Finite Group Databasebeta

← Group #135083

Character table — Group #135083

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12224444444444448888888824888816161616161616161616161616161616244488881616161616161616888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ141111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ151111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−iii−i
χ161111-1-1-1-111-1-111-1-1-1-1-1-11111-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-22200000000-2-200002222−2−2−2−22222−2−2−2−22-22-2000022−2−222−2−2000000000000
χ202222222222-2-2-2-22200000000-2-200002222−2−2−2−22222−2−2−2−2-22-220000−2−222−2−222000000000000
χ212222222222-2-2-2-22200000000-2-20000−2−2−2−22222−2−2−2−222222-22-20000−2−222−2−222000000000000
χ222222222222-2-2-2-22200000000-2-20000−2−2−2−22222−2−2−2−22222-22-22000022−2−222−2−2000000000000
χ2322222222-2-22222-2-222222222-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000
χ2422222222-2-22222-2-222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ2622222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022000022−2−2−2−22222−2−2−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022000022−2−2−2−22222−2−2−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ2922222222-2-2-2-2-2-2-2-200000000220000−2−22222−2−2−2−22222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ3022222222-2-2-2-2-2-2-2-200000000220000−2−22222−2−2−2−22222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ312222-2-2-2-22222-2-2-2-2000000002-200002222−2−2−2−2−2−2−2−222222-2-22000022−2−2−2−222000000000000
χ322222-2-2-2-22222-2-2-2-2000000002-200002222−2−2−2−2−2−2−2−22222-222-20000−2−22222−2−2000000000000
χ332222-2-2-2-22222-2-2-2-2000000002-20000−2−2−2−222222222−2−2−2−22-2-220000−2−22222−2−2000000000000
χ342222-2-2-2-22222-2-2-2-2000000002-20000−2−2−2−222222222−2−2−2−2-222-2000022−2−2−2−222000000000000
χ352222-2-2-2-222-2-222-2-22222-2-2-2-2-22-2-222000000000000000022-2-2-2-22200000000000000000000
χ362222-2-2-2-222-2-222-2-22222-2-2-2-2-22-2-2220000000000000000-2-22222-2-200000000000000000000
χ372222-2-2-2-2-2-222-2-22200000000-22000022−2−2−2−222−2−22222−2−200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i2000000000000
χ382222-2-2-2-2-2-222-2-22200000000-22000022−2−2−2−222−2−22222−2−20000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2000000000000
χ392222-2-2-2-2-2-222-2-22200000000-220000−2−22222−2−222−2−2−2−22200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i2000000000000
χ402222-2-2-2-2-2-222-2-22200000000-220000−2−22222−2−222−2−2−2−2220000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2000000000000
χ412222-2-2-2-2-2-2-2-222222222-2-2-2-22-222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ422222-2-2-2-2-2-2-2-222222222-2-2-2-22-222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ432222-2-2-2-2-2-2-2-22222-2-2-2-222222-2-2-22222-2-222-2-2-2-222-2-2220000000000000000000000000000
χ442222-2-2-2-2-2-2-2-22222-2-2-2-222222-2-2-222-2-222-2-22222-2-222-2-20000000000000000000000000000
χ4522-2-22i−2i2i−2i002i−2i2-2002i2i−2i−2i22-2-2000000002i−2i002i−2i002-2002-200000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ4622-2-22i−2i2i−2i002i−2i2-2002i2i−2i−2i22-2-2000000002i−2i002i−2i002-2002-20000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ4722-2-22i−2i2i−2i002i−2i2-2002i2i−2i−2i22-2-200000000−2i2i00−2i2i00-2200-2200000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ4822-2-22i−2i2i−2i002i−2i2-2002i2i−2i−2i22-2-200000000−2i2i00−2i2i00-2200-220000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ4922-2-2−2i2i−2i2i00−2i2i2-200−2i−2i2i2i22-2-2000000002i−2i002i−2i00-2200-2200000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ5022-2-2−2i2i−2i2i00−2i2i2-200−2i−2i2i2i22-2-2000000002i−2i002i−2i00-2200-220000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ5122-2-2−2i2i−2i2i00−2i2i2-200−2i−2i2i2i22-2-200000000−2i2i00−2i2i002-2002-200000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ5222-2-2−2i2i−2i2i00−2i2i2-200−2i−2i2i2i22-2-200000000−2i2i00−2i2i002-2002-20000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ5344-4-44i−4i4i−4i004i−4i4-400−4i−4i4i4i-4-44400000000000000000000000000000000000000000000000000
χ5444-4-44i−4i4i−4i00−4i4i-440000000000000000002i2−2i200−2i22i20022−2200−22220000000000000000000000000000
χ5544-4-44i−4i4i−4i00−4i4i-44000000000000000000−2i22i2002i2−2i200−22220022−220000000000000000000000000000
χ5644-4-4−4i4i−4i4i004i−4i-440000000000000000002i2−2i200−2i22i200−22220022−220000000000000000000000000000
χ5744-4-4−4i4i−4i4i004i−4i-44000000000000000000−2i22i2002i2−2i20022−2200−22220000000000000000000000000000
χ5844-4-4−4i4i−4i4i00−4i4i4-4004i4i−4i−4i-4-44400000000000000000000000000000000000000000000000000
χ594-44-444-4-40000000022−2222−2222−2222−220000002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ604-44-444-4-40000000022−2222−2222−2222−22000000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ500−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ614-44-444-4-400000000−2222−2222−2222−22220000002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ624-44-444-4-400000000−2222−2222−2222−2222000000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ700−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ634-44-4-4-4440000000022−2222−22−2222−22220000002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ644-44-4-4-4440000000022−2222−22−2222−2222000000−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ654-44-4-4-44400000000−2222−222222−2222−220000002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ500−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ664-44-4-4-44400000000−2222−222222−2222−22000000−2ζ+2ζ72ζ−2ζ700−2ζ3+2ζ52ζ3−2ζ5002ζ−2ζ7−2ζ+2ζ7002ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ674-4-444i−4i−4i4i4-400004i−4i2i2−2i2−2i22i222−22−22220022−222i2−2i200000000000000000000000000000000000000000000
χ684-4-444i−4i−4i4i4-400004i−4i−2i22i22i2−2i2−222222−2200−2222−2i22i200000000000000000000000000000000000000000000
χ694-4-444i−4i−4i4i-440000−4i4i2i2−2i2−2i22i222−22−222200−2222−2i22i200000000000000000000000000000000000000000000
χ704-4-444i−4i−4i4i-440000−4i4i−2i22i22i2−2i2−222222−220022−222i2−2i200000000000000000000000000000000000000000000
χ714-4-44−4i4i4i−4i4-40000−4i4i2i2−2i2−2i22i2−222222−2200−22222i2−2i200000000000000000000000000000000000000000000
χ724-4-44−4i4i4i−4i4-40000−4i4i−2i22i22i2−2i222−22−22220022−22−2i22i200000000000000000000000000000000000000000000
χ734-4-44−4i4i4i−4i-4400004i−4i2i2−2i2−2i22i2−222222−220022−22−2i22i200000000000000000000000000000000000000000000
χ744-4-44−4i4i4i−4i-4400004i−4i−2i22i22i2−2i222−22−222200−22222i2−2i200000000000000000000000000000000000000000000

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