Finite Group Databasebeta

← Group #501702

Character table — Group #501702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222222222222244444444444448888888888888888888888161616161616161632323232
order122224444881616161622448881616161616162444888888161616161616161616161616888888884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111-1-1-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ1011111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ1111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ1211111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ1311111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-111-1
χ1511111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-200002222-2-2-200000022-2-2-2-2-2-222000000000000000000000000
χ18222222222-2-200002222-2-2-2000000-2-222-2-222-2-2000000000000000000000000
χ19222222222-2-20000-2-2-2-2-2-2-2000000222222-2-2-2-2000000000000000000000000
χ20222222222-2-20000-2-2-2-2-2-2-2000000-2-2-2-2222222000000000000000000000000
χ21222-2-222-2-222222200002-2-222-2-2-2-2000000000000000000000000002i−2i2i−2i0000
χ22222-2-222-2-222222200002-2-222-2-2-2-200000000000000000000000000−2i2i−2i2i0000
χ23222-2-222-2-222-2-2-2-200002-2-2-2-22222000000000000000000000000002i−2i−2i2i0000
χ24222-2-222-2-222-2-2-2-200002-2-2-2-2222200000000000000000000000000−2i2i2i−2i0000
χ25222-2-2-2-2220022−2−22-22-20002−222−2−22-20000002-222−2−222−2−222−2−2000000000000
χ26222-2-2-2-2220022−2−22-22-20002−222−2−2-22000000-2222−2−2−2−222−2−222000000000000
χ27222-2-2-2-2220022−2−2-22-220002−222−2−22-2000000-22−2−22222−2−2−2−222000000000000
χ28222-2-2-2-2220022−2−2-22-220002−222−2−2-220000002-2−2−222−2−22222−2−2000000000000
χ29222-2-2-2-22200−2−2222-22-2000−22−2−2222-20000002-2−2−222−2−222−2−222000000000000
χ30222-2-2-2-22200−2−2222-22-2000−22−2−222-22000000-22−2−22222−2−222−2−2000000000000
χ31222-2-2-2-22200−2−222-22-22000−22−2−2222-2000000-2222−2−2−2−22222−2−2000000000000
χ32222-2-2-2-22200−2−222-22-22000−22−2−222-220000002-222−2−222−2−2−2−222000000000000
χ3322-22-22-22-20022−2−222-2-2000−222−22−2002i−2i002i−2i002−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ3422-22-22-22-20022−2−222-2-2000−222−22−200−2i2i00−2i2i002−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ3522-22-22-22-20022−2−2-2-222000−222−22−2002i−2i00−2i2i00−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ3622-22-22-22-20022−2−2-2-222000−222−22−200−2i2i002i−2i00−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ3722-22-22-22-200−2−22222-2-20002−2−22−22002i−2i002i−2i00−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ3822-22-22-22-200−2−22222-2-20002−2−22−2200−2i2i00−2i2i00−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ3922-22-22-22-200−2−222-2-2220002−2−22−22002i−2i00−2i2i002−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ4022-22-22-22-200−2−222-2-2220002−2−22−2200−2i2i002i−2i002−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ4122-22-2-22-222222220000-22-2-2-2-222-200000000000000000000002-22-200000000
χ4222-22-2-22-222222220000-22-2-2-2-222-20000000000000000000000-22-2200000000
χ4322-22-2-22-2222-2-2-2-20000-22-2222-2-2200000000000000000000002-2-2200000000
χ4422-22-2-22-2222-2-2-2-20000-22-2222-2-220000000000000000000000-222-200000000
χ4522-2-22-222-22222222-2-22-2-22-2-22-2-2200002-200002-2-2200000000000000000000
χ4622-2-22-222-2222222-222-2-2-22-2-22-2-220000-220000-222-200000000000000000000
χ4722-2-22-222-222-2-2-2-22-2-22-2-2222-222-200002-20000-222-200000000000000000000
χ4822-2-22-222-222-2-2-2-2-222-2-2-2222-222-20000-2200002-2-2200000000000000000000
χ4922-2-22-222-2-2-200002-2-2222-20000000000-22000000002i−2i−2i2i2i−2i−2i2i000000000000
χ5022-2-22-222-2-2-200002-2-2222-20000000000-2200000000−2i2i2i−2i−2i2i2i−2i000000000000
χ5122-2-22-222-2-2-20000-222-222-200000000002-2000000002i−2i−2i2i−2i2i2i−2i000000000000
χ5222-2-22-222-2-2-20000-222-222-200000000002-200000000−2i2i2i−2i2i−2i−2i2i000000000000
χ5344444-4-4-4-4002222−22−22000000022−22−22−2222220000000000000000000000000000000000
χ5444444-4-4-4-400−22−2222220000000−22222222−22−220000000000000000000000000000000000
χ55444-4-444-4-4-4-400000000-4440000000000000000000000000000000000000000
χ5644-44-4-44-44-4-4000000004-440000000000000000000000000000000000000000
χ5744-4-444-4-44002222−22−220000000−2222−2222−22220000000000000000000000000000000000
χ5844-4-444-4-4400−22−222222000000022−2222−2222−220000000000000000000000000000000000
χ598-8000000042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ500000000000000000000000000000000000000000000000
χ608-8000000042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ500000000000000000000000000000000000000000000000
χ618-80000000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ700000000000000000000000000000000000000000000000
χ628-80000000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ700000000000000000000000000000000000000000000000

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