Finite Group Databasebeta

← Group #264651

Character table — Group #264651

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order12222244444488884448888444444444444888888888888824444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-11111-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111-1-11111-1-111-1-1-1-111111-1-1-1-1-11-1-11-1-1-1-1-1-1-111
χ41111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-11-111-11-1-11111-1-1
χ511111111111111111111111-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-11111-11-1-11-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111-111-11-1-1-1-1-1-111
χ9111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-111-1-11-1
χ10111111111111-1-1-1-1111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-111-11
χ11111111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-111-1-1111-1
χ12111111111111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11
χ13111111111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-11111-1-1-1-1-1-11-111-1-1-1-111-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111111111-11111-1-1-1-111-11-1-1-1-111-1-11-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-11111-1-1-11
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-111-1-1111-1-1111-1
χ17222222222-2-222222-2-2-222-2-20000220000220000-2000000000-200-2000000000
χ18222222222-2-222222-2-2-222-2-20000-2-20000-2-20000-20000000002002000000000
χ19222222222-2-22-2-2-2-2-2-2-2-2-2220000220000-2-200002000000000200-2000000000
χ20222222222-2-22-2-2-2-2-2-2-2-2-2220000-2-200002200002000000000-2002000000000
χ21222222-2-2-2-2-2-20000-2220000222-200-2-22-20000000000022-2-200000000000000
χ22222222-2-2-2-2-2-20000-222000022-2200-2-2-2200000000000-2-22200000000000000
χ23222222-2-2-2-2-2-20000-2220000-2-22-200222-200000000000-2-22200000000000000
χ24222222-2-2-2-2-2-20000-2220000-2-2-220022-220000000000022-2-200000000000000
χ252222-2-222-2-2-2-2000022-2000000220000-2-2002i2i−2i−2i02i2i−2i−2i000000000000000000
χ262222-2-222-2-2-2-2000022-2000000220000-2-200−2i−2i2i2i0−2i−2i2i2i000000000000000000
χ272222-2-222-2-2-2-2000022-2000000-2-2000022002i2i−2i−2i0−2i−2i2i2i000000000000000000
χ282222-2-222-2-2-2-2000022-2000000-2-200002200−2i−2i2i2i02i2i−2i−2i000000000000000000
χ292222-2-2-2-222222222-22-2-2-222002-20000-22000000-2000000000000002-2000000
χ302222-2-2-2-222222222-22-2-2-22200-2200002-2000000-200000000000000-22000000
χ312222-2-2-2-22222-2-2-2-2-22-222-2-2002-20000-22000000200000000000000-22000000
χ322222-2-2-2-22222-2-2-2-2-22-222-2-200-2200002-20000002000000000000002-2000000
χ332222-2-2-2-22-2-2222222-22-2-2-2-20000000000000000200000000202-20-200000000
χ342222-2-2-2-22-2-2222222-22-2-2-2-20000000000000000200000000-20-220200000000
χ352222-2-2-2-22-2-22-2-2-2-22-2222220000000000000000-20000000020-2-20200000000
χ362222-2-2-2-22-2-22-2-2-2-22-2222220000000000000000-200000000-20220-200000000
χ3722-2-22-22-2-20022i2i−2i−2i0002i−2i0000002-200002i−2ii2−i2i2−i2000002−22−2000000002−2i2−i200
χ3822-2-22-22-2-20022i2i−2i−2i0002i−2i0000002-200002i−2i−i2i2−i2i200000−22−2200000000−22−i2i200
χ3922-2-22-22-2-20022i2i−2i−2i0002i−2i000000-220000−2i2ii2−i2i2−i2000002−22−200000000−22−i2i200
χ4022-2-22-22-2-20022i2i−2i−2i0002i−2i000000-220000−2i2i−i2i2−i2i200000−22−22000000002−2i2−i200
χ4122-2-22-22-2-2002−2i−2i2i2i000−2i2i0000002-20000−2i2ii2−i2i2−i200000−22−2200000000−22i2−i200
χ4222-2-22-22-2-2002−2i−2i2i2i000−2i2i0000002-20000−2i2i−i2i2−i2i2000002−22−2000000002−2−i2i200
χ4322-2-22-22-2-2002−2i−2i2i2i000−2i2i000000-2200002i−2ii2−i2i2−i200000−22−22000000002−2−i2i200
χ4422-2-22-22-2-2002−2i−2i2i2i000−2i2i000000-2200002i−2i−i2i2−i2i2000002−22−200000000−22i2−i200
χ45444444-4-4-444-400004-4-40000000000000000000000000000000000000000000
χ464444-4-444-444-40000-4-440000000000000000000000000000000000000000000
χ4744-4-44-4-44400-40000000000000000000000000000000022−22−222200000000000000
χ4844-4-44-4-44400-400000000000000000000000000000000−222222−2200000000000000
χ4944-4-4-444-4400-40000000000000000000000022−22−222200000000000000000000000
χ5044-4-4-444-4400-400000000000000000000000−222222−2200000000000000000000000
χ5144-4-4-44-44-40044i4i−4i−4i000−4i4i00000000000000000000000000000000000000000
χ5244-4-4-44-44-4004−4i−4i4i4i0004i−4i00000000000000000000000000000000000000000
χ534-4-44000004i−4i02i2−2i22i2−2i20000022−222i−2i00002-20000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ544-4-44000004i−4i02i2−2i22i2−2i20000022−22−2i2i0000-22000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ554-4-44000004i−4i0−2i22i2−2i22i200000−22222i−2i00002-2000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ564-4-44000004i−4i0−2i22i2−2i22i200000−2222−2i2i0000-220000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ574-4-4400000−4i4i02i2−2i22i2−2i200000−22222i−2i0000-22000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ584-4-4400000−4i4i02i2−2i22i2−2i200000−2222−2i2i00002-20000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ594-4-4400000−4i4i0−2i22i2−2i22i20000022−222i−2i0000-220000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ604-4-4400000−4i4i0−2i22i2−2i22i20000022−22−2i2i00002-2000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ618-88-80000000042−42−42420000000000000000000000000000000000000000000000
χ628-88-800000000−424242−420000000000000000000000000000000000000000000000

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