Finite Group Databasebeta

← Group #258331

Character table — Group #258331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ711111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ91111111111111-1-1-1-11111-1-11111-1-11-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-1
χ101111111111111-1-1-1-11111-1-11111-1-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-111
χ111111111111111-1-1-1-11111-1-11111-1-11-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-111
χ121111111111111-1-1-1-11111-1-11111-1-11-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-11111-1-1
χ131111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-111
χ141111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-11111-1-1
χ151111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-11-1-11111-1-111-1-1
χ161111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-111
χ1722222222222-2-22222-2-22-2-2-2000022-2-200000022220000000000000000-2-2000000000000
χ1822222222222-2-22222-2-22-2-2-2000022-2-2000000-2-2-2-2000000000000000022000000000000
χ1922222222222-2-2-2-2-2-2-2-22-2220000-2-2-2200000022-2-20000000000000000-22000000000000
χ2022222222222-2-2-2-2-2-2-2-22-2220000-2-2-22000000-2-22200000000000000002-2000000000000
χ2122222222-2-2-222222222-2-2222222-2-2-2-2-2-2-2-2220000000000000000000000000000000000
χ2222222222-2-2-222222222-2-222-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000
χ2322222222-2-2-222-2-2-2-222-2-2-2-2222222-22-2-222-2-20000000000000000000000000000000000
χ2422222222-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222-2222-2-2220000000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-22-2-20000-2-222000000000000000000000000000000002-22-20000
χ2622222222-2-2-2-2-22222-2-2-22-2-20000-2-22200000000000000000000000000000000-22-220000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-2000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22220000222-200000000000000000000000000000000-222-20000
χ2922-2-22-22-222-22-200002-2-2-2002i2i−2i−2i00202i−2i00000000000022-2-20000000000002i−2i00000000
χ3022-2-22-22-222-22-200002-2-2-2002i2i−2i−2i00202i−2i000000000000-2-222000000000000−2i2i00000000
χ3122-2-22-22-222-22-200002-2-2-200−2i−2i2i2i0020−2i2i00000000000022-2-2000000000000−2i2i00000000
χ3222-2-22-22-222-22-200002-2-2-200−2i−2i2i2i0020−2i2i000000000000-2-2220000000000002i−2i00000000
χ3322-2-22-22-2-2-222-200002-222002i2i−2i−2i00-20−2i2i000000002i2i−2i−2i000000000000002-20000000000
χ3422-2-22-22-2-2-222-200002-222002i2i−2i−2i00-20−2i2i00000000−2i−2i2i2i00000000000000-220000000000
χ3522-2-22-22-2-2-222-200002-22200−2i−2i2i2i00-202i−2i000000002i2i−2i−2i00000000000000-220000000000
χ3622-2-22-22-2-2-222-200002-22200−2i−2i2i2i00-202i−2i00000000−2i−2i2i2i000000000000002-20000000000
χ372-22-2-2-2220002222-2-2-2-2002-22-22-2000000002-2000000000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i2
χ382-22-2-2-2220002222-2-2-2-2002-22-22-2000000002-2000000000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i2
χ392-22-2-2-2220002222-2-2-2-2002-2-22-2200000000-22000000000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i2
χ402-22-2-2-2220002222-2-2-2-2002-2-22-2200000000-22000000000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i2
χ412-22-2-2-22200022-2-222-2-200-222-22-200000000-22000000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2
χ422-22-2-2-22200022-2-222-2-200-222-22-200000000-22000000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2
χ432-22-2-2-22200022-2-222-2-200-22-22-22000000002-2000000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2
χ442-22-2-2-22200022-2-222-2-200-22-22-22000000002-2000000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2
χ452-2-2-222-222-22002-22-200-200000002-2000000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000
χ462-2-2-222-222-22002-22-200-200000002-2000000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000
χ472-2-2-222-222-22002-22-200-200000002-200000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000
χ482-2-2-222-222-22002-22-200-200000002-200000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000
χ492-2-2-222-222-2200-22-2200-20000000-22000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000
χ502-2-2-222-222-2200-22-2200-20000000-22000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000
χ512-2-2-222-222-2200-22-2200-20000000-2200000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000
χ522-2-2-222-222-2200-22-2200-20000000-2200000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000
χ5344-44-4-4-44000004-4-44000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5444-44-4-4-44000004-4-4400000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5544-44-4-4-4400000-444-4000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5644-44-4-4-4400000-444-400000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5744-4-44-44-444-4-440000-44-4400000000-400000000000000000000000000000000000000000
χ5844-4-44-44-4-4-44-440000-444-400000000400000000000000000000000000000000000000000
χ594-4444-4-4-44-4-400000000400000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4444-4-4-44-4-40000000040000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ614-4444-4-4-4-44400000000-400000000000000000000022−22−222200000000000000000000000000
χ624-4444-4-4-4-44400000000-4000000000000000000000−222222−2200000000000000000000000000
χ634-44-4-4-444000-4-444-4-44400-44000000000000000000000000000000000000000000000000
χ644-44-4-4-444000-4-4-4-44444004-4000000000000000000000000000000000000000000000000
χ654-4-44-444-40004-40000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ664-4-44-444-40004-40000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ674-4-44-444-4000-4400004-4000000000000004i−4i000000000000000000000000000000000000
χ684-4-44-444-4000-4400004-400000000000000−4i4i000000000000000000000000000000000000
χ694-4-4-444-44-44-4004-44-40040000000-44000000000000000000000000000000000000000000
χ704-4-4-444-44-44-400-44-4400400000004-4000000000000000000000000000000000000000000
χ71888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000

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