Finite Group Databasebeta

← Group #315005

Character table — Group #315005

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224444448888888822244444444488888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111
χ5111111111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-111
χ17222222222222-2-2-2-22222-2-2-2-2002-2-200200000000000000000000-2200000000
χ18222222222222-2-2-2-22222-2-2-2-200-22200-2000000000000000000002-200000000
χ19222222222222-2-2-2-2-2-2-2-22222002-2-2002000000000000000000002-200000000
χ20222222222222-2-2-2-2-2-2-2-2222200-22200-200000000000000000000-2200000000
χ212222-2-2-2-222-2-222-2-2000000002222-2-2-2-222-2-200000000000000000000000000
χ222222-2-2-2-222-2-222-2-20000000022-2-22-2-22-2-22200000000000000000000000000
χ232222-2-2-2-222-2-222-2-200000000-2-222-222-2-2-22200000000000000000000000000
χ242222-2-2-2-222-2-222-2-200000000-2-2-2-2222222-2-200000000000000000000000000
χ252222-2-2-2-222-2-2-2-22200000000002-2200-200002i2i−2i−2i2i2i−2i−2i000000000000000000
χ262222-2-2-2-222-2-2-2-22200000000002-2200-20000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ272222-2-2-2-222-2-2-2-2220000000000-22-200200002i2i−2i−2i−2i−2i2i2i000000000000000000
χ282222-2-2-2-222-2-2-2-2220000000000-22-20020000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-2-2-2-2-2-2222-22-222-2-222-2-20000000000000000000000002i−2i2i−2i0000000000
χ302222-2-2-2-2-2-2222-22-222-2-222-2-2000000000000000000000000−2i2i−2i2i0000000000
χ312222-2-2-2-2-2-2222-22-2-2-222-2-2220000000000000000000000002i−2i−2i2i0000000000
χ322222-2-2-2-2-2-2222-22-2-2-222-2-222000000000000000000000000−2i2i2i−2i0000000000
χ332222-2-2-2-2-2-222-22-2222-2-2-2-222000000000000000000002i−2i2i−2i00000000000000
χ342222-2-2-2-2-2-222-22-2222-2-2-2-22200000000000000000000−2i2i−2i2i00000000000000
χ352222-2-2-2-2-2-222-22-22-2-22222-2-2000000000000000000002i−2i−2i2i00000000000000
χ362222-2-2-2-2-2-222-22-22-2-22222-2-200000000000000000000−2i2i2i−2i00000000000000
χ3744444444-4-4-4-44-4-440000000000000000000000000000000000000000000000
χ3844444444-4-4-4-4-444-40000000000000000000000000000000000000000000000
χ3944-4-44i−4i4i−4i000000002i2−2i222−2200002-20002i−2i0000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4044-4-44i−4i4i−4i000000002i2−2i222−220000-22000−2i2i000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4144-4-44i−4i4i−4i00000000−2i22i2−222200002-20002i−2i000000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4244-4-44i−4i4i−4i00000000−2i22i2−22220000-22000−2i2i0000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4344-4-4−4i4i−4i4i000000002i2−2i2−222200002-2000−2i2i0000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ4444-4-4−4i4i−4i4i000000002i2−2i2−22220000-220002i−2i000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4544-4-4−4i4i−4i4i00000000−2i22i222−2200002-2000−2i2i000000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4644-4-4−4i4i−4i4i00000000−2i22i222−220000-220002i−2i0000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ474-44-44i−4i−4i4i0000000000002i2−2i222−22000000002-22i−2i2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ484-44-44i−4i−4i4i0000000000002i2−2i222−2200000000-22−2i2i−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ494-44-44i−4i−4i4i000000000000−2i22i2−2222000000002-22i−2i−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ504-44-44i−4i−4i4i000000000000−2i22i2−222200000000-22−2i2i2ζ3−2ζ32ζ−2ζ0000000000000000000000
χ514-44-4−4i4i4i−4i0000000000002i2−2i2−2222000000002-2−2i2i2ζ−2ζ2ζ3−2ζ30000000000000000000000
χ524-44-4−4i4i4i−4i0000000000002i2−2i2−222200000000-222i−2i−2ζ2ζ−2ζ32ζ30000000000000000000000
χ534-44-4−4i4i4i−4i000000000000−2i22i222−22000000002-2−2i2i−2ζ2ζ−2ζ32ζ30000000000000000000000
χ544-44-4−4i4i4i−4i000000000000−2i22i222−2200000000-222i−2i2ζ−2ζ2ζ3−2ζ30000000000000000000000
χ554-4-4444-4-44-44-400000000000000000000000000000000000000000022−22000000
χ564-4-4444-4-44-44-4000000000000000000000000000000000000000000−2222000000
χ574-4-4444-4-4-44-440000000000000000000000000000000000000000000000002i2−2i2
χ584-4-4444-4-4-44-44000000000000000000000000000000000000000000000000−2i22i2
χ594-4-44-4-4444-4-44000000000000000000000000000000000000000000000022−2200
χ604-4-44-4-4444-4-440000000000000000000000000000000000000000000000−222200
χ614-4-44-4-444-444-40000000000000000000000000000000000000000000022−220000
χ624-4-44-4-444-444-400000000000000000000000000000000000000000000−22220000

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