Finite Group Databasebeta

← Group #264657

Character table — Group #264657

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order12222244444488884448888224444444444888888888888822444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-111111111-1-1-1-111111-1-1-1-11-11-1-1-1-1-1-1-1-1-111
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-11-1111-1-11111-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-111111-11-1-1-1-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-11-1111-1-1-1-1-1-111
χ9111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-111-1-11-1
χ10111111111111-1-1-1-1111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-111-1-11-1-1-1-111-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-11111-1-1-1-11-1-111-1-1-1-1-111-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111-11111-1-1-1-1-111-1-11-1-111-1-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111-1-1111-1
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-11
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111111-1-1-111111-1-1-11
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1111-111-1-1111-1
χ1722222222-2-2222222-2-2-222-2-20000000022220000-200000000-20-200000000000
χ1822222222-2-2222222-2-2-222-2-200000000-2-2-2-20000-20000000020200000000000
χ1922222222-2-222-2-2-2-2-2-2-2-2-2220000000022-2-20000200000000-20200000000000
χ2022222222-2-222-2-2-2-2-2-2-2-2-22200000000-2-222000020000000020-200000000000
χ21222222-2-2-2-2-2-20000-22200002-22-222-2-2000000000000022-2-200000000000000
χ22222222-2-2-2-2-2-20000-22200002-22-2-2-2220000000000000-2-22200000000000000
χ23222222-2-2-2-2-2-20000-2220000-22-2222-2-20000000000000-2-22200000000000000
χ24222222-2-2-2-2-2-20000-2220000-22-22-2-222000000000000022-2-200000000000000
χ252222-2-222-2-2-2-2000022-2000022-2-2000000002i2i−2i−2i02i2i−2i−2i000000000000000000
χ262222-2-222-2-2-2-2000022-2000022-2-200000000−2i−2i2i2i0−2i−2i2i2i000000000000000000
χ272222-2-222-2-2-2-2000022-20000-2-222000000002i2i−2i−2i0−2i−2i2i2i000000000000000000
χ282222-2-222-2-2-2-2000022-20000-2-22200000000−2i−2i2i2i02i2i−2i−2i000000000000000000
χ292222-2-2-2-222222222-22-2-2-2222-2-22000000000000-2000000000000002-2000000
χ302222-2-2-2-222222222-22-2-2-222-222-2000000000000-200000000000000-22000000
χ312222-2-2-2-22222-2-2-2-2-22-222-2-22-2-22000000000000200000000000000-22000000
χ322222-2-2-2-22222-2-2-2-2-22-222-2-2-222-20000000000002000000000000002-2000000
χ332222-2-2-2-2-2-22222222-22-2-2-2-200000000000000002000000000202-2-200000000
χ342222-2-2-2-2-2-22222222-22-2-2-2-200000000000000002000000000-20-22200000000
χ352222-2-2-2-2-2-222-2-2-2-22-2222220000000000000000-200000000020-22-200000000
χ362222-2-2-2-2-2-222-2-2-2-22-2222220000000000000000-2000000000-202-2200000000
χ3722-2-22-22-2002-22i2i−2i−2i0002i−2i00000000002i−2i2-22−22−200000i2−i2i2−i2000000002−2i2−i200
χ3822-2-22-22-2002-22i2i−2i−2i0002i−2i00000000002i−2i2-2−22−2200000−i2i2−i2i200000000−22−i2i200
χ3922-2-22-22-2002-22i2i−2i−2i0002i−2i0000000000−2i2i-222−22−200000i2−i2i2−i200000000−22−i2i200
χ4022-2-22-22-2002-22i2i−2i−2i0002i−2i0000000000−2i2i-22−22−2200000−i2i2−i2i2000000002−2i2−i200
χ4122-2-22-22-2002-2−2i−2i2i2i000−2i2i00000000002i−2i-222−22−200000−i2i2−i2i200000000−22i2−i200
χ4222-2-22-22-2002-2−2i−2i2i2i000−2i2i00000000002i−2i-22−22−2200000i2−i2i2−i2000000002−2−i2i200
χ4322-2-22-22-2002-2−2i−2i2i2i000−2i2i0000000000−2i2i2-22−22−200000−i2i2−i2i2000000002−2−i2i200
χ4422-2-22-22-2002-2−2i−2i2i2i000−2i2i0000000000−2i2i2-2−22−2200000i2−i2i2−i200000000−22i2−i200
χ45444444-4-444-4-400004-4-40000000000000000000000000000000000000000000
χ464444-4-44444-4-40000-4-440000000000000000000000000000000000000000000
χ4744-4-44-4-4400-44000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ4844-4-44-4-4400-4400000000000000000000000000000000−2i22i22i2−2i200000000000000
χ4944-4-4-444-400-44000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5044-4-4-444-400-4400000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5144-4-4-44-44004-44i4i−4i−4i000−4i4i00000000000000000000000000000000000000000
χ5244-4-4-44-44004-4−4i−4i4i4i0004i−4i00000000000000000000000000000000000000000
χ534-44-400004i−4i0022−2222−22000002i2−2i200002-22i−2i0000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ544-44-400004i−4i0022−2222−22000002i2−2i20000-22−2i2i000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ554-44-400004i−4i00−2222−222200000−2i22i200002-22i−2i000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ564-44-400004i−4i00−2222−222200000−2i22i20000-22−2i2i0000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ574-44-40000−4i4i0022−2222−2200000−2i22i200002-2−2i2i000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ584-44-40000−4i4i0022−2222−2200000−2i22i20000-222i−2i0000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ594-44-40000−4i4i00−2222−2222000002i2−2i200002-2−2i2i0000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ604-44-40000−4i4i00−2222−2222000002i2−2i20000-222i−2i000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ618-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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