Finite Group Databasebeta

← Group #101653

Character table — Group #101653

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444444444888888882444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111-1-11-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ7111111111111111111111-1-11-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-1
χ8111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-1111-1-1-11-1111-1-1-1ii−i−iii−i−i1-111-1-1i−ii−iii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1111-1-1-11-1111-1-1-1ii−i−iii−i−i1-1-1-111i−ii−i−i−iii-1-111−i−iii
χ1111111111-1-1-1-1111-1-1-11-1111-1-1-1−i−iii−i−iii1-111-1-1−ii−ii−i−iii11-1-1−i−iii
χ1211111111-1-1-1-1111-1-1-11-1111-1-1-1−i−iii−i−iii1-1-1-111−ii−iiii−i−i-1-111ii−i−i
χ1311111111-1-1-1-1111-1-1-11-11-1-1-111ii−i−i−i−iii-1111-1-1i−i−ii−i−iii-1-111ii−i−i
χ1411111111-1-1-1-1111-1-1-11-11-1-1-111ii−i−i−i−iii-11-1-111i−i−iiii−i−i11-1-1−i−iii
χ1511111111-1-1-1-1111-1-1-11-11-1-1-111−i−iiiii−i−i-1111-1-1−iii−iii−i−i-1-111−i−iii
χ1611111111-1-1-1-1111-1-1-11-11-1-1-111−i−iiiii−i−i-11-1-111−iii−i−i−iii11-1-1ii−i−i
χ1722222222222222-2-222-2-2-200-2000000222200000000-2-2000000000000
χ1822222222222222-2-222-2-2-200-2000000-2-2-2-20000000022000000000000
χ19222222222222-2-22-2-2-22-2-22222200000000-2-200000000000000000000
χ20222222222222-2-22-2-2-22-2-2-2-22-2-2000000002200000000000000000000
χ21222222222222-2-2-22-2-2-22200-20022220000000000-2-200000000000000
χ22222222222222-2-2-22-2-2-22200-200-2-2-2-200000000002200000000000000
χ2322222222-2-2-2-222-22-2-2-22-20020000002i2i−2i−2i00000000−2i2i000000000000
χ2422222222-2-2-2-222-22-2-2-22-2002000000−2i−2i2i2i000000002i−2i000000000000
χ2522222222-2-2-2-2-2-2222222-222-2-2-200000000-2200000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-222000000002-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22002002i2i−2i−2i0000000000−2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2200200−2i−2i2i2i00000000002i−2i00000000000000
χ2922-22-2-22-22i−2i2i−2i2-2002i−2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000002−2i2−i21+i−1−i1−i−1+i
χ3022-22-2-22-22i−2i2i−2i2-2002i−2i0000000000002ζ−2ζ2ζ3−2ζ300000000000000−22−i2i2−1−i1+i−1+i1−i
χ3122-22-2-22-22i−2i2i−2i2-2002i−2i000000000000−2ζ2ζ−2ζ32ζ3000000000000002−2i2−i2−1−i1+i−1+i1−i
χ3222-22-2-22-22i−2i2i−2i2-2002i−2i000000000000−2ζ2ζ−2ζ32ζ300000000000000−22−i2i21+i−1−i1−i−1+i
χ3322-22-2-22-2−2i2i−2i2i2-200−2i2i0000000000002ζ3−2ζ32ζ−2ζ000000000000002−2−i2i2−1+i1−i−1−i1+i
χ3422-22-2-22-2−2i2i−2i2i2-200−2i2i0000000000002ζ3−2ζ32ζ−2ζ00000000000000−22i2−i21−i−1+i1+i−1−i
χ3522-22-2-22-2−2i2i−2i2i2-200−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000002−2−i2i21−i−1+i1+i−1−i
χ3622-22-2-22-2−2i2i−2i2i2-200−2i2i000000000000−2ζ32ζ3−2ζ2ζ00000000000000−22i2−i2−1+i1−i−1−i1+i
χ37444-4-44-4-444-4-4000000000000000000000000000000002-22-200000000
χ38444-4-44-4-444-4-400000000000000000000000000000000-22-2200000000
χ39444-4-44-4-4-4-444000000000000000000000000000000002i−2i−2i2i00000000
χ40444-4-44-4-4-4-44400000000000000000000000000000000−2i2i2i−2i00000000
χ4144-44-4-44-44i−4i4i−4i-4400−4i4i00000000000000000000000000000000000000
χ4244-44-4-44-4−4i4i−4i4i-44004i−4i00000000000000000000000000000000000000
χ4344-4-44-4-444i−4i−4i4i0000000000000000000000002i−2i2-20000000000000000
χ4444-4-44-4-444i−4i−4i4i000000000000000000000000−2i2i-220000000000000000
χ4544-4-44-4-44−4i4i4i−4i0000000000000000000000002i−2i-220000000000000000
χ4644-4-44-4-44−4i4i4i−4i000000000000000000000000−2i2i2-20000000000000000
χ474-4444-4-4-40000004000-4004-4000000000000000000000000000000000
χ484-4444-4-4-40000004000-400-44000000000000000000000000000000000
χ494-4444-4-4-4000000-40004000004i−4i000000000000000000000000000000
χ504-4444-4-4-4000000-4000400000−4i4i000000000000000000000000000000
χ514-44-4-4-44400000004000-40000002i2−2i22i2−2i200000000000000000000000000
χ524-44-4-4-44400000004000-4000000−2i22i2−2i22i200000000000000000000000000
χ534-44-4-4-4440000000-4000400000022−22−222200000000000000000000000000
χ544-44-4-4-4440000000-40004000000−222222−2200000000000000000000000000
χ558-8-88-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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