Finite Group Databasebeta

← Group #125524

Character table — Group #125524

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222222244444488888888881616161616161616161616161616161632323232
order122222444488888888884444448888161616161616161616161616161616162444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ121111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ172222222222222222-2-2-2-222-2-2-2-222-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-22200000000000000000000
χ192222222222-2-2-2-2-2-2222222-2-2-2-2-2-22200000000000000000000
χ202222222222-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000
χ212222-2-222-2-200000022-2-200002i−2i2i−2i00i2−i2i2−i22−22−2000000000000
χ222222-2-222-2-200000022-2-200002i−2i2i−2i00−i2i2−i2i2−22−22000000000000
χ232222-2-222-2-200000022-2-20000−2i2i−2i2i00i2−i2i2−i2−22−22000000000000
χ242222-2-222-2-200000022-2-20000−2i2i−2i2i00−i2i2−i2i22−22−2000000000000
χ252222-2-222-2-2000000-2-22200002i−2i−2i2i002−2−22−i2i2i2−i2000000000000
χ262222-2-222-2-2000000-2-22200002i−2i−2i2i00−222−2i2−i2−i2i2000000000000
χ272222-2-222-2-2000000-2-2220000−2i2i2i−2i002−2−22i2−i2−i2i2000000000000
χ282222-2-222-2-2000000-2-2220000−2i2i2i−2i00−222−2−i2i2i2−i2000000000000
χ2922-2-22-22-22-22i2i−2i−2i2i−2i2i−2i2i−2i002-20000000000000000002ζ−2ζ2ζ3−2ζ30000
χ3022-2-22-22-22-22i2i−2i−2i2i−2i2i−2i2i−2i002-2000000000000000000−2ζ2ζ−2ζ32ζ30000
χ3122-2-22-22-22-22i2i−2i−2i2i−2i−2i2i−2i2i00-22000000000000002ζ−2ζ2ζ3−2ζ300000000
χ3222-2-22-22-22-22i2i−2i−2i2i−2i−2i2i−2i2i00-2200000000000000−2ζ2ζ−2ζ32ζ300000000
χ3322-2-22-22-22-2−2i−2i2i2i−2i2i2i−2i2i−2i00-22000000000000002ζ3−2ζ32ζ−2ζ00000000
χ3422-2-22-22-22-2−2i−2i2i2i−2i2i2i−2i2i−2i00-2200000000000000−2ζ32ζ3−2ζ2ζ00000000
χ3522-2-22-22-22-2−2i−2i2i2i−2i2i−2i2i−2i2i002-20000000000000000002ζ3−2ζ32ζ−2ζ0000
χ3622-2-22-22-22-2−2i−2i2i2i−2i2i−2i2i−2i2i002-2000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ37444444-4-4-4-400000000004-40000000000000000000000000000
χ38444444-4-4-4-40000000000-440000000000000000000000000000
χ394444-4-4-4-4444444-4-40000000000000000000000000000000000
χ404444-4-4-4-444-4-4-4-4440000000000000000000000000000000000
χ4144-4-44-4-44-440000000000000000004i−4i00000000000000000000
χ4244-4-44-4-44-44000000000000000000−4i4i00000000000000000000
χ4344-4-4-444-4-440000004i−4i−4i4i000000000000000000000000000000
χ4444-4-4-444-4-44000000−4i4i4i−4i000000000000000000000000000000
χ4544-4-4-44-444-44i4i−4i−4i−4i4i0000000000000000000000000000000000
χ4644-4-4-44-444-4−4i−4i4i4i4i−4i0000000000000000000000000000000000
χ478-88-80000004i2−4i24i2−4i2000000000000000000000000000000000000
χ488-88-8000000−4i24i2−4i24i2000000000000000000000000000000000000
χ498-8-8800000042−42−4242000000000000000000000000000000000000
χ508-8-88000000−424242−42000000000000000000000000000000000000

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