Finite Group Databasebeta

← Group #264642

Character table — Group #264642

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order12222244444488884448888222244444444888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-111-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ3111111111111111111111111111-1-111-1-111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-11111-1-1
χ511111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111111-1-1-1-111-1-111-1-11111-1-1
χ711111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-111-1-1-1-1-1-111
χ9111111111111-1-1-1-1111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111111-11-11-1-1-111-1-11-1
χ10111111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1111-1
χ11111111111111-1-1-1-1111-1-1-1-111-1-1-1-111-1-1111111-11111-1-1-1-11-11-11-1-1-1-1-111-11
χ12111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111111-1-1-11
χ13111111111111-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-11-11-11-1-1-1-111-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-111-11111-1-1-11
χ15111111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-1111111-11111-1-1-1-1-11-11-11-1-111-1-11-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-111-1-1111-1
χ17222222222-2-222222-2-2-222-2-22222000000000000-20000000000-2-20000000000
χ18222222222-2-222222-2-2-222-2-2-2-2-2-2000000000000-20000000000220000000000
χ19222222222-2-22-2-2-2-2-2-2-2-2-22222-2-200000000000020000000000-220000000000
χ20222222222-2-22-2-2-2-2-2-2-2-2-222-2-222000000000000200000000002-20000000000
χ21222222-2-2-2-2-2-20000-22200000000222-2-2-22-200000000022-2-200000000000000
χ22222222-2-2-2-2-2-20000-2220000000022-22-2-2-22000000000-2-22200000000000000
χ23222222-2-2-2-2-2-20000-22200000000-2-22-2222-2000000000-2-22200000000000000
χ24222222-2-2-2-2-2-20000-22200000000-2-2-2222-2200000000022-2-200000000000000
χ252222-2-222-2-2-2-2000022-200000000002200-2-22i2i−2i−2i02i2i−2i−2i000000000000000000
χ262222-2-222-2-2-2-2000022-200000000002200-2-2−2i−2i2i2i0−2i−2i2i2i000000000000000000
χ272222-2-222-2-2-2-2000022-20000000000-2-200222i2i−2i−2i0−2i−2i2i2i000000000000000000
χ282222-2-222-2-2-2-2000022-20000000000-2-20022−2i−2i2i2i02i2i−2i−2i000000000000000000
χ292222-2-2-2-222222222-22-2-2-2220000002-200-220000-2000000000000002-2000000
χ302222-2-2-2-222222222-22-2-2-222000000-22002-20000-200000000000000-22000000
χ312222-2-2-2-22222-2-2-2-2-22-222-2-20000002-200-220000200000000000000-22000000
χ322222-2-2-2-22222-2-2-2-2-22-222-2-2000000-22002-200002000000000000002-2000000
χ332222-2-2-2-22-2-2222222-22-2-2-2-200000000000000002000000002200-2-200000000
χ342222-2-2-2-22-2-2222222-22-2-2-2-20000000000000000200000000-2-2002200000000
χ352222-2-2-2-22-2-22-2-2-2-22-2222220000000000000000-2000000002-200-2200000000
χ362222-2-2-2-22-2-22-2-2-2-22-2222220000000000000000-200000000-22002-200000000
χ3722-2-22-22-2200-222-2-20002-2002-22-2000000002−22−2000002−22−2000000002−22−200
χ3822-2-22-22-2200-222-2-20002-2002-22-200000000−22−2200000−22−2200000000−22−2200
χ3922-2-22-22-2200-222-2-20002-200-22-22000000002−22−2000002−22−200000000−22−2200
χ4022-2-22-22-2200-222-2-20002-200-22-2200000000−22−2200000−22−22000000002−22−200
χ4122-2-22-22-2200-2-2-222000-22002-2-22000000002−22−200000−22−2200000000−222−200
χ4222-2-22-22-2200-2-2-222000-22002-2-2200000000−22−22000002−22−2000000002−2−2200
χ4322-2-22-22-2200-2-2-222000-2200-222-2000000002−22−200000−22−22000000002−2−2200
χ4422-2-22-22-2200-2-2-222000-2200-222-200000000−22−22000002−22−200000000−222−200
χ45444444-4-4-444-400004-4-40000000000000000000000000000000000000000000
χ464444-4-444-444-40000-4-440000000000000000000000000000000000000000000
χ4744-4-44-4-44-40040000000000000000000000000000000022−22−222200000000000000
χ4844-4-44-4-44-400400000000000000000000000000000000−222222−2200000000000000
χ4944-4-4-444-4-4004000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ5044-4-4-444-4-400400000000000000000000000−2i22i22i2−2i200000000000000000000000
χ5144-4-4-44-44400-444-4-4000-4400000000000000000000000000000000000000000
χ5244-4-4-44-44400-4-4-4440004-400000000000000000000000000000000000000000
χ534-44-4000004i−4i022−2222−22000002i2−2i200002-2002i−2i00000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ544-44-4000004i−4i022−2222−22000002i2−2i20000-2200−2i2i0000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ554-44-4000004i−4i0−2222−222200000−2i22i200002-2002i−2i0000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ564-44-4000004i−4i0−2222−222200000−2i22i20000-2200−2i2i00000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ574-44-400000−4i4i022−2222−2200000−2i22i200002-200−2i2i0000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ584-44-400000−4i4i022−2222−2200000−2i22i20000-22002i−2i00000002ζ3−2ζ32ζ−2ζ000000000000000000
χ594-44-400000−4i4i0−2222−2222000002i2−2i200002-200−2i2i00000002ζ3−2ζ32ζ−2ζ000000000000000000
χ604-44-400000−4i4i0−2222−2222000002i2−2i20000-22002i−2i0000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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