Finite Group Databasebeta

← Group #417444

Character table — Group #417444

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222222222224444444422224444222222444444444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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
χ51111111111111111111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111
χ9111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ10111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ11111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ12111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-222222222-2-2000022-2-200000000-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2220000-2-22200000000-2-20000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000-2-22200000000220000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222000022-2-200000000220000000000000000000000000000
χ21222222-2-2-2-2-22-22-2-20000000022-2-22i2i−2i−2i0000002i−2i0000000000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ22222222-2-2-2-2-22-22-2-20000000022-2-22i2i−2i−2i0000002i−2i0000000000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ23222222-2-2-2-2-22-22-2-20000000022-2-2−2i−2i2i2i000000−2i2i0000000000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ24222222-2-2-2-2-22-22-2-20000000022-2-2−2i−2i2i2i000000−2i2i0000000000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ25222222-2-2-2-2-22-22-2-200000000-2-2222i2i−2i−2i000000−2i2i0000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ26222222-2-2-2-2-22-22-2-200000000-2-2222i2i−2i−2i000000−2i2i0000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ27222222-2-2-2-2-22-22-2-200000000-2-222−2i−2i2i2i0000002i−2i0000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ28222222-2-2-2-2-22-22-2-200000000-2-222−2i−2i2i2i0000002i−2i0000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ292222-2-222-2-2-2-22-2-22222-22-2-2-200000000000000000000002i2i−2i−2i0022-2-20000000000002i−2i2i−2i00000000
χ302222-2-222-2-2-2-22-2-22222-22-2-2-200000000000000000000002i2i−2i−2i00-2-222000000000000−2i2i−2i2i00000000
χ312222-2-222-2-2-2-22-2-22222-22-2-2-20000000000000000000000−2i−2i2i2i0022-2-2000000000000−2i2i−2i2i00000000
χ322222-2-222-2-2-2-22-2-22222-22-2-2-20000000000000000000000−2i−2i2i2i00-2-2220000000000002i−2i2i−2i00000000
χ3322-2-222-2-22-2-2-22-2222-2-2-2222-200000000000000000022-2-20000002-22-2000000002-22-2000000000000
χ3422-2-222-2-22-2-2-22-2222-2-2-2222-200000000000000000022-2-2000000-22-2200000000-22-22000000000000
χ3522-2-222-2-22-2-2-22-2222-2-2-2222-2000000000000000000-2-2220000002-22-200000000-22-22000000000000
χ3622-2-222-2-22-2-2-22-2222-2-2-2222-2000000000000000000-2-222000000-22-22000000002-22-2000000000000
χ3722-2-2-2-2-2-2-222222-222-2-222-2-222-22-200000000000000000000002-22-2-22000000000000000000002-200
χ3822-2-2-2-2-2-2-222222-222-2-222-2-222-22-200000000000000000000002-2-222-200000000000000000000-2200
χ3922-2-2-2-2-2-2-222222-222-2-222-2-22-22-220000000000000000000000-222-2-2200000000000000000000-2200
χ4022-2-2-2-2-2-2-222222-222-2-222-2-22-22-220000000000000000000000-22-222-2000000000000000000002-200
χ4122-2-2-2-2-2-2-222222-22-222-2-222-22-22-200000022-2-2000000000000-2200000000000000000000002-20000
χ4222-2-2-2-2-2-2-222222-22-222-2-222-22-22-2000000-2-222000000000000-220000000000000000000000-220000
χ4322-2-2-2-2-2-2-222222-22-222-2-222-2-22-2200000022-2-20000000000002-20000000000000000000000-220000
χ4422-2-2-2-2-2-2-222222-22-222-2-222-2-22-22000000-2-2220000000000002-200000000000000000000002-20000
χ452-22-22-22-222-22-2-2-2222-22-22-2-200000000002-22-2000000002i−2i2i−2i00000000002i−2i2i−2i0000000000000000
χ462-22-22-22-222-22-2-2-2222-22-22-2-200000000002-22-200000000−2i2i−2i2i0000000000−2i2i−2i2i0000000000000000
χ472-22-22-22-222-22-2-2-2222-22-22-2-20000000000-22-22000000002i−2i2i−2i0000000000−2i2i−2i2i0000000000000000
χ482-22-22-22-222-22-2-2-2222-22-22-2-20000000000-22-2200000000−2i2i−2i2i00000000002i−2i2i−2i0000000000000000
χ492-22-2-222-2-2-22-2-222222-2-2-2-22200002-22-22-20000000000002-2-2200000000000000000000000000002-2
χ502-22-2-222-2-2-22-2-222222-2-2-2-22200002-22-22-2000000000000-222-20000000000000000000000000000-22
χ512-22-2-222-2-2-22-2-222222-2-2-2-2220000-22-22-220000000000002-2-220000000000000000000000000000-22
χ522-22-2-222-2-2-22-2-222222-2-2-2-2220000-22-22-22000000000000-222-200000000000000000000000000002-2
χ532-22-2-222-2-2-22-2-2222-2-22222-2-200002-22-2-22000000002-22-2000000000000000000000000002-2000000
χ542-22-2-222-2-2-22-2-2222-2-22222-2-200002-22-2-2200000000-22-2200000000000000000000000000-22000000
χ552-22-2-222-2-2-22-2-2222-2-22222-2-20000-22-222-2000000002-22-200000000000000000000000000-22000000
χ562-22-2-222-2-2-22-2-2222-2-22222-2-20000-22-222-200000000-22-22000000000000000000000000002-2000000
χ572-2-22-22-22-22-22-2-222-22-2-222-2200000000002-2-2200002-2-2200000000002-22-200000000000000000000
χ582-2-22-22-22-22-22-2-222-22-2-222-2200000000002-2-220000-222-20000000000-22-2200000000000000000000
χ592-2-22-22-22-22-22-2-222-22-2-222-220000000000-222-200002-2-220000000000-22-2200000000000000000000
χ602-2-22-22-22-22-22-2-222-22-2-222-220000000000-222-20000-222-200000000002-22-200000000000000000000
χ614444-4-444-4-4-4-44-4-44-4-4-44-444400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4444-4-4-44-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ634444-4-4-4-4444-4-4-44-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ6444-4-44444-444-4-4-4-4-400000000000000000000000000000000000000000000000022−22−2222000000000000
χ6544-4-44444-444-4-4-4-4-4000000000000000000000000000000000000000000000000−222222−22000000000000
χ6644-4-444-4-44-4-4-44-444-4444-4-4-4400000000000000000000000000000000000000000000000000000000
χ6744-4-4-4-4444-4-44-444-4000000004-4-440000000000000000000000000000000000000000000000000000
χ6844-4-4-4-4444-4-44-444-400000000-444-40000000000000000000000000000000000000000000000000000
χ694-44-44-44-444-44-4-4-44-4-44-44-44400000000000000000000000000000000000000000000000000000000
χ704-44-44-4-44-4-4444-44-40000000000000000000000000000000000000000000022−22−22220000000000000000
χ714-44-44-4-44-4-4444-44-400000000000000000000000000000000000000000000−222222−220000000000000000
χ724-44-4-44-4444-4-444-4-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ734-44-4-44-4444-4-444-4-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ744-4-444-44-4-44-4-4444-40000000000000000000000004-400000000000000000000000000000000000000
χ754-4-444-44-4-44-4-4444-4000000000000000000000000-4400000000000000000000000000000000000000
χ764-4-444-4-444-44-4-44-444-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ774-4-444-4-444-44-4-44-44-44-444-44-400000000000000000000000000000000000000000000000000000000
χ784-4-44-444-44-4444-4-4-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ794-4-44-444-44-4444-4-4-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ804-4-44-44-44-44-44-4-4444-444-4-44-400000000000000000000000000000000000000000000000000000000

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