Finite Group Databasebeta

← Group #117816

Character table — Group #117816

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244444444888888888888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ9111-1-1-1-1111-1-1-1-1111-111-1-1-111-11111-1-1-1-11111-1-1-1-11-1ii−i−iii−i−i1-1ii−i−iii−i−i
χ10111-1-1-1-1111-1-1-1-1111-111-1-1-111-11111-1-1-1-11111-1-1-1-11-1−i−iii−i−iii1-1−i−iii−i−iii
χ11111-1-1-1-1111-1-1-1-1111-111-1-1-111-11111-1-1-1-1-1-1-1-11111-11ii−i−i−i−iii-11ii−i−i−i−iii
χ12111-1-1-1-1111-1-1-1-1111-111-1-1-111-11111-1-1-1-1-1-1-1-11111-11−i−iiiii−i−i-11−i−iiiii−i−i
χ13111-1-1-1-1111-1-1-1-1111-111-1-1-111-1-1-1-1-111111111-1-1-1-1-11ii−i−iii−i−i-11−i−iii−i−iii
χ14111-1-1-1-1111-1-1-1-1111-111-1-1-111-1-1-1-1-111111111-1-1-1-1-11−i−iii−i−iii-11ii−i−iii−i−i
χ15111-1-1-1-1111-1-1-1-1111-111-1-1-111-1-1-1-1-11111-1-1-1-111111-1ii−i−i−i−iii1-1−i−iiiii−i−i
χ16111-1-1-1-1111-1-1-1-1111-111-1-1-111-1-1-1-1-11111-1-1-1-111111-1−i−iiiii−i−i1-1ii−i−i−i−iii
χ172222222222222222-2-22-22-2-2-2-2-200000000000000000000000000002-22-20000
χ182222222222222222-2-22-22-2-2-2-2-20000000000000000000000000000-22-220000
χ192222222222-2-222-2-222-2-2-22-2-22-200000000000000000000002-22-20000000000
χ202222222222-2-222-2-222-2-2-22-2-22-20000000000000000000000-22-220000000000
χ212222222222-2-222-2-2-2-2-22-2-222-2200000000000000002200000000-2-200000000
χ222222222222-2-222-2-2-2-2-22-2-222-220000000000000000-2-2000000002200000000
χ2322222222-2-222-2-22222-2-2-2-2-22-22000000000000000000000000000000002-22-2
χ2422222222-2-222-2-22222-2-2-2-2-22-2200000000000000000000000000000000-22-22
χ2522222222-2-222-2-222-2-2-22-222-22-20000000022-2-222-2-200000000000000000000
χ2622222222-2-222-2-222-2-2-22-222-22-200000000-2-222-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-222222-22-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222222-22-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-2-22-222-22220000000000000000002-22-200000000000000
χ3022222222-2-2-2-2-2-2-2-2-2-22-222-2222000000000000000000-22-2200000000000000
χ31222-2-2-2-222222-2-2-2-22-2-2-22-22-22200000000000000000000002i−2i−2i2i0000000000
χ32222-2-2-2-222222-2-2-2-22-2-2-22-22-2220000000000000000000000−2i2i2i−2i0000000000
χ33222-2-2-2-222222-2-2-2-2-22-2222-22-2-200000000000000002-200000000-2200000000
χ34222-2-2-2-222222-2-2-2-2-22-2222-22-2-20000000000000000-22000000002-200000000
χ35222-2-2-2-2222-2-2-2-222-222-2-222-2-2200000000000000000000000000002i−2i−2i2i0000
χ36222-2-2-2-2222-2-2-2-222-222-2-222-2-220000000000000000000000000000−2i2i2i−2i0000
χ37222-2-2-2-22-2-22222-2-22-222-22-2-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ38222-2-2-2-22-2-22222-2-22-222-22-2-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ39222-2-2-2-22-2-22222-2-2-222-2-2-2222-20000000000000000002i−2i−2i2i00000000000000
χ40222-2-2-2-22-2-22222-2-2-222-2-2-2222-2000000000000000000−2i2i2i−2i00000000000000
χ41222-2-2-2-22-2-2-2-222222-2-2-22222-2-2000000000000000000000000000000002i−2i−2i2i
χ42222-2-2-2-22-2-2-2-222222-2-2-22222-2-200000000000000000000000000000000−2i2i2i−2i
χ43222-2-2-2-22-2-2-2-22222-22-222-2-2-2220000000022-2-2-2-22200000000000000000000
χ44222-2-2-2-22-2-2-2-22222-22-222-2-2-22200000000-2-22222-2-200000000000000000000
χ4544-444-4-4-4004i−4i004i−4i00000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ4644-444-4-4-4004i−4i004i−4i0000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ4744-444-4-4-400−4i4i00−4i4i00000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ4844-444-4-4-400−4i4i00−4i4i0000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ4944-4-4-444-4004i−4i00−4i4i00000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ5044-4-4-444-4004i−4i00−4i4i0000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ5144-4-4-444-400−4i4i004i−4i00000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ5244-4-4-444-400−4i4i004i−4i0000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ534-444-44-4-44-4004-4000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ544-444-44-4-44-4004-400000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ554-444-44-4-4-4400-44000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ564-444-44-4-4-4400-4400000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ574-44-44-44-44-400-44000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ584-44-44-44-44-400-4400000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ594-44-44-44-4-44004-4000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ604-44-44-44-4-44004-400000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ618-8-88-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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