Finite Group Databasebeta

← Group #153384

Character table — Group #153384

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222244444444448888888888888888888888883232323232323232
order122222444488888816161616161616164488161616163232323232323232323232323232323244448888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
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
χ232222-2-2-222-22222-2-22-22-22-22-20000000000000000000000000000002i−2i
χ242222-2-2-222-22222-2-22-22-22-22-2000000000000000000000000000000−2i2i
χ252222-2-2-222-22222-2-2-22-22-22-2200000000000000000000000000002i−2i00
χ262222-2-2-222-22222-2-2-22-22-22-220000000000000000000000000000−2i2i00
χ2722-2-22-222-2-222-2-22-20000000000002-22-22−22−22−22−22−22−22−22−200000000
χ2822-2-22-222-2-222-2-22-20000000000002-22-2−22−22−22−22−22−22−22−2200000000
χ2922-2-22-222-2-222-2-22-2000000000000-22-222−22−22−22−2−22−22−22−2200000000
χ3022-2-22-222-2-222-2-22-2000000000000-22-22−22−22−22−222−22−22−22−200000000
χ3122-2-22-222-2-2-2-222-222-22-2-22-2200000000000000002-22-2-22-2200000000
χ3222-2-22-222-2-2-2-222-222-22-2-22-220000000000000000-22-222-22-200000000
χ3322-2-22-222-2-2-2-222-22-22-222-22-2000000002-22-2-22-220000000000000000
χ3422-2-22-222-2-2-2-222-22-22-222-22-200000000-22-222-22-20000000000000000
χ3522-2-22-2-2-2220000002−2−22−222−2002-22−2−22ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ3622-2-22-2-2-2220000002−2−22−222−2002-22−2−22−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ3722-2-22-2-2-2220000002−2−22−222−200-22−222−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ3822-2-22-2-2-2220000002−2−22−222−200-22−222−2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ3922-2-22-2-2-222000000−222−22−2−22002-2−222−2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ4022-2-22-2-2-222000000−222−22−2−22002-2−222−2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ4122-2-22-2-2-222000000−222−22−2−2200-222−2−22ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ4222-2-22-2-2-222000000−222−22−2−2200-222−2−22−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ4322-2-2-22-22-22-2-2222-22222-2-2-2-20000000000000000000000002i−2i000000
χ4422-2-2-22-22-22-2-2222-22222-2-2-2-2000000000000000000000000−2i2i000000
χ4522-2-2-22-22-22-2-2222-2-2-2-2-22222000000000000000000000000002-20000
χ4622-2-2-22-22-22-2-2222-2-2-2-2-2222200000000000000000000000000-220000
χ474444-4-44-4-4400000022−22−222222−22−222200000000000000000000000000000000
χ484444-4-44-4-44000000−222222−22−222222−2200000000000000000000000000000000
χ494444-4-4-444-4-4-4-4-4440000000000000000000000000000000000000000
χ5044-4-4-444-44-40000002222−22−22−22−22222200000000000000000000000000000000
χ5144-4-4-444-44-4000000−22−2222222222−22−2200000000000000000000000000000000
χ5244-4-4-44-44-4444-4-4-440000000000000000000000000000000000000000
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.