4i0000000000000000000000000000000000000000
χ4244-4-44i4i−4i−4i-44−4i4i000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ4344-4-44i4i−4i−4i-44−4i4i00000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ4444-4-4−4i−4i4i4i4-4−4i4i-444i−4i0000000000000000000000000000000000000000
χ4544-4-4−4i−4i4i4i-444i−4i000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ4644-4-4−4i−4i4i4i-444i−4i00000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ474-44-44i−4i4i−4i00000000002-22i−2i002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ484-44-44i−4i4i−4i00000000002-22i−2i00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ494-44-44i−4i4i−4i0000000000-22−2i2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ504-44-44i−4i4i−4i0000000000-22−2i2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ514-44-4−4i4i−4i4i00000000002-2−2i2i002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ524-44-4−4i4i−4i4i00000000002-2−2i2i00−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ534-44-4−4i4i−4i4i0000000000-222i−2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ544-44-4−4i4i−4i4i0000000000-222i−2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ558-8-888-8-88000000000000000000000000000000000000000000000000
χ568-8-88-888-8000000000000000000000000000000000000000000000000

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