Finite Group Databasebeta

← Group #153319

Character table — Group #153319

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1122222222222224444444448888888888888888888888883232323232323232
order12222444488161616168881616161616164488161616163232323232323232323232323232323222244488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ922222222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ1022222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ11222222222-2-20000-2-2-200000022-2-200002222−2−2−2−22222−2−2−2−200000000
χ12222222222-2-20000-2-2-200000022-2-20000−2−2−2−22222−2−2−2−2222200000000
χ13222222222-2-20000-2-2-2000000-2-22200002222−2−2−2−2−2−2−2−2222200000000
χ14222222222-2-20000-2-2-2000000-2-2220000−2−2−2−222222222−2−2−2−200000000
χ15222-2-222-2-20022−2−2000222−2−2−22i−2i00i2i2−i2−i2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700000000
χ16222-2-222-2-20022−2−2000222−2−2−22i−2i00i2i2−i2−i2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700000000
χ17222-2-222-2-20022−2−2000222−2−2−2−2i2i00−i2−i2i2i2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700000000
χ18222-2-222-2-20022−2−2000222−2−2−2−2i2i00−i2−i2i2i2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700000000
χ19222-2-222-2-200−2−222000−2−2−22222i−2i00−i2−i2i2i2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500000000
χ20222-2-222-2-200−2−222000−2−2−22222i−2i00−i2−i2i2i2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500000000
χ21222-2-222-2-200−2−222000−2−2−2222−2i2i00i2i2−i2−i2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500000000
χ22222-2-222-2-200−2−222000−2−2−2222−2i2i00i2i2−i2−i2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500000000
χ23222-2-2-2-2222222222-2-22-2-22-2-2000000000000000000000000002-20000
χ24222-2-2-2-2222222222-2-22-2-22-2-200000000000000000000000000-220000
χ25222-2-2-2-22222-2-2-2-22-2-2-222-22200000000000000000000000000002i−2i00
χ26222-2-2-2-22222-2-2-2-22-2-2-222-2220000000000000000000000000000−2i2i00
χ2722-22-2-222-2222222-2-22-22-2-22-2000000002-22-22-22-20000000000000000
χ2822-22-2-222-2222222-2-22-22-2-22-200000000-22-22-22-220000000000000000
χ2922-22-2-222-222-2-2-2-2-2-222-222-2200000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ3022-22-2-222-222-2-2-2-2-2-222-222-220000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ3122-22-2-222-2-2-2000022-200000000002i−2i2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ3222-22-2-222-2-2-2000022-200000000002i−2i2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ3322-22-2-222-2-2-2000022-20000000000−2i2i−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ3422-22-2-222-2-2-2000022-20000000000−2i2i−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ3522-2-222-22-2222222-22-2-2-22-2-220000000000000000000000002-2000000
χ3622-2-222-22-2222222-22-2-2-22-2-22000000000000000000000000-22000000
χ3722-2-222-22-222-2-2-2-2-22-222-222-20000000000000000000000000000002i−2i
χ3822-2-222-22-222-2-2-2-2-22-222-222-2000000000000000000000000000000−2i2i
χ3922-2-22-22-220022−2−2000−22−22−22002-22−2−22ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ4022-2-22-22-220022−2−2000−22−22−22002-22−2−22−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ4122-2-22-22-220022−2−2000−22−22−2200-22−222−2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ700000000
χ4222-2-22-22-220022−2−2000−22−22−2200-22−222−2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ700000000
χ4322-2-22-22-2200−2−2220002−22−22−2002-2−222−2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ4422-2-22-22-2200−2−2220002−22−22−2002-2−222−2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ4522-2-22-22-2200−2−2220002−22−22−200-222−2−22ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ500000000
χ4622-2-22-22-2200−2−2220002−22−22−200-222−2−22−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ500000000
χ4744444-4-4-4-4002222−22−2200022−22−22−22222200000000000000000000000000000000
χ4844444-4-4-4-400−22−222222000−22222222−22−2200000000000000000000000000000000
χ49444-4-4-4-444-4-40000-44400000000000000000000000000000000000000
χ5044-44-44-4-44002222−22−22000−22−22222222−2200000000000000000000000000000000
χ5144-44-44-4-4400−22−2222220002222−22−22−222200000000000000000000000000000000
χ5244-4-444-44-4-4-400004-4400000000000000000000000000000000000000
χ538-8000000042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ500000000000000000000000000000000000000000
χ548-8000000042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ500000000000000000000000000000000000000000
χ558-80000000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ700000000000000000000000000000000000000000
χ568-80000000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ700000000000000000000000000000000000000000

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