Finite Group Databasebeta

← Group #491113

Character table — Group #491113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222224444444444444444444444444888888888888888883232323232323232
order12224444888824444888816161616161616161616161616161616224488888161616161616161622448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111-11-111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-11-11-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-11-1111-1-1
χ9111111111111-1-11-1-111-1-11111-1-1-1-1111111111-11-1-111-1-111-1-1-1-1-1-111-1-1-111-1
χ10111111111111-1-11-1-111-1-11111-1-1-1-1111111111-11-1-111-1-111-1-1-1-1-1-1-1-1111-1-11
χ11111111111111-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1111111-1-11-1-11
χ12111111111111-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-11111-1-111-111-1
χ13111111111111-1-11-1-111-1-1-1-1-1-1111111111111-11-11-1-1-111-1-111-1-1-1-11-1-11-11-11
χ14111111111111-1-11-1-111-1-1-1-1-1-1111111111111-11-11-1-1-111-1-111-1-1-1-1-111-11-11-1
χ15111111111111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-11111111-1-111-11-1
χ16111111111111-1-11-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1111111-111-1-11-11
χ1722222222-2-2-2-222222-2-2-2-200000000000000002222-2-2-2-2-20000000000000000
χ1822222222-2-2-2-222222-2-2-2-20000000000000000-2-2-2-2-222220000000000000000
χ1922222222-2-2-2-2-2-22-2-2-2-22200000000000000002-22-22-2-2220000000000000000
χ2022222222-2-2-2-2-2-22-2-2-2-2220000000000000000-22-22222-2-20000000000000000
χ2122222-22-2222222-2-2-2-2-22222222222000000000000-20000-2-2-2-2000000000000
χ2222222-22-2222222-2-2-2-2-222-2-2-2-2-2-2-2-2000000000000-200002222000000000000
χ2322222-22-22222-2-2-222-2-2-2-22222-2-2-2-200000000000020000-2-222000000000000
χ2422222-22-22222-2-2-222-2-2-2-2-2-2-2-222220000000000002000022-2-2000000000000
χ2522222-22-2-2-2-2-222-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i00002000000002i2i−2i−2i00000000
χ2622222-22-2-2-2-2-222-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i0000200000000−2i−2i2i2i00000000
χ2722222-22-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i0000-200000000−2i−2i2i2i00000000
χ2822222-22-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i0000-2000000002i2i−2i−2i00000000
χ292222-22-2200002-2-22-2000022−2−222−2−222−2−222−2−22-2-22000002−22−22−22−200000000
χ302222-22-2200002-2-22-2000022−2−222−2−2−2−222−2−222-222-2000002−22−2−22−2200000000
χ312222-22-2200002-2-22-20000−2−222−2−22222−2−222−2−2-222-200000−22−222−22−200000000
χ322222-22-2200002-2-22-20000−2−222−2−222−2−222−2−2222-2-2200000−22−22−22−2200000000
χ332222-22-220000-22-2-22000022−2−2−2−22222−2−222−2−222-2-2000002−2−22−22−2200000000
χ342222-22-220000-22-2-22000022−2−2−2−222−2−222−2−222-2-222000002−2−222−22−200000000
χ352222-22-220000-22-2-220000−2−22222−2−222−2−222−2−2-2-22200000−222−2−22−2200000000
χ362222-22-220000-22-2-220000−2−22222−2−2−2−222−2−22222-2-200000−222−22−22−200000000
χ372222-2-2-2-200002-22-22000022−2−222−2−2i2i2−i2−i2−i2−i2i2i2000002i−2i2i−2i−22−22i2−i2−i2i200000000
χ382222-2-2-2-200002-22-22000022−2−222−2−2−i2−i2i2i2i2i2−i2−i200000−2i2i−2i2i−22−22−i2i2i2−i200000000
χ392222-2-2-2-200002-22-220000−2−222−2−222i2i2−i2−i2−i2−i2i2i200000−2i2i−2i2i2−22−2i2−i2−i2i200000000
χ402222-2-2-2-200002-22-220000−2−222−2−222−i2−i2i2i2i2i2−i2−i2000002i−2i2i−2i2−22−2−i2i2i2−i200000000
χ412222-2-2-2-20000-2222-2000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000002i−2i−2i2i−222−2−i2i2i2−i200000000
χ422222-2-2-2-20000-2222-2000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000−2i2i2i−2i−222−2i2−i2−i2i200000000
χ432222-2-2-2-20000-2222-20000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000−2i2i2i−2i2−2−22−i2i2i2−i200000000
χ442222-2-2-2-20000-2222-20000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000002i−2i−2i2i2−2−22i2−i2−i2i200000000
χ4544-4-440-40000000000004i−4i22−2222−222i2−2i22i2−2i2000000000000000000000000000000000
χ4644-4-440-40000000000004i−4i−2222−2222−2i22i2−2i22i2000000000000000000000000000000000
χ4744-4-440-4000000000000−4i4i22−2222−22−2i22i2−2i22i2000000000000000000000000000000000
χ4844-4-440-4000000000000−4i4i−2222−22222i2−2i22i2−2i2000000000000000000000000000000000
χ4944-4-4-404044-4-400000000000004i−4i−4i4i000000000000000000000000000000000
χ5044-4-4-404044-4-40000000000000−4i4i4i−4i000000000000000000000000000000000
χ5144-4-4-4040-4-4440000000004-4-440000000000000000000000000000000000000
χ5244-4-4-4040-4-444000000000-444-40000000000000000000000000000000000000
χ534-44-4040-422−2222−220000022−2200000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000
χ544-44-4040-422−2222−220000022−220000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000
χ554-44-4040-4−2222−222200000−222200000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000
χ564-44-4040-4−2222−222200000−22220000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000
χ574-44-40-40422−2222−2200000−222200000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000
χ584-44-40-40422−2222−2200000−22220000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000
χ594-44-40-404−2222−22220000022−2200000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000
χ604-44-40-404−2222−22220000022−220000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000
χ618-8-88000042−42−424200000000000000000000000000000000000000000000000000
χ628-8-880000−424242−4200000000000000000000000000000000000000000000000000

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