Finite Group Databasebeta

← Group #265270

Character table — Group #265270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444444444444444448888161616161616161616161616161632323232
order12222222224444444444444488888888888888882444222444444488884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1111-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-11-111-1-1-1-1-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111-1-11
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1-11-11-1-111-1-1-11-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-111-11-1-1-111-1-11-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-111-1-1111-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-11111-1-111-111-1
χ172222222222-2-2-2-2-2-22222-2-2-2-200000000000000002-2-22000000002-200000000
χ182222222222-2-2-2-2-2-22222-2-2-2-20000000000000000-222-200000000-2200000000
χ192222222222-2-2-2-2-2-2-2-2-2-2222200000000000000002-2-2200000000-2200000000
χ202222222222-2-2-2-2-2-2-2-2-2-222220000000000000000-222-2000000002-200000000
χ2122222-2-2-2-22-2-2222-2000000002222-2-2-2-200000000000022000-2-200000000000
χ2222222-2-2-2-22-2-2222-2000000002222-2-2-2-2000000000000-2-20002200000000000
χ2322222-2-2-2-22-2-2222-200000000-2-2-2-222220000000000002-2000-2200000000000
χ2422222-2-2-2-22-2-2222-200000000-2-2-2-22222000000000000-220002-200000000000
χ252222-222-2-2-22222-2-20000000022-2-222-2-20000000022-2-20000000000002-20000
χ262222-222-2-2-22222-2-20000000022-2-222-2-200000000-2-222000000000000-220000
χ272222-222-2-2-22222-2-200000000-2-222-2-2220000000022-2-2000000000000-220000
χ282222-222-2-2-22222-2-200000000-2-222-2-22200000000-2-2220000000000002-20000
χ292222-222-2-2-2-2-2-2-22200000000000000002i2i2i2i−2i−2i−2i−2i2-22-200000000002i−2i000000
χ302222-222-2-2-2-2-2-2-22200000000000000002i2i2i2i−2i−2i−2i−2i-22-220000000000−2i2i000000
χ312222-222-2-2-2-2-2-2-2220000000000000000−2i−2i−2i−2i2i2i2i2i2-22-20000000000−2i2i000000
χ322222-222-2-2-2-2-2-2-2220000000000000000−2i−2i−2i−2i2i2i2i2i-22-2200000000002i−2i000000
χ332222-2-2-222-2-2-222-220000000022-2-2-2-2220000000000000022-200-20000000000
χ342222-2-2-222-2-2-222-220000000022-2-2-2-22200000000000000-2-220020000000000
χ352222-2-2-222-2-2-222-2200000000-2-22222-2-2000000000000002-2200-20000000000
χ362222-2-2-222-2-2-222-2200000000-2-22222-2-200000000000000-22-20020000000000
χ3744444-4-4-4-4444-4-4-440000000000000000000000000000000000000000000000
χ384444-4-4-444-444-4-44-40000000000000000000000000000000000000000000000
χ3944-4-4000000004-4002i2i−2i−2i2i2i−2i−2i004-400002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ4044-4-4000000004-4002i2i−2i−2i2i2i−2i−2i00-440000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ4144-4-4000000004-400−2i−2i2i2i−2i−2i2i2i004-40000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ4244-4-4000000004-400−2i−2i2i2i−2i−2i2i2i00-4400002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ4344-4-400000000-44002i2i−2i−2i−2i−2i2i2i0000004i−4i22-2-2-2-2220000000000000000000000
χ4444-4-400000000-44002i2i−2i−2i−2i−2i2i2i000000−4i4i-2-22222-2-20000000000000000000000
χ4544-4-400000000-4400−2i−2i2i2i2i2i−2i−2i0000004i−4i-2-22222-2-20000000000000000000000
χ4644-4-400000000-4400−2i−2i2i2i2i2i−2i−2i000000−4i4i22-2-2-2-2220000000000000000000000
χ474-44-40000004i−4i00002-22-22i−2i2i−2i22−22002i2−2i2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ484-44-40000004i−4i00002-22-22i−2i2i−2i−222200−2i22i200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ494-44-40000004i−4i0000-22-22−2i2i−2i2i22−22002i2−2i200−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ504-44-40000004i−4i0000-22-22−2i2i−2i2i−222200−2i22i2002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ514-44-4000000−4i4i00002-22-2−2i2i−2i2i22−2200−2i22i200−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ524-44-4000000−4i4i00002-22-2−2i2i−2i2i−2222002i2−2i2002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ534-44-4000000−4i4i0000-22-222i−2i2i−2i22−2200−2i22i2002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ544-44-4000000−4i4i0000-22-222i−2i2i−2i−2222002i2−2i200−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ554-4-4444-44-4-400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000
χ564-4-4444-44-4-40000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000
χ574-4-444-44-44-40000004i−4i−4i4i000000000000000000000000000000000000000000
χ584-4-444-44-44-4000000−4i4i4i−4i000000000000000000000000000000000000000000
χ594-4-44-44-4-444000000000000000000000022−22−222222−22−22220000000000000000000000
χ604-4-44-44-4-4440000000000000000000000−222222−22−222222−220000000000000000000000
χ614-4-44-4-444-4400000000004-4-4400000000000000000000000000000000000000
χ624-4-44-4-444-440000000000-444-400000000000000000000000000000000000000

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