Finite Group Databasebeta

← Group #233413

Character table — Group #233413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ911111111-1-1-1-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ1011111111-1-1-1-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ1111111111-1-1-1-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111
χ1211111111-1-1-1-111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-111-1-1-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-222-2-2-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ18222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ19222222222222-2-2-2-2-2-222-2-2-2-222-2-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222000000000000000022-2-222-2-2000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2220000000000000000-2-222-2-222000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-22222-2-222-2-2-2-22222-2-2000000000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-22222-2-222-2-2-2-22222-2-20000000000000000-2-22222-2-2000000000000000000000000
χ29222-22-2-2-222-2-22-222-2-200002-20000000022−2−222−2−222−2−222−2−22−22−22−22−2002-2002-20000000000000000
χ30222-22-2-2-222-2-22-222-2-200002-20000000022−2−222−2−222−2−222−2−2−22−22−22−2200-2200-220000000000000000
χ31222-22-2-2-222-2-22-222-2-200002-200000000−2−222−2−222−2−222−2−2222−22−22−22−200-2200-220000000000000000
χ32222-22-2-2-222-2-22-222-2-200002-200000000−2−222−2−222−2−222−2−222−22−22−22−22002-2002-20000000000000000
χ33222-22-2-2-222-2-2-22-2-2220000-220000000022−2−2−2−22222−2−2−2−2222−2−222−2−222-2002-2000000000000000000
χ34222-22-2-2-222-2-2-22-2-2220000-220000000022−2−2−2−22222−2−2−2−222−222−2−222−2-2200-22000000000000000000
χ35222-22-2-2-222-2-2-22-2-2220000-2200000000−2−22222−2−2−2−22222−2−22−2−222−2−22-2200-22000000000000000000
χ36222-22-2-2-222-2-2-22-2-2220000-2200000000−2−22222−2−2−2−22222−2−2−222−2−222−22-2002-2000000000000000000
χ37222-22-2-2-2-2-2222-2-2-22200002-20000000022−2−222−2−2−2−222−2−2222−22−2−22−22002-200-220000000000000000
χ38222-22-2-2-2-2-2222-2-2-22200002-20000000022−2−222−2−2−2−222−2−222−22−222−22−200-22002-20000000000000000
χ39222-22-2-2-2-2-2222-2-2-22200002-200000000−2−222−2−22222−2−222−2−22−22−2−22−2200-22002-20000000000000000
χ40222-22-2-2-2-2-2222-2-2-22200002-200000000−2−222−2−22222−2−222−2−2−22−222−22−2002-200-220000000000000000
χ41222-22-2-2-2-2-222-2222-2-20000-220000000022−2−2−2−222−2−22222−2−22−2−22−222−22-200-22000000000000000000
χ42222-22-2-2-2-2-222-2222-2-20000-220000000022−2−2−2−222−2−22222−2−2−222−22−2−22-22002-2000000000000000000
χ43222-22-2-2-2-2-222-2222-2-20000-2200000000−2−22222−2−222−2−2−2−2222−2−22−222−2-22002-2000000000000000000
χ44222-22-2-2-2-2-222-2222-2-20000-2200000000−2−22222−2−222−2−2−2−222−222−22−2−222-200-22000000000000000000
χ452-2-2-22-2222-22-2222-22-22222-2-2-2-2-2-22-22-2000000000000000000000000000000002i−2i2i−2i000000000000
χ462-2-2-22-2222-22-2222-22-22222-2-2-2-2-2-22-22-200000000000000000000000000000000−2i2i−2i2i000000000000
χ472-2-2-22-2222-22-2222-22-2-2-2-2-2-2-22222-22-22000000000000000000000000000000000000002-20000002-2
χ482-2-2-22-2222-22-2222-22-2-2-2-2-2-2-22222-22-2200000000000000000000000000000000000000-22000000-22
χ492-2-2-22-2222-22-2-2-2-22-2222-2-222-2-2222-2-2200000000000000000000000000000000000000002-22-20000
χ502-2-2-22-2222-22-2-2-2-22-2222-2-222-2-2222-2-220000000000000000000000000000000000000000-22-220000
χ512-2-2-22-2222-22-2-2-2-22-22-2-2222222-2-2-222-20000000000000000000000000000000000002-20000002-200
χ522-2-2-22-2222-22-2-2-2-22-22-2-2222222-2-2-222-2000000000000000000000000000000000000-22000000-2200
χ532-2-2-22-222-22-2222-22-222222-2-2-2-2-2-2-22-22000000000000000000000000000000002i−2i−2i2i000000000000
χ542-2-2-22-222-22-2222-22-222222-2-2-2-2-2-2-22-2200000000000000000000000000000000−2i2i2i−2i000000000000
χ552-2-2-22-222-22-2222-22-22-2-2-2-2-2-222222-22-2000000000000000000000000000000000000002-2000000-22
χ562-2-2-22-222-22-2222-22-22-2-2-2-2-2-222222-22-200000000000000000000000000000000000000-220000002-2
χ572-2-2-22-222-22-22-2-22-22-222-2-222-2-222-222-200000000000000000000000000000000000000002-2-220000
χ582-2-2-22-222-22-22-2-22-22-222-2-222-2-222-222-20000000000000000000000000000000000000000-222-20000
χ592-2-2-22-222-22-22-2-22-22-2-2-2222222-2-22-2-220000000000000000000000000000000000002-2000000-2200
χ602-2-2-22-222-22-22-2-22-22-2-2-2222222-2-22-2-22000000000000000000000000000000000000-220000002-200
χ6144-44-4-44-400000000004-400004-400000000004-44-40000000000000000000000000000000000000000
χ6244-44-4-44-400000000004-400004-40000000000-44-440000000000000000000000000000000000000000
χ6344-44-4-44-40000000000-440000-440000004-44-400000000000000000000000000000000000000000000
χ6444-44-4-44-40000000000-440000-44000000-44-4400000000000000000000000000000000000000000000
χ6544-4-4-44-440000000000004-400004-4000022−22−222222−22−22220000000000000000000000000000000000000000
χ6644-4-4-44-440000000000004-400004-40000−222222−22−222222−220000000000000000000000000000000000000000
χ6744-4-4-44-44000000000000-440000-44000022−22−2222−222222−220000000000000000000000000000000000000000
χ6844-4-4-44-44000000000000-440000-440000−222222−2222−22−22220000000000000000000000000000000000000000
χ694-444-4-4-440000000000004-40000-440000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000
χ704-444-4-4-440000000000004-40000-44000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000
χ714-444-4-4-44000000000000-4400004-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000
χ724-444-4-4-44000000000000-4400004-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000
χ734-44-4-444-400000000004-40000-440000000000000000004i−4i−4i4i00000000000000000000000000000000
χ744-44-4-444-400000000004-40000-44000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ754-44-4-444-40000000000-4400004-4000000000000004i−4i−4i4i000000000000000000000000000000000000
χ764-44-4-444-40000000000-4400004-400000000000000−4i4i4i−4i000000000000000000000000000000000000
χ774-4-4444-4-44-4-444-44-4-440000-4400000000000000000000000000000000000000000000000000000000
χ784-4-4444-4-44-4-44-44-444-400004-400000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-4-444-44-4-444-40000-4400000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-444-4-444-4-4400004-400000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).