Finite Group Databasebeta

← Group #263282

Character table — Group #263282

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444488888888888888888888881616161616161616161632323232
order12222244444444448888444444444444888888888822244444888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-111
χ41111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-11-1-111-1-1
χ511111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ611111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-111-1-1
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-11-1-1-1-111
χ91111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-1-11-11-1-11-11-1
χ101111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-111-11-1-1-1-11-11
χ111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111-1-111-111-1
χ121111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-111111-1-11
χ131111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-11-1-11-11-1-1-11-11
χ141111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-11-111-11-1-1-11-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1111-1-1111-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-11111-111-1
χ172222222-2-222-2-22-2-200002222-2-2-2-222-2-2000000000000000000000000
χ182222222-2-222-2-22-2-2000022-2-2-2-222-2-222000000000000000000000000
χ192222222-2-222-2-22-2-20000-2-22222-2-2-2-222000000000000000000000000
χ202222222-2-222-2-22-2-20000-2-2-2-2222222-2-2000000000000000000000000
χ21222222-222-2-222-2-2-22222002-2002-200000000-2-20000000000002-20000
χ22222222-222-2-222-2-2-2222200-2200-2200000000-2-2000000000000-220000
χ23222222-222-2-222-2-2-2-2-2-2-2002-2002-20000000022000000000000-220000
χ24222222-222-2-222-2-2-2-2-2-2-200-2200-2200000000220000000000002-20000
χ25222222-2-2-2-2-2-2-2-2220000002-200-2200002i2i−2i−2i002i2i−2i−2i00000000000000
χ26222222-2-2-2-2-2-2-2-2220000002-200-220000−2i−2i2i2i00−2i−2i2i2i00000000000000
χ27222222-2-2-2-2-2-2-2-222000000-22002-200002i2i−2i−2i00−2i−2i2i2i00000000000000
χ28222222-2-2-2-2-2-2-2-222000000-22002-20000−2i−2i2i2i002i2i−2i−2i00000000000000
χ292222-2-22-2-2-2-22222-222-2-200000000000000002-2000022000-2-20000000
χ302222-2-22-2-2-2-22222-222-2-200000000000000002-20000-2-2000220000000
χ312222-2-22-2-2-2-22222-2-2-2220000000000000000-2200002-2000-220000000
χ322222-2-22-2-2-2-22222-2-2-2220000000000000000-220000-220002-20000000
χ332222-2-2-2-2-22222-2-2222-2-20000000000000000-220000002-2200-2000000
χ342222-2-2-2-2-22222-2-2222-2-20000000000000000-22000000-22-2002000000
χ352222-2-2-2-2-22222-2-22-2-22200000000000000002-200000022-200-2000000
χ362222-2-2-2-2-22222-2-22-2-22200000000000000002-2000000-2-22002000000
χ374444-4-4444-4-4-4-44-440000000000000000000000000000000000000000
χ384444-4-4-44444-4-4-44-40000000000000000000000000000000000000000
χ394-44-40004i−4i000000022−222i2−2i2000000002-22i−2i2ζ−2ζ2ζ3−2ζ300000000000000000000
χ404-44-40004i−4i000000022−222i2−2i200000000-22−2i2i−2ζ2ζ−2ζ32ζ300000000000000000000
χ414-44-40004i−4i0000000−2222−2i22i2000000002-22i−2i−2ζ2ζ−2ζ32ζ300000000000000000000
χ424-44-40004i−4i0000000−2222−2i22i200000000-22−2i2i2ζ−2ζ2ζ3−2ζ300000000000000000000
χ434-44-4000−4i4i000000022−22−2i22i2000000002-2−2i2i−2ζ32ζ3−2ζ2ζ00000000000000000000
χ444-44-4000−4i4i000000022−22−2i22i200000000-222i−2i2ζ3−2ζ32ζ−2ζ00000000000000000000
χ454-44-4000−4i4i0000000−22222i2−2i2000000002-2−2i2i2ζ3−2ζ32ζ−2ζ00000000000000000000
χ464-44-4000−4i4i0000000−22222i2−2i200000000-222i−2i−2ζ32ζ3−2ζ2ζ00000000000000000000
χ474-4-444-44004-400-40000000000000000000000002i2−2i22i2−2i200000000000000
χ484-4-444-44004-400-4000000000000000000000000−2i22i2−2i22i200000000000000
χ494-4-444-4-400-4400400000000000000000000000022−22−222200000000000000
χ504-4-444-4-400-44004000000000000000000000000−222222−2200000000000000
χ514-4-44-44400-4400-40000004i−4i0000000000000000000000000000000000
χ524-4-44-44400-4400-4000000−4i4i0000000000000000000000000000000000
χ534-4-44-44-4004-400400000000004-4000000000000000000000000000000
χ544-4-44-44-4004-40040000000000-44000000000000000000000000000000
χ5588-8-800000008-80000000000000000000000000000000000000000000
χ5688-8-80000000-880000000000000000000000000000000000000000000

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