Finite Group Databasebeta

← Group #419421

Character table — Group #419421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222222222224444444444444444222222444444444444444444888888888888888822444444
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
χ51111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111
χ9111111111111111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ10111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ12111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111
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
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000-2-22200000000220000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2-22200000000-2-20000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222000022-2-200000000220000000000000000000000000000
χ21222222-2-2-2-22-2-2-2-2222-2-222-2-200002i2i−2i−2i000000000000002i2i−2i−2i2i−2i000000000000000000000000002-2
χ22222222-2-2-2-22-2-2-2-2222-2-222-2-200002i2i−2i−2i00000000000000−2i−2i2i2i2i−2i00000000000000000000000000-22
χ23222222-2-2-2-22-2-2-2-2222-2-222-2-20000−2i−2i2i2i000000000000002i2i−2i−2i−2i2i00000000000000000000000000-22
χ24222222-2-2-2-22-2-2-2-2222-2-222-2-20000−2i−2i2i2i00000000000000−2i−2i2i2i−2i2i000000000000000000000000002-2
χ25222222-2-2-2-22-2-2-2-22-2-222-2-22200002i2i−2i−2i00000000002i2i−2i−2i0000−2i2i000000000000000000002-2000000
χ26222222-2-2-2-22-2-2-2-22-2-222-2-22200002i2i−2i−2i0000000000−2i−2i2i2i0000−2i2i00000000000000000000-22000000
χ27222222-2-2-2-22-2-2-2-22-2-222-2-2220000−2i−2i2i2i00000000002i2i−2i−2i00002i−2i00000000000000000000-22000000
χ28222222-2-2-2-22-2-2-2-22-2-222-2-2220000−2i−2i2i2i0000000000−2i−2i2i2i00002i−2i000000000000000000002-2000000
χ292222-2-22-22-2-22-22-2-2000000002i2i−2i−2i2-22-20000002i−2i000000000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000
χ302222-2-22-22-2-22-22-2-2000000002i2i−2i−2i2-22-20000002i−2i0000000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000
χ312222-2-22-22-2-22-22-2-2000000002i2i−2i−2i-22-22000000−2i2i000000000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000
χ322222-2-22-22-2-22-22-2-2000000002i2i−2i−2i-22-22000000−2i2i0000000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000
χ332222-2-22-22-2-22-22-2-200000000−2i−2i2i2i2-22-2000000−2i2i000000000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000
χ342222-2-22-22-2-22-22-2-200000000−2i−2i2i2i2-22-2000000−2i2i0000000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000
χ352222-2-22-22-2-22-22-2-200000000−2i−2i2i2i-22-220000002i−2i000000000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000
χ362222-2-22-22-2-22-22-2-200000000−2i−2i2i2i-22-220000002i−2i0000000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000
χ3722-2-22-222222-2-2-2-2-22-2-2-22-2220000000000000000002i−2i2i−2i0000002i2i−2i−2i000000002-22-2000000000000
χ3822-2-22-222222-2-2-2-2-22-2-2-22-2220000000000000000002i−2i2i−2i000000−2i−2i2i2i00000000-22-22000000000000
χ3922-2-22-222222-2-2-2-2-22-2-2-22-222000000000000000000−2i2i−2i2i0000002i2i−2i−2i00000000-22-22000000000000
χ4022-2-22-222222-2-2-2-2-22-2-2-22-222000000000000000000−2i2i−2i2i000000−2i−2i2i2i000000002-22-2000000000000
χ4122-2-22-2-2-2-2-222222-2-22-2-2-2222000000000022-2-200002-2-2200000000002-22-200000000000000000000
χ4222-2-22-2-2-2-2-222222-2-22-2-2-2222000000000022-2-20000-222-20000000000-22-2200000000000000000000
χ4322-2-22-2-2-2-2-222222-2-22-2-2-22220000000000-2-22200002-2-220000000000-22-2200000000000000000000
χ4422-2-22-2-2-2-2-222222-2-22-2-2-22220000000000-2-2220000-222-200000000002-22-200000000000000000000
χ452-22-2-2222-2-22-2-222-2222-2-2-22-200000000002-22-2000000002i−2i2i−2i00000000002i−2i2i−2i0000000000000000
χ462-22-2-2222-2-22-2-222-2222-2-2-22-200000000002-22-200000000−2i2i−2i2i0000000000−2i2i−2i2i0000000000000000
χ472-22-2-2222-2-22-2-222-2222-2-2-22-20000000000-22-22000000002i−2i2i−2i0000000000−2i2i−2i2i0000000000000000
χ482-22-2-2222-2-22-2-222-2222-2-2-22-20000000000-22-2200000000−2i2i−2i2i00000000002i−2i2i−2i0000000000000000
χ492-22-2-22-2-222222-2-2-222-22-2-2-2200000000000000000000002-2-22002i−2i2i−2i0000000000002i−2i2i−2i00000000
χ502-22-2-22-2-222222-2-2-222-22-2-2-2200000000000000000000002-2-2200−2i2i−2i2i000000000000−2i2i−2i2i00000000
χ512-22-2-22-2-222222-2-2-222-22-2-2-220000000000000000000000-222-2002i−2i2i−2i000000000000−2i2i−2i2i00000000
χ522-22-2-22-2-222222-2-2-222-22-2-2-220000000000000000000000-222-200−2i2i−2i2i0000000000002i−2i2i−2i00000000
χ532-2-22-2-2-2-2222-2-22222-22-2-22-222-22-200002-20000000000000000002-2-22000000000000000000002-200
χ542-2-22-2-2-2-2222-2-22222-22-2-22-222-22-200002-2000000000000000000-222-200000000000000000000-2200
χ552-2-22-2-2-2-2222-2-22222-22-2-22-22-22-220000-220000000000000000002-2-2200000000000000000000-2200
χ562-2-22-2-2-2-2222-2-22222-22-2-22-22-22-220000-22000000000000000000-222-2000000000000000000002-200
χ572-2-22-2-2-2-2222-2-2222-22-222-22-22-22-20000-222-2-220000000000000000000000000000000000002-20000
χ582-2-22-2-2-2-2222-2-2222-22-222-22-22-22-20000-22-222-2000000000000000000000000000000000000-220000
χ592-2-22-2-2-2-2222-2-2222-22-222-22-2-22-2200002-22-2-22000000000000000000000000000000000000-220000
χ602-2-22-2-2-2-2222-2-2222-22-222-22-2-22-2200002-2-222-20000000000000000000000000000000000002-20000
χ614444-4-4-44-44-4-44-44-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ624444-4-4-44-44-4-44-44-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ6344-4-44-444444-4-4-4-4-4-4444-44-4-400000000000000000000000000000000000000000000000000000000
χ6444-4-44-4-4-4-4-444444-44-4444-4-4-400000000000000000000000000000000000000000000000000000000
χ6544-4-4-444-44-4-4-44-44400000000000000000000000000000000000000000000000022−22−2222000000000000
χ6644-4-4-444-44-4-4-44-444000000000000000000000000000000000000000000000000−222222−22000000000000
χ6744-4-4-44-44-44-44-44-44000000000000000000000000000000000000000022−22−222200000000000000000000
χ6844-4-4-44-44-44-44-44-440000000000000000000000000000000000000000−222222−2200000000000000000000
χ694-44-44-44-4-44-4-444-440000000000000000000000000000000000000000000022−22−22220000000000000000
χ704-44-44-44-4-44-4-444-4400000000000000000000000000000000000000000000−222222−220000000000000000
χ714-44-44-4-444-4-44-4-444000000000000000000000000000000000000000000000000000022−22−222200000000
χ724-44-44-4-444-4-44-4-4440000000000000000000000000000000000000000000000000000−222222−2200000000
χ734-44-4-4444-4-44-4-444-4-4-4-4444-4400000000000000000000000000000000000000000000000000000000
χ744-44-4-44-4-444444-4-4-4-4-44-4444-400000000000000000000000000000000000000000000000000000000
χ754-4-44444-4-44-44-4-44-40000000000000000000000004i−4i00000000000000000000000000000000000000
χ764-4-44444-4-44-44-4-44-4000000000000000000000000−4i4i00000000000000000000000000000000000000
χ774-4-4444-444-4-4-444-4-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ784-4-4444-444-4-4-444-4-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ794-4-44-4-444-4-4444-4-444-4-44-444-400000000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-4-4444-4-44-444-44-4-4400000000000000000000000000000000000000000000000000000000

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