Finite Group Databasebeta

← Group #326668

Character table — Group #326668

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224444444444444444444444888888888888224488888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-11111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-11-1111-1-1-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11-11-1-1-111-1-1-1-111-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-11-1111-1-1-1-111-1-111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ172222222222222222-2-2-2-2-2-2-2-20000000022-2-200000000000000002-200000000
χ182222222222222222-2-2-2-2-2-2-2-200000000-2-2220000000000000000-2200000000
χ19222222222222-2-2-2-22222-2-2-2-20000000022-2-20000000000000000-2200000000
χ20222222222222-2-2-2-22222-2-2-2-200000000-2-22200000000000000002-200000000
χ212222-2-2-2-222-2-20000000022-2-2000022-2-22i−2i2i−2i2i2i−2i−2i0000000000000000000000
χ222222-2-2-2-222-2-20000000022-2-2000022-2-2−2i2i−2i2i−2i−2i2i2i0000000000000000000000
χ232222-2-2-2-222-2-20000000022-2-20000-2-2222i−2i2i−2i−2i−2i2i2i0000000000000000000000
χ242222-2-2-2-222-2-20000000022-2-20000-2-222−2i2i−2i2i2i2i−2i−2i0000000000000000000000
χ252222-2-2-2-222-2-200000000-2-22222-2-200002i−2i−2i2i00002i2i−2i−2i000000000000000000
χ262222-2-2-2-222-2-200000000-2-22222-2-20000−2i2i2i−2i0000−2i−2i2i2i000000000000000000
χ272222-2-2-2-222-2-200000000-2-222-2-22200002i−2i−2i2i0000−2i−2i2i2i000000000000000000
χ282222-2-2-2-222-2-200000000-2-222-2-2220000−2i2i2i−2i00002i2i−2i−2i000000000000000000
χ292222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i2-22-200000000000000000000020-2002i−2i0000000000
χ302222-2-2-2-2-2-2222i2i−2i−2i2i2i−2i−2i2-22-2000000000000000000000-20200−2i2i0000000000
χ312222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22-220000000000000000000020-202i−2i000000000000
χ322222-2-2-2-2-2-2222i2i−2i−2i−2i−2i2i2i-22-2200000000000000000000-2020−2i2i000000000000
χ332222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22-220000000000000000000020-20−2i2i000000000000
χ342222-2-2-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22-2200000000000000000000-20202i−2i000000000000
χ352222-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i2-22-200000000000000000000020-200−2i2i0000000000
χ362222-2-2-2-2-2-222−2i−2i2i2i−2i−2i2i2i2-22-2000000000000000000000-202002i−2i0000000000
χ3744444444-4-4-4-4000000004-4-4400000000000000000000000000000000000000
χ3844444444-4-4-4-400000000-444-400000000000000000000000000000000000000
χ3944-4-44i−4i4i−4i000000002+2i−2−2i2−2i−2+2i00002-22i−2i2-22i−2i000000000000000000000000000000
χ4044-4-44i−4i4i−4i000000002+2i−2−2i2−2i−2+2i0000-22−2i2i-22−2i2i000000000000000000000000000000
χ4144-4-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i00002-22i−2i-22−2i2i000000000000000000000000000000
χ4244-4-44i−4i4i−4i00000000−2−2i2+2i−2+2i2−2i0000-22−2i2i2-22i−2i000000000000000000000000000000
χ4344-4-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i00002-2−2i2i2-2−2i2i000000000000000000000000000000
χ4444-4-4−4i4i−4i4i000000002−2i−2+2i2+2i−2−2i0000-222i−2i-222i−2i000000000000000000000000000000
χ4544-4-4−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i00002-2−2i2i-222i−2i000000000000000000000000000000
χ4644-4-4−4i4i−4i4i00000000−2+2i2−2i−2−2i2+2i0000-222i−2i2-2−2i2i000000000000000000000000000000
χ474-44-44i−4i−4i4i00002−2i−2+2i2+2i−2−2i000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000
χ484-44-44i−4i−4i4i00002−2i−2+2i2+2i−2−2i00000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ494-44-44i−4i−4i4i0000−2+2i2−2i−2−2i2+2i000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ504-44-44i−4i−4i4i0000−2+2i2−2i−2−2i2+2i00000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000
χ514-44-4−4i4i4i−4i00002+2i−2−2i2−2i−2+2i000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ524-44-4−4i4i4i−4i00002+2i−2−2i2−2i−2+2i00000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ534-44-4−4i4i4i−4i0000−2−2i2+2i−2+2i2−2i000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ544-44-4−4i4i4i−4i0000−2−2i2+2i−2+2i2−2i00000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ554-4-4444-4-44-4-440000000000000000000000000000000000000000002i2−2i2000000
χ564-4-4444-4-44-4-44000000000000000000000000000000000000000000−2i22i2000000
χ574-4-4444-4-4-444-40000000000000000000000000000000000000000000000002i2−2i2
χ584-4-4444-4-4-444-4000000000000000000000000000000000000000000000000−2i22i2
χ594-4-44-4-4444-44-400000000000000000000000000000000000000000000002i2−2i200
χ604-4-44-4-4444-44-40000000000000000000000000000000000000000000000−2i22i200
χ614-4-44-4-444-44-440000000000000000000000000000000000000000000022−220000
χ624-4-44-4-444-44-4400000000000000000000000000000000000000000000−22220000

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