Finite Group Databasebeta

← Group #143675

Character table — Group #143675

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
χ1122222222-2-222-2-2-2-200000000000022-2-22222−2−2−2−22222−2−2−2−200000000
χ1222222222-2-222-2-2-2-200000000000022-2-2−2−2−2−22222−2−2−2−2222200000000
χ1322222222-2-222-2-2-2-2000000000000-2-2222222−2−2−2−2−2−2−2−2222200000000
χ1422222222-2-222-2-2-2-2000000000000-2-222−2−2−2−222222222−2−2−2−200000000
χ15222222-2-222-2-2-2-22-222-2-222-2-2000000000000000022-2-222-2-200000000
χ16222222-2-222-2-2-2-22-222-2-222-2-20000000000000000-2-222-2-22200000000
χ17222222-2-222-2-2-2-22-2-2-222-2-2220000000022-2-222-2-20000000000000000
χ18222222-2-222-2-2-2-22-2-2-222-2-22200000000-2-222-2-2220000000000000000
χ19222222-2-2-2-2-2-222-220000000022-2-2000022−2−2−2−22222−2−2−2−22200000000
χ20222222-2-2-2-2-2-222-220000000022-2-20000−2−22222−2−2−2−22222−2−200000000
χ21222222-2-2-2-2-2-222-2200000000-2-222000022−2−2−2−222−2−22222−2−200000000
χ22222222-2-2-2-2-2-222-2200000000-2-2220000−2−22222−2−222−2−2−2−22200000000
χ232222-2-22222-2-2-2-2-222222-2-2-2-20000000000000000000000000000002i−2i
χ242222-2-22222-2-2-2-2-222222-2-2-2-2000000000000000000000000000000−2i2i
χ252222-2-22222-2-2-2-2-22-2-2-2-2222200000000000000000000000000002-200
χ262222-2-22222-2-2-2-2-22-2-2-2-222220000000000000000000000000000-2200
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
χ312-22-22-22-2002-200002−22−22−22−22−22−2002-2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ322-22-22-22-2002-200002−22−22−22−22−22−2002-2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ332-22-22-22-2002-200002−22−22−22−2−22−2200-22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ342-22-22-22-2002-200002−22−22−22−2−22−2200-22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ352-22-22-22-2002-20000−22−22−22−222−22−200-22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ362-22-22-22-2002-20000−22−22−22−222−22−200-22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ372-22-22-22-2002-20000−22−22−22−22−22−22002-2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ382-22-22-22-2002-20000−22−22−22−22−22−22002-2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ392-22-22-2-2200-2200002−2−222−2−222−2−222-200ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ402-22-22-2-2200-2200002−2−222−2−222−2−222-200−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ412-22-22-2-2200-2200002−2−222−2−22−222−2-2200ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ422-22-22-2-2200-2200002−2−222−2−22−222−2-2200−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ432-22-22-2-2200-220000−222−2−222−22−2−22-2200ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ442-22-22-2-2200-220000−222−2−222−22−2−22-2200−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ452-22-22-2-2200-220000−222−2−222−2−222−22-200ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ462-22-22-2-2200-220000−222−2−222−2−222−22-200−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ474444-4-444-4-4-4-4444-40000000000000000000000000000000000000000
χ484444-4-4-4-4-4-444-4-4440000000000000000000000000000000000000000
χ494-44-4-444-400-44000022−2222−22−2222−222200000000000000000000000000000000
χ504-44-4-444-400-440000−2222−222222−2222−2200000000000000000000000000000000
χ514-44-4-44-44004-4000022−22−2222−222222−2200000000000000000000000000000000
χ524-44-4-44-44004-40000−222222−2222−22−222200000000000000000000000000000000
χ5388-8-800008-80000000000000000000000000000000000000000000000
χ5488-8-80000-880000000000000000000000000000000000000000000000
χ558-8-88000000008-8000000000000000000000000000000000000000000
χ568-8-8800000000-88000000000000000000000000000000000000000000

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