Finite Group Databasebeta

← Group #153324

Character table — Group #153324

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444488888816161616161616164488161616163232323232323232323232323232323244444444
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
χ112222222222-2-2-2-2-2-20000000022-2-200002222−2−2−2−22222−2−2−2−200000000
χ122222222222-2-2-2-2-2-20000000022-2-20000−2−2−2−22222−2−2−2−2222200000000
χ132222222222-2-2-2-2-2-200000000-2-22200002222−2−2−2−2−2−2−2−2222200000000
χ142222222222-2-2-2-2-2-200000000-2-2220000−2−2−2−222222222−2−2−2−200000000
χ15222222-2-2-2-200000022−2−222−2−22-20022−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500000000
χ16222222-2-2-2-200000022−2−222−2−22-20022−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500000000
χ17222222-2-2-2-200000022−2−222−2−2-2200−2−222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500000000
χ18222222-2-2-2-200000022−2−222−2−2-2200−2−222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500000000
χ19222222-2-2-2-2000000−2−222−2−2222-200−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700000000
χ20222222-2-2-2-2000000−2−222−2−2222-200−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700000000
χ21222222-2-2-2-2000000−2−222−2−222-220022−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700000000
χ22222222-2-2-2-2000000−2−222−2−222-220022−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700000000
χ232222-2-2-2-2222222-2-22-22-22-22-200000000000000000000000020-200000
χ242222-2-2-2-2222222-2-22-22-22-22-2000000000000000000000000-20200000
χ252222-2-2-2-2222222-2-2-22-22-22-22000000000000000000000000020-20000
χ262222-2-2-2-2222222-2-2-22-22-22-220000000000000000000000000-2020000
χ2722-2-22-22-22-20000002−2−22−222−2002-22−22−2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ2822-2-22-22-22-20000002−2−22−222−2002-22−22−2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ2922-2-22-22-22-20000002−2−22−222−200-22−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000000
χ3022-2-22-22-22-20000002−2−22−222−200-22−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000000
χ3122-2-22-22-22-2000000−222−22−2−22002-2−22−22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ3222-2-22-22-22-2000000−222−22−2−22002-2−22−22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ3322-2-22-22-22-2000000−222−22−2−2200-222−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000000
χ3422-2-22-22-22-2000000−222−22−2−2200-222−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000000
χ3522-2-22-2-22-2222-2-22-20000000000002-2-222−2−222−2−222−2−22−222−200000000
χ3622-2-22-2-22-2222-2-22-20000000000002-2-22−222−2−222−2−222−22−2−2200000000
χ3722-2-22-2-22-2222-2-22-2000000000000-222-22−2−222−2−22−222−22−2−2200000000
χ3822-2-22-2-22-2222-2-22-2000000000000-222-2−222−2−222−22−2−22−222−200000000
χ3922-2-22-2-22-22-2-222-222-22-2-22-2200000000000000002-2-222-2-2200000000
χ4022-2-22-2-22-22-2-222-222-22-2-22-220000000000000000-222-2-222-200000000
χ4122-2-22-2-22-22-2-222-22-22-222-22-2000000002-2-22-222-20000000000000000
χ4222-2-22-2-22-22-2-222-22-22-222-22-200000000-222-22-2-220000000000000000
χ4322-2-2-222-2-22-2-2222-22222-2-2-2-20000000000000000000000000000002-2
χ4422-2-2-222-2-22-2-2222-22222-2-2-2-2000000000000000000000000000000-22
χ4522-2-2-222-2-22-2-2222-2-2-2-2-2222200000000000000000000000000002i−2i00
χ4622-2-2-222-2-22-2-2222-2-2-2-2-222220000000000000000000000000000−2i2i00
χ474444-4-444-4-400000022−22−222222−22−222200000000000000000000000000000000
χ484444-4-444-4-4000000−222222−22−222222−2200000000000000000000000000000000
χ494444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000
χ5044-4-4-444-4-4444-4-4-440000000000000000000000000000000000000000
χ5144-4-4-44-444-40000002222−22−22−22−22222200000000000000000000000000000000
χ5244-4-4-44-444-4000000−22−2222222222−22−2200000000000000000000000000000000
χ538-88-800000042−4242−42000000000000000000000000000000000000000000
χ548-88-8000000−4242−4242000000000000000000000000000000000000000000
χ558-8-8800000042−42−4242000000000000000000000000000000000000000000
χ568-8-88000000−424242−42000000000000000000000000000000000000000000

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