Finite Group Databasebeta

← Group #418409

Character table — Group #418409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111111111111222222224444444488888888888888888888888888888888888888881616161616161616
order12222222222222224444444444444444222244444444444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ10111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ11111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ12111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ172222222222222222-2-2-2-2-2-2-2-2222222220000-2-2-2-20000-2-22200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000022220000-2-2-2-200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-222220000-2-222000022-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022-2-20000222200000000000000000000000000000000
χ212222222-2-2-2-2-2-2-2-2222-2-2-22-2200000000000000002i2i−2i−2i0000000022-2-200002i2i−2i−2i0000000000000000
χ222222222-2-2-2-2-2-2-2-2222-2-2-22-2200000000000000002i2i−2i−2i00000000-2-2220000−2i−2i2i2i0000000000000000
χ232222222-2-2-2-2-2-2-2-2222-2-2-22-220000000000000000−2i−2i2i2i0000000022-2-20000−2i−2i2i2i0000000000000000
χ242222222-2-2-2-2-2-2-2-2222-2-2-22-220000000000000000−2i−2i2i2i00000000-2-22200002i2i−2i−2i0000000000000000
χ252222-2-2-22-222-2-2-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000002-200000000i2i2−i2−i22−22−222−2−2i2i2−i2−i200000000
χ262222-2-2-22-222-2-2-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000002-200000000−i2−i2i2i2−22−22−2−222−i2−i2i2i200000000
χ272222-2-2-22-222-2-2-22-2000000002i2i−2i−2i−2i−2i2i2i00000000000000-2200000000i2i2−i2−i22−22−2−2−222−i2−i2i2i200000000
χ282222-2-2-22-222-2-2-22-2000000002i2i−2i−2i−2i−2i2i2i00000000000000-2200000000−i2−i2i2i2−22−2222−2−2i2i2−i2−i200000000
χ292222-2-2-22-222-2-2-22-200000000−2i−2i2i2i2i2i−2i−2i00000000000000-2200000000i2i2−i2−i2−22−2222−2−2−i2−i2i2i200000000
χ302222-2-2-22-222-2-2-22-200000000−2i−2i2i2i2i2i−2i−2i00000000000000-2200000000−i2−i2i2i22−22−2−2−222i2i2−i2−i200000000
χ312222-2-2-22-222-2-2-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000002-200000000i2i2−i2−i2−22−22−2−222i2i2−i2−i200000000
χ322222-2-2-22-222-2-2-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000002-200000000−i2−i2i2i22−22−222−2−2−i2−i2i2i200000000
χ3322-2-22-2-222-222-2-2-222-222-22-2-200000000000000002i−2i2i−2i00002i2i−2i−2i00002-22-200000000000000000000
χ3422-2-22-2-222-222-2-2-222-222-22-2-200000000000000002i−2i2i−2i0000−2i−2i2i2i0000-22-2200000000000000000000
χ3522-2-22-2-222-222-2-2-222-222-22-2-20000000000000000−2i2i−2i2i00002i2i−2i−2i0000-22-2200000000000000000000
χ3622-2-22-2-222-222-2-2-222-222-22-2-20000000000000000−2i2i−2i2i0000−2i−2i2i2i00002-22-200000000000000000000
χ3722-2-22-2-2-2-22-2-222222-2-2-2222-22-22-20000000000002-2-222-2000000000000000000000000002-2000000
χ3822-2-22-2-2-2-22-2-222222-2-2-2222-22-22-2000000000000-222-22-200000000000000000000000000-22000000
χ3922-2-22-2-2-2-22-2-222222-2-2-2222-2-22-220000000000002-2-22-2200000000000000000000000000-22000000
χ4022-2-22-2-2-2-22-2-222222-2-2-2222-2-22-22000000000000-222-2-22000000000000000000000000002-2000000
χ4122-2-22-2-2-2-22-2-22222-2222-2-2-222-22-2000022-2-200000000-22000000000000000000000000000000002-2
χ4222-2-22-2-2-2-22-2-22222-2222-2-2-222-22-20000-2-22200000000-2200000000000000000000000000000000-22
χ4322-2-22-2-2-2-22-2-22222-2222-2-2-22-22-22000022-2-2000000002-200000000000000000000000000000000-22
χ4422-2-22-2-2-2-22-2-22222-2222-2-2-22-22-220000-2-222000000002-2000000000000000000000000000000002-2
χ452-22-2-22-22-2-2-222-222-2-22-222-22000000002-22-200000000000000002-22-20000000000002-22-200000000
χ462-22-2-22-22-2-2-222-222-2-22-222-22000000002-22-20000000000000000-22-22000000000000-22-2200000000
χ472-22-2-22-22-2-2-222-222-2-22-222-2200000000-22-2200000000000000002-22-2000000000000-22-2200000000
χ482-22-2-22-22-2-2-222-222-2-22-222-2200000000-22-220000000000000000-22-220000000000002-22-200000000
χ492-22-2-22-2-2222-2-22-22222-22-2-2-200002-22-200002-200000000002i−2i2i−2i00000000000000000000002i−2i0000
χ502-22-2-22-2-2222-2-22-22222-22-2-2-200002-22-200002-20000000000−2i2i−2i2i0000000000000000000000−2i2i0000
χ512-22-2-22-2-2222-2-22-22222-22-2-2-20000-22-220000-2200000000002i−2i2i−2i0000000000000000000000−2i2i0000
χ522-22-2-22-2-2222-2-22-22222-22-2-2-20000-22-220000-220000000000−2i2i−2i2i00000000000000000000002i−2i0000
χ532-22-2-22-2-2222-2-22-22-2-2-22-222200002-22-20000-22000000000000002-2-22000000000000000000002-200
χ542-22-2-22-2-2222-2-22-22-2-2-22-222200002-22-20000-2200000000000000-222-200000000000000000000-2200
χ552-22-2-22-2-2222-2-22-22-2-2-22-22220000-22-2200002-2000000000000002-2-2200000000000000000000-2200
χ562-22-2-22-2-2222-2-22-22-2-2-22-22220000-22-2200002-200000000000000-222-2000000000000000000002-200
χ572-2-22-2-22-22-22-22-2222-22-2-2-222000000002-2-220000000000002-2-220000000000002-22-2000000000000
χ582-2-22-2-22-22-22-22-2222-22-2-2-222000000002-2-22000000000000-222-2000000000000-22-22000000000000
χ592-2-22-2-22-22-22-22-2222-22-2-2-22200000000-222-20000000000002-2-22000000000000-22-22000000000000
χ602-2-22-2-22-22-22-22-2222-22-2-2-22200000000-222-2000000000000-222-20000000000002-22-2000000000000
χ614444444-4-4-4-4-4-4-4-44-4-4444-44-400000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-4-4444-4-4000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ634444-4-4-4-44-4-4444-4-400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ6444-4-44-4-444-444-4-4-44-44-4-44-44400000000000000000000000000000000000000000000000000000000
χ6544-4-4-4444-4-44-444-4-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ6644-4-4-4444-4-44-444-4-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6744-4-4-444-444-44-4-44-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6844-4-4-444-444-44-4-44-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ694-44-44-4444-4-4-4-444-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ704-44-44-4444-4-4-4-444-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ714-44-44-44-4-44444-4-4-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ724-44-44-44-4-44444-4-4-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ734-44-4-44-44-4-4-444-44444-44-4-44-400000000000000000000000000000000000000000000000000000000
χ744-4-4444-4444-4-44-4-4-400000000000000000000004-40000000000000000000000000000000000000000
χ754-4-4444-4444-4-44-4-4-40000000000000000000000-440000000000000000000000000000000000000000
χ764-4-4444-4-4-4-444-444-400000000000000000000000000000000000000000000000022−22−2222000000000000
χ774-4-4444-4-4-4-444-444-4000000000000000000000000000000000000000000000000−222222−22000000000000
χ784-4-44-4-444-44-44-44-444-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ794-4-44-4-444-44-44-44-44-444-4-444-400000000000000000000000000000000000000000000000000000000
χ804-4-44-4-44-44-44-44-444-44-4444-4-400000000000000000000000000000000000000000000000000000000

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