Finite Group Databasebeta

← Group #143678

Character table — Group #143678

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444444444488888888888888881616161616161616161616161616161622444444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ92222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ102222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1122222222-2-2-2-222-2-200000000000022-2-22222−2−2−2−22222−2−2−2−200000000
χ1222222222-2-2-2-222-2-200000000000022-2-2−2−2−2−22222−2−2−2−2222200000000
χ1322222222-2-2-2-222-2-2000000000000-2-2222222−2−2−2−2−2−2−2−2222200000000
χ1422222222-2-2-2-222-2-2000000000000-2-222−2−2−2−222222222−2−2−2−200000000
χ15222222-2-222-2-2-2-22-20000000022-2-2000022−2−222−2−222−2−222−2−200000000
χ16222222-2-222-2-2-2-22-20000000022-2-20000−2−222−2−222−2−222−2−22200000000
χ17222222-2-222-2-2-2-22-200000000-2-222000022−2−222−2−2−2−222−2−22200000000
χ18222222-2-222-2-2-2-22-200000000-2-2220000−2−222−2−22222−2−222−2−200000000
χ19222222-2-2-2-222-2-2-2222-2-222-2-2000000000000000022-2-2-2-22200000000
χ20222222-2-2-2-222-2-2-2222-2-222-2-20000000000000000-2-22222-2-200000000
χ21222222-2-2-2-222-2-2-22-2-222-2-2220000000022-2-2-2-2220000000000000000
χ22222222-2-2-2-222-2-2-22-2-222-2-22200000000-2-22222-2-20000000000000000
χ232222-2-222-2-222-2-22-22222-2-2-2-20000000000000000000000000000002i−2i
χ242222-2-222-2-222-2-22-22222-2-2-2-2000000000000000000000000000000−2i2i
χ252222-2-222-2-222-2-22-2-2-2-2-2222200000000000000000000000000002-200
χ262222-2-222-2-222-2-22-2-2-2-2-222220000000000000000000000000000-2200
χ272222-2-2-2-2222222-2-222-2-2-2-22200000000000000000000000020-200000
χ282222-2-2-2-2222222-2-222-2-2-2-222000000000000000000000000-20200000
χ292222-2-2-2-2222222-2-2-2-22222-2-2000000000000000000000000020-20000
χ302222-2-2-2-2222222-2-2-2-22222-2-20000000000000000000000000-2020000
χ312-2-22-222-200002-2002−22−22−22−22−22−2002-2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ322-2-22-222-200002-2002−22−22−22−22−22−2002-2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ332-2-22-222-200002-2002−22−22−22−2−22−2200-22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ342-2-22-222-200002-2002−22−22−22−2−22−2200-22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ352-2-22-222-200002-200−22−22−22−222−22−200-22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ362-2-22-222-200002-200−22−22−22−222−22−200-22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ372-2-22-222-200002-200−22−22−22−22−22−22002-2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ382-2-22-222-200002-200−22−22−22−22−22−22002-2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ392-2-22-22-220000-22002−2−222−2−222−2−222-200ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ402-2-22-22-220000-22002−2−222−2−222−2−222-200−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ412-2-22-22-220000-22002−2−222−2−22−222−2-2200ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ422-2-22-22-220000-22002−2−222−2−22−222−2-2200−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ432-2-22-22-220000-2200−222−2−222−22−2−22-2200ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ442-2-22-22-220000-2200−222−2−222−22−2−22-2200−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ452-2-22-22-220000-2200−222−2−222−2−222−22-200ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ462-2-22-22-220000-2200−222−2−222−2−222−22-200−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ474444-4-44444-4-4-4-4-440000000000000000000000000000000000000000
χ484444-4-4-4-4-4-4-4-444440000000000000000000000000000000000000000
χ494-4-444-44-40000-440022−2222−22−2222−222200000000000000000000000000000000
χ504-4-444-44-40000-4400−2222−222222−2222−2200000000000000000000000000000000
χ514-4-444-4-4400004-40022−22−2222−222222−2200000000000000000000000000000000
χ524-4-444-4-4400004-400−222222−2222−22−222200000000000000000000000000000000
χ5388-8-80000008-800000000000000000000000000000000000000000000
χ5488-8-8000000-8800000000000000000000000000000000000000000000
χ558-88-800008-80000000000000000000000000000000000000000000000
χ568-88-80000-880000000000000000000000000000000000000000000000

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