Finite Group Databasebeta

← Group #507942

Character table — Group #507942

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order1244222444444444448888444444448888888888888822444444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-11-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-11-11111-1-1-1-1-1-111-1-1-1-11111
χ711111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-11-1-1-1-1111111-1-1-1-1-1-11111
χ811111111111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111-1-1
χ101111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111111-11-1-1-1-1-11111-1-111-1-111-1-111
χ111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11-111111-1-1-1-111-1-1-1-111-1-111
χ121111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1
χ131111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-11111-1-1
χ151111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-111-1-11111-1-1
χ161111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ17222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222000000000000000000000000
χ192222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-2000000000000000000000000
χ202222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2122-2-22-2-22i2i−2i−2i2i2i−2i−2i-222000022-2-22i−2i2i−2i0000000000000000000000000000002−2i2−i2i2−i22−2
χ2222-2-22-2-22i2i−2i−2i2i2i−2i−2i-222000022-2-22i−2i2i−2i000000000000000000000000000000−22−i2i2−i2i2−22
χ2322-2-22-2-22i2i−2i−2i−2i−2i2i2i-2220000-2-2222i−2i−2i2i0000000000000000000000000000002−2i2−i2−i2i2−22
χ2422-2-22-2-22i2i−2i−2i−2i−2i2i2i-2220000-2-2222i−2i−2i2i000000000000000000000000000000−22−i2i2i2−i22−2
χ2522-2-22-2-2−2i−2i2i2i2i2i−2i−2i-2220000-2-222−2i2i2i−2i0000000000000000000000000000002−2−i2i2i2−i2−22
χ2622-2-22-2-2−2i−2i2i2i2i2i−2i−2i-2220000-2-222−2i2i2i−2i000000000000000000000000000000−22i2−i2−i2i22−2
χ2722-2-22-2-2−2i−2i2i2i−2i−2i2i2i-222000022-2-2−2i2i−2i2i0000000000000000000000000000002−2−i2i2−i2i22−2
χ2822-2-22-2-2−2i−2i2i2i−2i−2i2i2i-222000022-2-2−2i2i−2i2i000000000000000000000000000000−22i2−i2i2−i2−22
χ2922-2-2-22-200002i2i−2i−2i22-222-2-2000000−2i2i00002-200002i2i−2i−2i00002-20000002i−2i0000000000
χ3022-2-2-22-200002i2i−2i−2i22-222-2-2000000−2i2i00002-200002i2i−2i−2i0000-22000000−2i2i0000000000
χ3122-2-2-22-200002i2i−2i−2i22-2-2-222000000−2i2i0000-220000−2i−2i2i2i20-2000002i−2i00000000000000
χ3222-2-2-22-200002i2i−2i−2i22-2-2-222000000−2i2i0000-220000−2i−2i2i2i-20200000−2i2i00000000000000
χ3322-2-2-22-20000−2i−2i2i2i22-222-2-20000002i−2i00002-20000−2i−2i2i2i00002-2000000−2i2i0000000000
χ3422-2-2-22-20000−2i−2i2i2i22-222-2-20000002i−2i00002-20000−2i−2i2i2i0000-220000002i−2i0000000000
χ3522-2-2-22-20000−2i−2i2i2i22-2-2-2220000002i−2i0000-2200002i2i−2i−2i20-200000−2i2i00000000000000
χ3622-2-2-22-20000−2i−2i2i2i22-2-2-2220000002i−2i0000-2200002i2i−2i−2i-202000002i−2i00000000000000
χ3722-2-2-2-222i2i−2i−2i00002-2222-2-20000−2i2i000000-222i2i−2i−2i00000000002-20000002i−2i00000000
χ3822-2-2-2-222i2i−2i−2i00002-2222-2-20000−2i2i000000-222i2i−2i−2i0000000000-22000000−2i2i00000000
χ3922-2-2-2-222i2i−2i−2i00002-22-2-2220000−2i2i0000002-2−2i−2i2i2i0000020-20000002i−2i000000000000
χ4022-2-2-2-222i2i−2i−2i00002-22-2-2220000−2i2i0000002-2−2i−2i2i2i00000-202000000−2i2i000000000000
χ4122-2-2-2-22−2i−2i2i2i00002-2222-2-200002i−2i000000-22−2i−2i2i2i00000000002-2000000−2i2i00000000
χ4222-2-2-2-22−2i−2i2i2i00002-2222-2-200002i−2i000000-22−2i−2i2i2i0000000000-220000002i−2i00000000
χ4322-2-2-2-22−2i−2i2i2i00002-22-2-22200002i−2i0000002-22i2i−2i−2i0000020-2000000−2i2i000000000000
χ4422-2-2-2-22−2i−2i2i2i00002-22-2-22200002i−2i0000002-22i2i−2i−2i00000-2020000002i−2i000000000000
χ4544444-4-4000000004-4-44444000000000000-4-400000000000000000000000000000000
χ4644444-4-4000000004-4-4-4-4-4-40000000000004400000000000000000000000000000000
χ474444-44-444440000-4-4400000000-4-40000000000000000000000000000000000000000
χ484444-44-4-4-4-4-40000-4-4400000000440000000000000000000000000000000000000000
χ494444-4-4400004444-44-40000000000-4-400000000000000000000000000000000000000
χ504444-4-440000-4-4-4-4-44-400000000004400000000000000000000000000000000000000
χ5144-4-444400000000-4-4-40000000000004i4i−4i−4i0000000000000000000000000000000000
χ5244-4-444400000000-4-4-4000000000000−4i−4i4i4i0000000000000000000000000000000000
χ534-44i−4i0002+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i0002i2−2i222−222-22i−2i00002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ544-44i−4i0002+2i−2−2i2−2i−2+2i2+2i−2−2i2−2i−2+2i000−2i22i2−22222-22i−2i0000−2ζ2ζ−2ζ32ζ300−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ554-44i−4i0002+2i−2−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i0002i2−2i222−22-22−2i2i0000−2ζ2ζ−2ζ32ζ3002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ564-44i−4i0002+2i−2−2i2−2i−2+2i−2−2i2+2i−2+2i2−2i000−2i22i2−2222-22−2i2i00002ζ−2ζ2ζ3−2ζ300−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ574-44i−4i000−2−2i2+2i−2+2i2−2i2+2i−2−2i2−2i−2+2i0002i2−2i222−22-22−2i2i0000−2ζ2ζ−2ζ32ζ300−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ584-44i−4i000−2−2i2+2i−2+2i2−2i2+2i−2−2i2−2i−2+2i000−2i22i2−2222-22−2i2i00002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ594-44i−4i000−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i0002i2−2i222−222-22i−2i00002ζ−2ζ2ζ3−2ζ300−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ604-44i−4i000−2−2i2+2i−2+2i2−2i−2−2i2+2i−2+2i2−2i000−2i22i2−22222-22i−2i0000−2ζ2ζ−2ζ32ζ3002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ614-4−4i4i0002−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i0002i2−2i2−22222-2−2i2i00002ζ3−2ζ32ζ−2ζ002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ624-4−4i4i0002−2i−2+2i2+2i−2−2i2−2i−2+2i2+2i−2−2i000−2i22i222−222-2−2i2i0000−2ζ32ζ3−2ζ2ζ00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ634-4−4i4i0002−2i−2+2i2+2i−2−2i−2+2i2−2i−2−2i2+2i0002i2−2i2−2222-222i−2i0000−2ζ32ζ3−2ζ2ζ002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ644-4−4i4i0002−2i−2+2i2+2i−2−2i−2+2i2−2i−2−2i2+2i000−2i22i222−22-222i−2i00002ζ3−2ζ32ζ−2ζ00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ654-4−4i4i000−2+2i2−2i−2−2i2+2i2−2i−2+2i2+2i−2−2i0002i2−2i2−2222-222i−2i0000−2ζ32ζ3−2ζ2ζ00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ664-4−4i4i000−2+2i2−2i−2−2i2+2i2−2i−2+2i2+2i−2−2i000−2i22i222−22-222i−2i00002ζ3−2ζ32ζ−2ζ002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ674-4−4i4i000−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i0002i2−2i2−22222-2−2i2i00002ζ3−2ζ32ζ−2ζ00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ684-4−4i4i000−2+2i2−2i−2−2i2+2i−2+2i2−2i−2−2i2+2i000−2i22i222−222-2−2i2i0000−2ζ32ζ3−2ζ2ζ002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000

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