Finite Group Databasebeta

← Group #150985

Character table — Group #150985

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12224444448888161616161616161624448888881616161616161616161616163232323232323232323232323232323222448888
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
χ511111-1-1111111111111111-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111-1-1111111111111111-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111-1-1111111111111111-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111-1-1111111111111111-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-11111-11111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111-11111-11111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111-11111-11111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111-11111-11111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111-1-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141111-1-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151111-1-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161111-1-1-111-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222-2-2-2-2000000002222-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−200000000
χ192222222222-2-2-2-2000000002222-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−22200000000
χ202222222-2-2200002222−2−2−2−2-2-22-200000022−2−222−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ212222222-2-2200002222−2−2−2−2-2-22-200000022−2−222−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ222222222-2-220000−2−2−2−22222-2-22-2000000−2−222−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ232222222-2-220000−2−2−2−22222-2-22-2000000−2−222−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ2422222-2-22222222-2-2-2-2-2-2-2-2-22-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2522222-2-2222-2-2-2-200000000-22-2-2-2-2222200000000000022−2−222−2−2−2−222−2−22200000000
χ2622222-2-2222-2-2-2-200000000-22-2-2-2-22222000000000000−2−222−2−22222−2−222−2−200000000
χ2722222-2-2-2-2200002222−2−2−2−22-2-2200000022−2−2−2−222−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ2822222-2-2-2-2200002222−2−2−2−22-2-2200000022−2−2−2−222−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ2922222-2-2-2-220000−2−2−2−222222-2-22000000−2−22222−2−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ3022222-2-2-2-220000−2−2−2−222222-2-22000000−2−22222−2−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ312222-22222-22222222222222-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ322222-22222-2-2-2-2-2000000002-2-2-222-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ332222-22222-2-2-2-2-2000000002-2-2-222-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ342222-222-2-2-200002222−2−2−2−2-22-22000000−2−222−2−22222−2−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ352222-222-2-2-200002222−2−2−2−2-22-22000000−2−222−2−22222−2−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ362222-222-2-2-20000−2−2−2−22222-22-2200000022−2−222−2−2−2−222ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ372222-222-2-2-20000−2−2−2−22222-22-2200000022−2−222−2−2−2−222−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ382222-2-2-222-2222222222222-2-222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000
χ392222-2-2-222-2-2-2-2-200000000-2-2222222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ402222-2-2-222-2-2-2-2-200000000-2-2222222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ412222-2-2-2-2-2-200002222−2−2−2−2222-2000000−2−22222−2−2−2−222ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ422222-2-2-2-2-2-200002222−2−2−2−2222-2000000−2−22222−2−2−2−222−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ432222-2-2-2-2-2-20000−2−2−2−22222222-200000022−2−2−2−22222−2−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ442222-2-2-2-2-2-20000−2−2−2−22222222-200000022−2−2−2−22222−2−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ4544-4-404i−4i0002222−22−222ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ50000002i2−2i200000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000
χ4644-4-404i−4i0002222−22−22−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ50000002i2−2i20000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ4744-4-404i−4i000−22−2222222ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ5−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7000000−2i22i200000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ4844-4-404i−4i000−22−222222−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ52ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ7000000−2i22i20000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ4944-4-40−4i4i0002222−22−222ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ5000000−2i22i20000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ5044-4-40−4i4i0002222−22−22−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5000000−2i22i200000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000
χ5144-4-40−4i4i000−22−2222222ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ5−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ−2ζ70000002i2−2i20000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ5244-4-40−4i4i000−22−222222−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ52ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ70000002i2−2i200000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ534-44-440000-422−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5000022−2200002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ544-44-440000-422−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5000022−220000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ554-44-440000-4−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ70000−222200002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ564-44-440000-4−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ70000−22220000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ574-44-4-40000422−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ50000−22220000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000
χ584-44-4-40000422−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ50000−222200002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000
χ594-44-4-400004−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7000022−220000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000
χ604-44-4-400004−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7000022−2200002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000
χ614-4-440004-40000022−22−2222−222222−22000000004-4000022−2222−220000000000000000000000000000
χ624-4-440004-40000022−22−2222−222222−2200000000-440000−2222−22220000000000000000000000000000
χ634-4-440004-400000−222222−2222−22−2222000000004-40000−2222−22220000000000000000000000000000
χ644-4-440004-400000−222222−2222−22−222200000000-44000022−2222−220000000000000000000000000000
χ654-4-44000-4404-4-444-4-444-4-440000000000000000000000000000000000000000000000
χ664-4-44000-4404-4-44-444-4-444-40000000000000000000000000000000000000000000000
χ674-4-44000-440-444-400000000000000000000004-4-440000000000000000000000000000
χ684-4-44000-440-444-40000000000000000000000-444-40000000000000000000000000000

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