Finite Group Databasebeta

← Group #134860

Character table — Group #134860

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122244444488881616161616161616244488888816161616161616161616161644448888161616161616161688888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1i−ii−ii−ii−i
χ101111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii
χ111111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111i−ii−i−ii−ii
χ121111-1-111-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111−ii−iii−ii−i
χ131111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111i−i−iii−i−ii
χ141111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111−iii−i−iii−i
χ151111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1i−i−ii−iii−i
χ161111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1−iii−ii−i−ii
χ172222222222-2-2-2-2000000002222-2-2-2-2-2-20000000000002222-2-2-2-20000000000000000
χ182222222222-2-2-2-2000000002222-2-2-2-2-2-2000000000000-2-2-2-222220000000000000000
χ19222222-2-22200002222−2−2−2−2-22-2-200000022−2−22222−2−2−2−22-22-2000022−2−222−2−200000000
χ20222222-2-22200002222−2−2−2−2-22-2-200000022−2−22222−2−2−2−2-22-220000−2−222−2−22200000000
χ21222222-2-2220000−2−2−2−22222-22-2-2000000−2−222−2−2−2−222222-22-20000−2−222−2−22200000000
χ22222222-2-2220000−2−2−2−22222-22-2-2000000−2−222−2−2−2−22222-22-22000022−2−222−2−200000000
χ2322222-2222-2222222222222-2-22-2-2-222-2-2-2-2-2-222-2-222-2-2000000000000000000000000
χ2422222-2222-22222-2-2-2-2-2-2-2-2-2-22-2-2-222-2-22222-2-222-2-222000000000000000000000000
χ2522222-2222-2-2-2-2-200000000-2-22-222-2-222000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ2622222-2222-2-2-2-2-200000000-2-22-222-2-22200000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ2722222-2-2-22-200002222−2−2−2−22-2-22000000−2−22222−2−2−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i200000000
χ2822222-2-2-22-200002222−2−2−2−22-2-22000000−2−22222−2−2−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i200000000
χ2922222-2-2-22-20000−2−2−2−222222-2-2200000022−2−2−2−22222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200000000
χ3022222-2-2-22-20000−2−2−2−222222-2-2200000022−2−2−2−22222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200000000
χ312222-2222-22222222222222-2-2-22-2-2-2-222-2-2-2-2-2-222-2-222000000000000000000000000
χ322222-2222-222222-2-2-2-2-2-2-2-2-2-2-22-2-2-2-222222222-2-222-2-2000000000000000000000000
χ332222-2222-22-2-2-2-200000000-2-2-222222-2-2000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ342222-2222-22-2-2-2-200000000-2-2-222222-2-200000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ352222-22-2-2-2200002222−2−2−2−22-22-2000000−2−222−2−22222−2−200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i200000000
χ362222-22-2-2-2200002222−2−2−2−22-22-2000000−2−222−2−22222−2−20000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i200000000
χ372222-22-2-2-220000−2−2−2−222222-22-200000022−2−222−2−2−2−22200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i200000000
χ382222-22-2-2-220000−2−2−2−222222-22-200000022−2−222−2−2−2−2220000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i200000000
χ392222-2-222-2-2-2-2-2-20000000022-2-2-2-2222200000000000022-2-2-2-2220000000000000000
χ402222-2-222-2-2-2-2-2-20000000022-2-2-2-22222000000000000-2-22222-2-20000000000000000
χ412222-2-2-2-2-2-200002222−2−2−2−2-222200000022−2−2−2−2−2−222222-2-22000022−2−2−2−22200000000
χ422222-2-2-2-2-2-200002222−2−2−2−2-222200000022−2−2−2−2−2−22222-222-20000−2−22222−2−200000000
χ432222-2-2-2-2-2-20000−2−2−2−22222-2222000000−2−2222222−2−2−2−22-2-220000−2−22222−2−200000000
χ442222-2-2-2-2-2-20000−2−2−2−22222-2222000000−2−2222222−2−2−2−2-222-2000022−2−2−2−22200000000
χ4544-4-4004-40044-4-444-4-444-4-40000000000000000000000000000000000000000000000
χ4644-4-4004-40044-4-4-4-444-4-4440000000000000000000000000000000000000000000000
χ4744-4-4004-400-4-4440000000000000000004i−4i4i−4i00000000000000000000000000000000
χ4844-4-4004-400-4-444000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ4944-4-400-440000002222−22−22−22−22222200004i−4i00002i2−2i2−2i22i200000000000000000000000000000000
χ5044-4-400-440000002222−22−22−22−2222220000−4i4i0000−2i22i22i2−2i200000000000000000000000000000000
χ5144-4-400-44000000−22−2222222222−22−2200004i−4i0000−2i22i22i2−2i200000000000000000000000000000000
χ5244-4-400-44000000−22−2222222222−22−220000−4i4i00002i2−2i2−2i22i200000000000000000000000000000000
χ534-44-404000-422−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ50000000022−220000002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ544-44-404000-422−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ50000000022−22000000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ554-44-404000-4−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ700000000−22220000002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ564-44-404000-4−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ700000000−2222000000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ574-44-40-4000422−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ500000000−2222000000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ584-44-40-4000422−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ500000000−22220000002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ594-44-40-40004−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ70000000022−22000000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ604-44-40-40004−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ70000000022−220000002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ614-4-444000-4022−22−22222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000022−220000002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ624-4-444000-4022−22−2222−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000022−22000000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ634-4-444000-40−222222−222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000−22220000002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ644-4-444000-40−222222−22−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000−2222000000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ654-4-44-40004022−22−22222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000−2222000000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ664-4-44-40004022−22−2222−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000−22220000002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ674-4-44-400040−222222−222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000022−22000000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ684-4-44-400040−222222−22−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000022−220000002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ700000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.