Finite Group Databasebeta

← Group #345883

Character table — Group #345883

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444488888888888888888888888816161616161616161632323232
order12222244444444444442244444488888888888888884444488884488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111
χ51111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-111-1-111-1-1-1-11-1
χ61111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ71111111111111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-111-1-111-1-1-11
χ81111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111111-1
χ91111111111111-1-1-1-11111-1-111-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11-1-11
χ101111111111111-1-1-1-11111-1-111-1-111111111-1-1-1-11111-1-1-111-1-1-1-1-111-1
χ111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111111-11-1
χ121111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111-11-11
χ131111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-111-11-1-1
χ141111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-111
χ151111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-1111
χ161111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-11-1-1-1
χ17222222222-2-22-22222-2-222-2-2-2-2-2-200000000000000002000000000000
χ18222222222-2-22-22222-2-2-2-22222-2-20000000000000000-2000000000000
χ19222222222-2-22-2-2-2-2-2-2-22222-2-2220000000000000000-2000000000000
χ20222222222-2-22-2-2-2-2-2-2-2-2-2-2-2222200000000000000002000000000000
χ212222-2-22-2-2-2-22200002-2000000002i2i−2i−2i00002i2i−2i−2i000002-20000000000
χ222222-2-22-2-2-2-22200002-2000000002i2i−2i−2i0000−2i−2i2i2i00000-220000000000
χ232222-2-22-2-2-2-22200002-200000000−2i−2i2i2i00002i2i−2i−2i00000-220000000000
χ242222-2-22-2-2-2-22200002-200000000−2i−2i2i2i0000−2i−2i2i2i000002-20000000000
χ252222-2-2-222-2-2-220000-220000000000002i2i−2i−2i00002i2i−2i−2i0002-200000000
χ262222-2-2-222-2-2-220000-220000000000002i2i−2i−2i0000−2i−2i2i2i000-2200000000
χ272222-2-2-222-2-2-220000-22000000000000−2i−2i2i2i00002i2i−2i−2i000-2200000000
χ282222-2-2-222-2-2-220000-22000000000000−2i−2i2i2i0000−2i−2i2i2i0002-200000000
χ2922-2-22-2-22-200202i2i−2i−2i00002-22i−2i002−22−2i2−i2i2−i20000000000000i2−i22−20000
χ3022-2-22-2-22-200202i2i−2i−2i00002-22i−2i00−22−22−i2i2−i2i20000000000000−i2i2−220000
χ3122-2-22-2-22-200202i2i−2i−2i0000-22−2i2i002−22−2−i2i2−i2i20000000000000i2−i2−220000
χ3222-2-22-2-22-200202i2i−2i−2i0000-22−2i2i00−22−22i2−i2i2−i20000000000000−i2i22−20000
χ3322-2-22-2-22-20020−2i−2i2i2i00002-2−2i2i002−22−2−i2i2−i2i20000000000000−i2i22−20000
χ3422-2-22-2-22-20020−2i−2i2i2i00002-2−2i2i00−22−22i2−i2i2−i20000000000000i2−i2−220000
χ3522-2-22-2-22-20020−2i−2i2i2i0000-222i−2i002−22−2i2−i2i2−i20000000000000−i2i2−220000
χ3622-2-22-2-22-20020−2i−2i2i2i0000-222i−2i00−22−22−i2i2−i2i20000000000000i2−i22−20000
χ37444444-4-4-444-440000-4-40000000000000000000000000000000000000
χ38444444-4-4-4-4-4-4-40000440000000000000000000000000000000000000
χ394444-4-44-4-4444-40000-440000000000000000000000000000000000000
χ404444-4-4-44444-4-400004-40000000000000000000000000000000000000
χ4144-4-44-44-4400-400000004-400000000000000000000000000000000000
χ4244-4-44-44-4400-40000000-4400000000000000000000000000000000000
χ4344-4-4-4444-400-4000000000000000000022−22−2222000000000000000000000
χ4444-4-4-4444-400-40000000000000000000−222222−22000000000000000000000
χ4544-4-4-44-4-440040000000000000002i2−2i2−2i22i20000000000000000000000000
χ4644-4-4-44-4-44004000000000000000−2i22i22i2−2i20000000000000000000000000
χ474-44-4000004i−4i002-22-2000000002i−2i000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000
χ484-44-4000004i−4i002-22-2000000002i−2i00000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000
χ494-44-4000004i−4i00-22-2200000000−2i2i000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000
χ504-44-4000004i−4i00-22-2200000000−2i2i00000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000
χ514-44-400000−4i4i002-22-200000000−2i2i000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000
χ524-44-400000−4i4i002-22-200000000−2i2i00000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000
χ534-44-400000−4i4i00-22-22000000002i−2i000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000
χ544-44-400000−4i4i00-22-22000000002i−2i00000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000
χ558-8-880000000004i−4i−4i4i000000000000000000000000000000000000000
χ568-8-88000000000−4i4i4i−4i000000000000000000000000000000000000000

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