Finite Group Databasebeta

← Group #268408

Character table — Group #268408

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444222444444444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-1-1-1-1-1
χ7111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-111111111-1-1-1-111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11111-1
χ1011111111-1-1-1-111111111-1-1-1-111-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1111-11
χ1111111111-1-1-1-111111111-1-1-1-111-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-11
χ1211111111-1-1-1-111111111-1-1-1-111-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ1411111111-1-1-1-111111111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11
χ1511111111-1-1-1-111111111-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111-11
χ1611111111-1-1-1-111111111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1111-1
χ1722222222222222-2-222-2-222-2-2-2-2-2000022220000000000000000000000000000-20-200000
χ1822222222222222-2-222-2-222-2-2-2-2-20000-2-2-2-2000000000000000000000000000020200000
χ19222222222222-2-222-2-222-2-222-2-2-22222000000000000000000000000000000000-20-20000
χ20222222222222-2-222-2-222-2-222-2-2-2-2-2-2-20000000000000000000000000000000002020000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000000022-2-200000000000000000000000000002-200
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-222200000000-2-2220000000000000000000000000000-2200
χ2322222222-2-2-2-222-2-222-2-2-2-222-2-22000022-2-20000000000000000000000000000-20200000
χ2422222222-2-2-2-222-2-222-2-2-2-222-2-220000-2-222000000000000000000000000000020-200000
χ2522222222-2-2-2-2-2-222-2-22222-2-2-2-2222-2-200000000000000000000000000000000020-20000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-22-2-222000000000000000000000000000000000-2020000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000022-2-20000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000-2-22200000000000000000000000000002-200
χ2922-22-2-22-22i2i−2i−2i002-2002-2002i−2i0002-22i−2i00000000i2i2−i2−i222−2−200000000i2i2−i2−i222−2−200000000
χ3022-22-2-22-22i2i−2i−2i002-2002-2002i−2i0002-22i−2i00000000−i2−i2i2i2−2−22200000000−i2−i2i2i2−2−22200000000
χ3122-22-2-22-22i2i−2i−2i002-2002-2002i−2i000-22−2i2i00000000i2i2−i2−i222−2−200000000−i2−i2i2i2−2−22200000000
χ3222-22-2-22-22i2i−2i−2i002-2002-2002i−2i000-22−2i2i00000000−i2−i2i2i2−2−22200000000i2i2−i2−i222−2−200000000
χ3322-22-2-22-2−2i−2i2i2i002-2002-200−2i2i0002-2−2i2i00000000i2i2−i2−i2−2−22200000000i2i2−i2−i2−2−22200000000
χ3422-22-2-22-2−2i−2i2i2i002-2002-200−2i2i0002-2−2i2i00000000−i2−i2i2i222−2−200000000−i2−i2i2i222−2−200000000
χ3522-22-2-22-2−2i−2i2i2i002-2002-200−2i2i000-222i−2i00000000i2i2−i2−i2−2−22200000000−i2−i2i2i222−2−200000000
χ3622-22-2-22-2−2i−2i2i2i002-2002-200−2i2i000-222i−2i00000000−i2−i2i2i222−2−200000000i2i2−i2−i2−2−22200000000
χ3722-2-22-2-222i−2i2i−2i2-2002-2002i−2i0000000002i−2i2-200000000000022−2−2i2i2−i2−i2i2−i2i2−i22−22−200000000
χ3822-2-22-2-222i−2i2i−2i2-2002-2002i−2i0000000002i−2i2-2000000000000−2−222−i2−i2i2i2−i2i2−i2i2−22−2200000000
χ3922-2-22-2-222i−2i2i−2i2-2002-2002i−2i000000000−2i2i-2200000000000022−2−2i2i2−i2−i2−i2i2−i2i2−22−2200000000
χ4022-2-22-2-222i−2i2i−2i2-2002-2002i−2i000000000−2i2i-22000000000000−2−222−i2−i2i2i2i2−i2i2−i22−22−200000000
χ4122-2-22-2-22−2i2i−2i2i2-2002-200−2i2i0000000002i−2i-2200000000000022−2−2−i2−i2i2i2i2−i2i2−i2−22−2200000000
χ4222-2-22-2-22−2i2i−2i2i2-2002-200−2i2i0000000002i−2i-22000000000000−2−222i2i2−i2−i2−i2i2−i2i22−22−200000000
χ4322-2-22-2-22−2i2i−2i2i2-2002-200−2i2i000000000−2i2i2-200000000000022−2−2−i2−i2i2i2−i2i2−i2i22−22−200000000
χ4422-2-22-2-22−2i2i−2i2i2-2002-200−2i2i000000000−2i2i2-2000000000000−2−222i2i2−i2−i2i2−i2i2−i2−22−2200000000
χ452-2-2-2-222200002222-2-2-2-200002-20000000002-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-2-2-2-222200002222-2-2-2-200002-20000000002-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-2-2-2-222200002222-2-2-2-200002-2000000000-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ482-2-2-2-222200002222-2-2-2-200002-2000000000-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ492-2-2-2-22220000-2-2-2-2222200002-20000000002-2-222-22-2000000002-22-20000000000000000
χ502-2-2-2-22220000-2-2-2-2222200002-20000000002-2-22-22-2200000000-22-220000000000000000
χ512-2-2-2-22220000-2-2-2-2222200002-2000000000-222-22-22-200000000-22-220000000000000000
χ522-2-2-2-22220000-2-2-2-2222200002-2000000000-222-2-22-22000000002-22-20000000000000000
χ53444-4-44-4-44-4-4400000000000000000000000000000000000000000002-2-222-2-2200000000
χ54444-4-44-4-44-4-440000000000000000000000000000000000000000000-222-2-222-200000000
χ55444-4-44-4-4-444-400000000000000000000000000000000000000000002-2-22-222-200000000
χ56444-4-44-4-4-444-40000000000000000000000000000000000000000000-222-22-2-2200000000
χ5744-44-4-44-44i4i−4i−4i00-4400-4400−4i4i00000000000000000000000000000000000000000000000
χ5844-44-4-44-4−4i−4i4i4i00-4400-44004i−4i00000000000000000000000000000000000000000000000
χ5944-4-44-4-444i−4i4i−4i-4400-4400−4i4i0000000000000000000000000000000000000000000000000
χ6044-4-44-4-44−4i4i−4i4i-4400-44004i−4i0000000000000000000000000000000000000000000000000
χ614-444-4-4-4400004-400-44000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ624-444-4-4-4400004-400-4400000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ634-444-4-4-440000-44004-40000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ644-444-4-4-440000-44004-4000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ654-44-44-44-40000004-400-44000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ664-44-44-44-40000004-400-4400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ674-44-44-44-4000000-44004-400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ684-44-44-44-4000000-44004-40000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-4-4-4-4444000044-4-4-4-4440000-44000000000000000000000000000000000000000000000
χ704-4-4-4-44440000-4-44444-4-40000-44000000000000000000000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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