Finite Group Databasebeta

← Group #263307

Character table — Group #263307

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244444444888888888888888888888888161616161616161632323232
order12222244448888888844444444444444444488888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-111-1-1
χ611111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-11-11-1-111-1-111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-1-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-11111-1-1
χ91111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-11-1
χ101111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11-11
χ111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-11-1-11-11
χ121111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-11-111-11-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-11-1-111-1-111-1-11
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1-111-1-111-1-111-1
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-111-1-11-111-1
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-111-1-111-11-1-11
χ17222222222222222222-2-222-2-2-2-22-2000000000000-2-222-2-20000000000000000
χ18222222222222222222-2-2-2-222-2-2-22000000000000-2-2-2-2220000000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22-200000000000022-2-2220000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-220000000000002222-2-20000000000000000
χ21222222-2-2-2-200000000222222-2-2-2-2000000002i2i−2i−2i0000002i2i−2i−2i000000000000
χ22222222-2-2-2-200000000222222-2-2-2-200000000−2i−2i2i2i000000−2i−2i2i2i000000000000
χ23222222-2-2-2-20000000022-2-2-2-2-2-222000000002i2i−2i−2i000000−2i−2i2i2i000000000000
χ24222222-2-2-2-20000000022-2-2-2-2-2-22200000000−2i−2i2i2i0000002i2i−2i−2i000000000000
χ25222222-2-2-2-200000000-2-222-2-222-2222-2-222-2-200000000000000000000000000
χ26222222-2-2-2-200000000-2-222-2-222-22-2-222-2-22200000000000000000000000000
χ27222222-2-2-2-200000000-2-2-2-222222-222-2-2-2-22200000000000000000000000000
χ28222222-2-2-2-200000000-2-2-2-222222-2-2-22222-2-200000000000000000000000000
χ292222-2-22-2-222222-2-2-2-22-200002-2000000000000002-200000000020200-2-20000
χ302222-2-22-2-222222-2-2-2-22-200002-2000000000000002-2000000000-20-200220000
χ312222-2-22-2-222222-2-2-2-2-220000-2200000000000000-22000000002020-2-2000000
χ322222-2-22-2-222222-2-2-2-2-220000-2200000000000000-2200000000-20-2022000000
χ332222-2-22-2-22-2-2-2-222222-200002-200000000000000-2200000000020-200-220000
χ342222-2-22-2-22-2-2-2-222222-200002-200000000000000-22000000000-202002-20000
χ352222-2-22-2-22-2-2-2-22222-220000-22000000000000002-20000000020-20-22000000
χ362222-2-22-2-22-2-2-2-22222-220000-22000000000000002-200000000-20202-2000000
χ374444-4-4-444-4000000004-40000-44000000000000000000000000000000000000
χ384444-4-4-444-400000000-4400004-4000000000000000000000000000000000000
χ3944-4-400400-444-4-40000000000000000002-22-22-22-20000000000000000000000
χ4044-4-400400-444-4-4000000000000000000-22-22-22-220000000000000000000000
χ4144-4-400400-4-4-4440000000000000000002-22-2-22-220000000000000000000000
χ4244-4-400400-4-4-444000000000000000000-22-222-22-20000000000000000000000
χ4344-4-400-400400004i4i−4i−4i000000000000002-2-222i−2i−2i2i0000000000000000000000
χ4444-4-400-400400004i4i−4i−4i00000000000000-222-2−2i2i2i−2i0000000000000000000000
χ4544-4-400-40040000−4i−4i4i4i000000000000002-2-22−2i2i2i−2i0000000000000000000000
χ4644-4-400-40040000−4i−4i4i4i00000000000000-222-22i−2i−2i2i0000000000000000000000
χ474-44-40004i−4i02i2−2i22i2−2i222−2222−2200000000002-22i−2i000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ484-44-40004i−4i02i2−2i22i2−2i222−2222−220000000000-22−2i2i00000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ494-44-40004i−4i0−2i22i2−2i22i2−2222−222200000000002-22i−2i00000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ504-44-40004i−4i0−2i22i2−2i22i2−2222−22220000000000-22−2i2i000000000000002ζ3−2ζ32ζ−2ζ000000000000
χ514-44-4000−4i4i02i2−2i22i2−2i2−2222−222200000000002-2−2i2i000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ524-44-4000−4i4i02i2−2i22i2−2i2−2222−22220000000000-222i−2i00000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ534-44-4000−4i4i0−2i22i2−2i22i222−2222−2200000000002-2−2i2i00000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ544-44-4000−4i4i0−2i22i2−2i22i222−2222−220000000000-222i−2i000000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ554-4-444-400002i2−2i2−2i22i22i2−2i2−2i22i200004-4000000000000000000002i2−2i20000000000000000
χ564-4-444-400002i2−2i2−2i22i22i2−2i2−2i22i20000-4400000000000000000000−2i22i20000000000000000
χ574-4-444-40000−2i22i22i2−2i2−2i22i22i2−2i200004-400000000000000000000−2i22i20000000000000000
χ584-4-444-40000−2i22i22i2−2i2−2i22i22i2−2i20000-44000000000000000000002i2−2i20000000000000000
χ594-4-44-4400002i2−2i2−2i22i2−2i22i22i2−2i2004-4000000000000000000002i2−2i2000000000000000000
χ604-4-44-4400002i2−2i2−2i22i2−2i22i22i2−2i200-4400000000000000000000−2i22i2000000000000000000
χ614-4-44-440000−2i22i22i2−2i22i2−2i2−2i22i2004-400000000000000000000−2i22i2000000000000000000
χ624-4-44-440000−2i22i22i2−2i22i2−2i2−2i22i200-44000000000000000000002i2−2i2000000000000000000

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