Finite Group Databasebeta

← Group #503270

Character table — Group #503270

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222222222222244444444444448888888888888888888888161616161616161632323232
order122224444881616161622448881616161616164444888888161616161616161616161616222244442444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ6111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ7111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ911111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11-1
χ1011111111111-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11
χ1111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-11-11-11-1-11-11
χ1211111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11-11-111-11-1
χ1311111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-11
χ1411111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-111-1-111-1-111-1
χ1511111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11-1-111-1-11-111-1
χ1611111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-111-1-111-11-1-11
χ17222222222-2-200002222-2-2-20000002222-2-2-2-2-2-2000000000000000000000000
χ18222222222-2-200002222-2-2-2000000-2-2-2-22222-2-2000000000000000000000000
χ19222222222-2-20000-2-2-2-2-2-2-200000022-2-2-2-22222000000000000000000000000
χ20222222222-2-20000-2-2-2-2-2-2-2000000-2-22222-2-222000000000000000000000000
χ2122222-2-2-2-20022−2−22-22-2000222−2−2−22-22-200000022−2−222−2−222−2−2000000000000
χ2222222-2-2-2-20022−2−22-22-2000222−2−2−2-22-2200000022−2−2−2−222−2−222000000000000
χ2322222-2-2-2-20022−2−2-22-22000222−2−2−22-2-22000000−2−22222−2−2−2−222000000000000
χ2422222-2-2-2-20022−2−2-22-22000222−2−2−2-222-2000000−2−222−2−22222−2−2000000000000
χ2522222-2-2-2-200−2−2222-22-2000−2−2−22222-22-2000000−2−222−2−222−2−222000000000000
χ2622222-2-2-2-200−2−2222-22-2000−2−2−2222-22-22000000−2−22222−2−222−2−2000000000000
χ2722222-2-2-2-200−2−222-22-22000−2−2−22222-2-2200000022−2−2−2−22222−2−2000000000000
χ2822222-2-2-2-200−2−222-22-22000−2−2−2222-222-200000022−2−222−2−2−2−222000000000000
χ29222-2-2-22-222222220000-22-22-2-22-2-200000000000000000000002-200-22000000
χ30222-2-2-22-222222220000-22-22-2-22-2-20000000000000000000000-22002-2000000
χ31222-2-2-22-2222-2-2-2-20000-22-2-222-22200000000000000000000002200-2-2000000
χ32222-2-2-22-2222-2-2-2-20000-22-2-222-2220000000000000000000000-2-20022000000
χ3322-22-2-2-2222222220000-2-22-22-2-22-20000000000000000000000002-200-220000
χ3422-22-2-2-2222222220000-2-22-22-2-22-2000000000000000000000000-22002-20000
χ3522-22-2-2-22222-2-2-2-20000-2-222-222-220000000000000000000000002200-2-20000
χ3622-22-2-2-22222-2-2-2-20000-2-222-222-22000000000000000000000000-2-200220000
χ3722-2-222-2-222222222-2-222-2-2-2-22-2-22000000002-22-22-200000000000000000000
χ3822-2-222-2-22222222-222-22-2-2-2-22-2-2200000000-22-22-2200000000000000000000
χ3922-2-222-2-2222-2-2-2-22-2-222-2-222-222-2000000002-2-22-2200000000000000000000
χ4022-2-222-2-2222-2-2-2-2-222-22-2-222-222-200000000-222-22-200000000000000000000
χ4122-2-222-2-22-2-200002-2-22-22200000000000000-2200002-22-22-22-2000000000000
χ4222-2-222-2-22-2-200002-2-22-22200000000000000-220000-22-22-22-22000000000000
χ4322-2-222-2-22-2-20000-222-2-222000000000000002-200002-22-2-22-22000000000000
χ4422-2-222-2-22-2-20000-222-2-222000000000000002-20000-22-222-22-2000000000000
χ4522-2-22-222-20022−2−222-2-2000−2−2222−200002-22-2002−2−222−2−222−2−22000000000000
χ4622-2-22-222-20022−2−222-2-2000−2−2222−20000-22-22002−2−22−222−2−222−2000000000000
χ4722-2-22-222-20022−2−2-2-222000−2−2222−200002-2-2200−222−22−2−22−222−2000000000000
χ4822-2-22-222-20022−2−2-2-222000−2−2222−20000-222-200−222−2−222−22−2−22000000000000
χ4922-2-22-222-200−2−22222-2-200022−2−2−2200002-22-200−222−2−222−2−222−2000000000000
χ5022-2-22-222-200−2−22222-2-200022−2−2−220000-22-2200−222−22−2−222−2−22000000000000
χ5122-2-22-222-200−2−222-2-22200022−2−2−2200002-2-22002−2−22−222−22−2−22000000000000
χ5222-2-22-222-200−2−222-2-22200022−2−2−220000-222-2002−2−222−2−22−222−2000000000000
χ53444-4-44-44-4002222−22−22000000022−22−22−2222220000000000000000000000000000000000
χ54444-4-44-44-400−22−2222220000000−22222222−22−220000000000000000000000000000000000
χ55444-4-4-44-44-4-4000000004-440000000000000000000000000000000000000000
χ5644-44-444-4-4002222−22−220000000−2222−2222−22220000000000000000000000000000000000
χ5744-44-444-4-400−22−222222000000022−2222−2222−220000000000000000000000000000000000
χ5844-44-4-4-444-4-40000000044-40000000000000000000000000000000000000000
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).