Finite Group Databasebeta

← Group #317129

Character table — Group #317129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224444448888888822224444888888888888224444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111-11-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-11-11-1-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11-11-1-1-1-1-111-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-11-1-111-1-111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1-1-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-11111-1-111-1-1
χ17222222222222-2-2-2-22222-2-2-2-20000000022-2-20000000000002-2000000000000
χ18222222222222-2-2-2-22222-2-2-2-200000000-2-222000000000000-22000000000000
χ19222222222222-2-2-2-2-2-2-2-222220000000022-2-2000000000000-22000000000000
χ20222222222222-2-2-2-2-2-2-2-2222200000000-2-2220000000000002-2000000000000
χ212222-2-2-2-222-2-22-22-200000000002200-2-22i−2i2i−2i2i2i−2i−2i0000000000000000000000
χ222222-2-2-2-222-2-22-22-200000000002200-2-2−2i2i−2i2i−2i−2i2i2i0000000000000000000000
χ232222-2-2-2-222-2-22-22-20000000000-2-200222i−2i2i−2i−2i−2i2i2i0000000000000000000000
χ242222-2-2-2-222-2-22-22-20000000000-2-20022−2i2i−2i2i2i2i−2i−2i0000000000000000000000
χ252222-2-2-2-222-2-2-22-22000000002200-2-2002i−2i−2i2i00002i2i−2i−2i000000000000000000
χ262222-2-2-2-222-2-2-22-22000000002200-2-200−2i2i2i−2i0000−2i−2i2i2i000000000000000000
χ272222-2-2-2-222-2-2-22-2200000000-2-20022002i−2i−2i2i0000−2i−2i2i2i000000000000000000
χ282222-2-2-2-222-2-2-22-2200000000-2-2002200−2i2i2i−2i00002i2i−2i−2i000000000000000000
χ292222-2-2-2-2-2-22222-2-222-2-222-2-2000000000000000000000000002i−2i2i−2i00000000
χ302222-2-2-2-2-2-22222-2-222-2-222-2-200000000000000000000000000−2i2i−2i2i00000000
χ312222-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-2-2-222-2-22222-2-2-2-2220000000000000000000022-2-200000000000000
χ342222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000-2-22200000000000000
χ352222-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000000002-2-2200000000000000
χ362222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000-222-200000000000000
χ3744444444-4-4-4-44-4-440000000000000000000000000000000000000000000000
χ3844444444-4-4-4-4-444-40000000000000000000000000000000000000000000000
χ3944-4-44i4i−4i−4i0000000000002i2−2i222−22002-2002i−2i000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4044-4-44i4i−4i−4i0000000000002i2−2i222−2200-2200−2i2i00000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4144-4-44i4i−4i−4i000000000000−2i22i2−2222002-2002i−2i00000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4244-4-44i4i−4i−4i000000000000−2i22i2−222200-2200−2i2i000000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4344-4-4−4i−4i4i4i0000000000002i2−2i2−2222002-200−2i2i000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ4444-4-4−4i−4i4i4i0000000000002i2−2i2−222200-22002i−2i00000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4544-4-4−4i−4i4i4i000000000000−2i22i222−22002-200−2i2i00000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4644-4-4−4i−4i4i4i000000000000−2i22i222−2200-22002i−2i000000002ζ3−2ζ32ζ−2ζ000000000000000000
χ474-44-44i−4i4i−4i0000000022−222i2−2i200002-2002i−2i0000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ484-44-44i−4i4i−4i0000000022−222i2−2i20000-2200−2i2i000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ494-44-44i−4i4i−4i00000000−2222−2i22i200002-2002i−2i000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ504-44-44i−4i4i−4i00000000−2222−2i22i20000-2200−2i2i0000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ514-44-4−4i4i−4i4i0000000022−22−2i22i200002-200−2i2i000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ524-44-4−4i4i−4i4i0000000022−22−2i22i20000-22002i−2i0000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ534-44-4−4i4i−4i4i00000000−22222i2−2i200002-200−2i2i0000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ544-44-4−4i4i−4i4i00000000−22222i2−2i20000-22002i−2i000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ554-4-444-4-444-44-4000000000000000000000000000000000000000000000022−2200
χ564-4-444-4-444-44-40000000000000000000000000000000000000000000000−222200
χ574-4-444-4-44-44-4400000000000000000000000000000000000000000022−22000000
χ584-4-444-4-44-44-44000000000000000000000000000000000000000000−2222000000
χ594-4-44-444-44-4-440000000000000000000000000000000000000000000022−220000
χ604-4-44-444-44-4-4400000000000000000000000000000000000000000000−22220000
χ614-4-44-444-4-444-400000000000000000000000000000000000000000000000022−22
χ624-4-44-444-4-444-4000000000000000000000000000000000000000000000000−2222

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