Finite Group Databasebeta

← Group #143677

Character table — Group #143677

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444444444488888888888888881616161616161616161616161616161644444444
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
χ112222222222-2-2-2-2-2-200000000000022-2-22222−2−2−2−22222−2−2−2−200000000
χ122222222222-2-2-2-2-2-200000000000022-2-2−2−2−2−22222−2−2−2−2222200000000
χ132222222222-2-2-2-2-2-2000000000000-2-2222222−2−2−2−2−2−2−2−2222200000000
χ142222222222-2-2-2-2-2-2000000000000-2-222−2−2−2−222222222−2−2−2−200000000
χ15222222-2-2-2-222-2-22-222-2-222-2-2000000000000000022-2-222-2-200000000
χ16222222-2-2-2-222-2-22-222-2-222-2-20000000000000000-2-222-2-22200000000
χ17222222-2-2-2-222-2-22-2-2-222-2-2220000000022-2-222-2-20000000000000000
χ18222222-2-2-2-222-2-22-2-2-222-2-22200000000-2-222-2-2220000000000000000
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
χ232222-2-222-2-222-2-2-222222-2-2-2-20000000000000000000000000000002i−2i
χ242222-2-222-2-222-2-2-222222-2-2-2-2000000000000000000000000000000−2i2i
χ252222-2-222-2-222-2-2-22-2-2-2-2222200000000000000000000000000002-200
χ262222-2-222-2-222-2-2-22-2-2-2-222220000000000000000000000000000-2200
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
χ3122-2-22-22-22-20000002−22−22−22−22−22−2002-2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ3222-2-22-22-22-20000002−22−22−22−22−22−2002-2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ3322-2-22-22-22-20000002−22−22−22−2−22−2200-22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ3422-2-22-22-22-20000002−22−22−22−2−22−2200-22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ3522-2-22-22-22-2000000−22−22−22−222−22−200-22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ3622-2-22-22-22-2000000−22−22−22−222−22−200-22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ3722-2-22-22-22-2000000−22−22−22−22−22−22002-2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ3822-2-22-22-22-2000000−22−22−22−22−22−22002-2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ3922-2-22-2-22-220000002−2−222−2−222−2−222-200ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ4022-2-22-2-22-220000002−2−222−2−222−2−222-200−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ4122-2-22-2-22-220000002−2−222−2−22−222−2-2200ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ4222-2-22-2-22-220000002−2−222−2−22−222−2-2200−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ4322-2-22-2-22-22000000−222−2−222−22−2−22-2200ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ4422-2-22-2-22-22000000−222−2−222−22−2−22-2200−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ4522-2-22-2-22-22000000−222−2−222−2−222−22-200ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ4622-2-22-2-22-22000000−222−2−222−2−222−22-200−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ474444-4-444-4-4-4-4444-40000000000000000000000000000000000000000
χ484444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000
χ4944-4-4-444-4-4400000022−2222−22−2222−222200000000000000000000000000000000
χ5044-4-4-444-4-44000000−2222−222222−2222−2200000000000000000000000000000000
χ5144-4-4-44-444-400000022−22−2222−222222−2200000000000000000000000000000000
χ5244-4-4-44-444-4000000−222222−2222−22−222200000000000000000000000000000000
χ538-88-80000008-800000000000000000000000000000000000000000000
χ548-88-8000000-8800000000000000000000000000000000000000000000
χ558-8-88000000008-8000000000000000000000000000000000000000000
χ568-8-8800000000-88000000000000000000000000000000000000000000

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