Finite Group Databasebeta

← Group #150021

Character table — Group #150021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size11112244448888888888888161616161616161616161616323232323232
order12222244444444444448888248888888888448888
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ41111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1111-1-1-1-11111-1111iiii−i−i−i−i-1-1ii−i−i
χ61111111111-1-1111-1-1-1-11111-1111−i−i−i−iiiii-1-1−i−iii
χ71111111111-1-1111-1-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i11−i−iii
χ81111111111-1-1111-1-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii11ii−i−i
χ91111111-1-1111-111-1-1-1-111111-1-1-1ii−i−iii−i−i-11i−ii−i
χ101111111-1-1111-111-1-1-1-111111-1-1-1−i−iii−i−iii-11−ii−ii
χ111111111-1-1111-111-1-1-1-1-1-1-1-11-111ii−i−iii−i−i1-1−ii−ii
χ121111111-1-1111-111-1-1-1-1-1-1-1-11-111−i−iii−i−iii1-1i−ii−i
χ131111111-1-11-1-1-11111111111-1-1-1-111-1-1-1-1111-11-1-11
χ141111111-1-11-1-1-11111111111-1-1-1-1-1-11111-1-11-1-111-1
χ151111111-1-11-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-11-111-1
χ161111111-1-11-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-111-1-11
χ172222222222222-2-222-2-20000-2-20000000000000000
χ182222222222-2-22-2-2-2-22200002-20000000000000000
χ192222222-2-2222-2-2-2-2-2220000-220000000000000000
χ202222222-2-22-2-2-2-2-222-2-20000220000000000000000
χ2122-2-22-2-20020002-22i−2i2i−2i00000000002ζ3−2ζ32ζ−2ζ00000000
χ2222-2-22-2-20020002-22i−2i2i−2i0000000000−2ζ32ζ3−2ζ2ζ00000000
χ2322-2-22-2-20020002-2−2i2i−2i2i00000000002ζ−2ζ2ζ3−2ζ300000000
χ2422-2-22-2-20020002-2−2i2i−2i2i0000000000−2ζ2ζ−2ζ32ζ300000000
χ2522-2-22-2-2002000-222i−2i−2i2i000000002ζ−2ζ00002ζ3−2ζ3000000
χ2622-2-22-2-2002000-222i−2i−2i2i00000000−2ζ2ζ0000−2ζ32ζ3000000
χ2722-2-22-2-2002000-22−2i2i2i−2i000000002ζ3−2ζ300002ζ−2ζ000000
χ2822-2-22-2-2002000-22−2i2i2i−2i00000000−2ζ32ζ30000−2ζ2ζ000000
χ29444444-444-400-40000000000000000000000000000
χ30444444-4-4-4-40040000000000000000000000000000
χ3144-4-44-4400-44-400000000000000000000000000000
χ3244-4-44-4400-4-4400000000000000000000000000000
χ3344-4-4-4404i−4i000000000022-2-2002i−2i00000000000000
χ3444-4-4-4404i−4i0000000000-2-22200−2i2i00000000000000
χ3544-4-4-440−4i4i000000000022-2-200−2i2i00000000000000
χ3644-4-4-440−4i4i0000000000-2-222002i−2i00000000000000
χ378888-8-800000000000000000000000000000000000
χ388-88-80000000000000002i2−2i22i2−2i2000000000000000000
χ398-88-8000000000000000−2i22i2−2i22i2000000000000000000
χ408-8-880000000000000002i2−2i2−2i22i2000000000000000000
χ418-8-88000000000000000−2i22i22i2−2i2000000000000000000

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