Finite Group Databasebeta

← Group #427804

Character table — Group #427804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222222222224444444444444444222222444444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ41111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ9111111111111111111111111-1-1-1-11111-1-1111111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ14111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-222222222220000-2-2-2-200000000-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000022-2-200000000220000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000-2-22200000000220000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000222200000000-2-20000000000000000000000000000
χ21222222-2-2-2-2-2-2-2-22222-2-222-2-22i2i−2i−2i0000000000002i−2i2i2i−2i−2i0000000000000000000000000000002-200
χ22222222-2-2-2-2-2-2-2-22222-2-222-2-22i2i−2i−2i0000000000002i−2i−2i−2i2i2i000000000000000000000000000000-2200
χ23222222-2-2-2-2-2-2-2-22222-2-222-2-2−2i−2i2i2i000000000000−2i2i2i2i−2i−2i000000000000000000000000000000-2200
χ24222222-2-2-2-2-2-2-2-22222-2-222-2-2−2i−2i2i2i000000000000−2i2i−2i−2i2i2i0000000000000000000000000000002-200
χ25222222-2-2-2-2-2-2-2-222-2-222-2-2222i2i−2i−2i00000022-2-200−2i2i0000000000000000000000000000002i−2i000000
χ26222222-2-2-2-2-2-2-2-222-2-222-2-2222i2i−2i−2i000000-2-22200−2i2i000000000000000000000000000000−2i2i000000
χ27222222-2-2-2-2-2-2-2-222-2-222-2-222−2i−2i2i2i00000022-2-2002i−2i000000000000000000000000000000−2i2i000000
χ28222222-2-2-2-2-2-2-2-222-2-222-2-222−2i−2i2i2i000000-2-222002i−2i0000000000000000000000000000002i−2i000000
χ29222-2-2-2222-2-2-22-22-2000000002i−2i2i−2i2i2i−2i−2i2-2000000000000000000000022−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000
χ30222-2-2-2222-2-2-22-22-2000000002i−2i2i−2i2i2i−2i−2i2-20000000000000000000000−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000
χ31222-2-2-2222-2-2-22-22-2000000002i−2i2i−2i−2i−2i2i2i-22000000000000000000000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000
χ32222-2-2-2222-2-2-22-22-2000000002i−2i2i−2i−2i−2i2i2i-220000000000000000000000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000
χ33222-2-2-2222-2-2-22-22-200000000−2i2i−2i2i2i2i−2i−2i-22000000000000000000000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000
χ34222-2-2-2222-2-2-22-22-200000000−2i2i−2i2i2i2i−2i−2i-220000000000000000000000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000
χ35222-2-2-2222-2-2-22-22-200000000−2i2i−2i2i−2i−2i2i2i2-2000000000000000000000022−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000
χ36222-2-2-2222-2-2-22-22-200000000−2i2i−2i2i−2i−2i2i2i2-20000000000000000000000−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000
χ3722-22-2-222-2-222-2-2-222-22-22-22-200002i−2i2i−2i0000002i−2i00000000000022-2-200000000000000000000002i−2i
χ3822-22-2-222-2-222-2-2-222-22-22-22-200002i−2i2i−2i0000002i−2i000000000000-2-2220000000000000000000000−2i2i
χ3922-22-2-222-2-222-2-2-222-22-22-22-20000−2i2i−2i2i000000−2i2i00000000000022-2-20000000000000000000000−2i2i
χ4022-22-2-222-2-222-2-2-222-22-22-22-20000−2i2i−2i2i000000−2i2i000000000000-2-22200000000000000000000002i−2i
χ4122-22-2-222-2-222-2-2-22-22-22-22-2200002i−2i2i−2i000000−2i2i0000002i2i−2i−2i0000000000000000000000002-20000
χ4222-22-2-222-2-222-2-2-22-22-22-22-2200002i−2i2i−2i000000−2i2i000000−2i−2i2i2i000000000000000000000000-220000
χ4322-22-2-222-2-222-2-2-22-22-22-22-220000−2i2i−2i2i0000002i−2i0000002i2i−2i−2i000000000000000000000000-220000
χ4422-22-2-222-2-222-2-2-22-22-22-22-220000−2i2i−2i2i0000002i−2i000000−2i−2i2i2i0000000000000000000000002-20000
χ452-22-22-22-22-22-2-22-22222-2-2-2-220000000000000000002-22-22i−2i2i−2i000000000000002i−2i2i−2i000000000000
χ462-22-22-22-22-22-2-22-22222-2-2-2-220000000000000000002-22-2−2i2i−2i2i00000000000000−2i2i−2i2i000000000000
χ472-22-22-22-22-22-2-22-22222-2-2-2-22000000000000000000-22-222i−2i2i−2i00000000000000−2i2i−2i2i000000000000
χ482-22-22-22-22-22-2-22-22222-2-2-2-22000000000000000000-22-22−2i2i−2i2i000000000000002i−2i2i−2i000000000000
χ492-22-22-2-22-22-222-2-2222-22-2-22-20000000000000000002i−2i−2i2i0000002-22-20000000000002i−2i2i−2i00000000
χ502-22-22-2-22-22-222-2-2222-22-2-22-20000000000000000002i−2i−2i2i000000-22-22000000000000−2i2i−2i2i00000000
χ512-22-22-2-22-22-222-2-2222-22-2-22-2000000000000000000−2i2i2i−2i0000002-22-2000000000000−2i2i−2i2i00000000
χ522-22-22-2-22-22-222-2-2222-22-2-22-2000000000000000000−2i2i2i−2i000000-22-220000000000002i−2i2i−2i00000000
χ532-2-2-2-222-2-222-22-222-22-2-22-22200000000002-22-2000000002-2-220000002-22-200000000000000000000
χ542-2-2-2-222-2-222-22-222-22-2-22-22200000000002-22-200000000-222-2000000-22-2200000000000000000000
χ552-2-2-2-222-2-222-22-222-22-2-22-2220000000000-22-22000000002-2-22000000-22-2200000000000000000000
χ562-2-2-2-222-2-222-22-222-22-2-22-2220000000000-22-2200000000-222-20000002-22-200000000000000000000
χ572-2-2-2-22-222-2-22-22222-2-2-2-222200000000002-2-22000000000000002-2-2200002-22-20000000000000000
χ582-2-2-2-22-222-2-22-22222-2-2-2-222200000000002-2-2200000000000000-222-20000-22-220000000000000000
χ592-2-2-2-22-222-2-22-22222-2-2-2-22220000000000-222-2000000000000002-2-220000-22-220000000000000000
χ602-2-2-2-22-222-2-22-22222-2-2-2-22220000000000-222-200000000000000-222-200002-22-20000000000000000
χ61444-4-4-4-4-4-4444-444-4000000004-4-440000000000000000000000000000000000000000000000000000
χ62444-4-4-4-4-4-4444-444-400000000-444-40000000000000000000000000000000000000000000000000000
χ6344-44-4-4-4-444-4-444-444-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ6444-44-4-4-4-444-4-444-44-444-4-444-400000000000000000000000000000000000000000000000000000000
χ6544-4-44444-44-4-4-44-4-40000000000004-4-44000000000000000000000000000000000000000000000000
χ6644-4-44444-44-4-4-44-4-4000000000000-444-4000000000000000000000000000000000000000000000000
χ6744-4-444-4-44-4444-4-4-400000000000000000000000000000000004i−4i0000000000000000000000000000
χ6844-4-444-4-44-4444-4-4-40000000000000000000000000000000000−4i4i0000000000000000000000000000
χ694-444-444-444-44-4-4-4-400000000000000000000000000000000000000000000000022−22−2222000000000000
χ704-444-444-444-44-4-4-4-4000000000000000000000000000000000000000000000000−222222−22000000000000
χ714-444-44-44-4-44-444-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ724-444-44-44-4-44-444-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ734-44-44-44-44-44-4-44-44-4-4-44444-400000000000000000000000000000000000000000000000000000000
χ744-44-44-4-44-44-444-4-44-4-44-444-4400000000000000000000000000000000000000000000000000000000
χ754-4-444-44-4-4-4-44444-4000000000000000000000000000000000000000022−22−222200000000000000000000
χ764-4-444-44-4-4-4-44444-40000000000000000000000000000000000000000−222222−2200000000000000000000
χ774-4-444-4-44444-4-4-44-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ784-4-444-4-44444-4-4-44-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ794-4-4-4-444-4-444-44-4444-444-44-4-400000000000000000000000000000000000000000000000000000000
χ804-4-4-4-44-444-4-44-4444-44444-4-4-400000000000000000000000000000000000000000000000000000000

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