Finite Group Databasebeta

← Group #255443

Character table — Group #255443

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422244444444888888888888888822244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1
χ4111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111-1-111-1-1-1-11111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111
χ7111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-1111111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-11111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-111-1-11-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-111-1-1-1-111
χ1722222222222222-2-222-2-2-2-2220000-2-2-200220000220000000000000000-20000-200000000
χ1822222222222222-2-222-2-2-2-2220000-2-2-200-2-20000-2-2000000000000000020000200000000
χ192222222222-2-2-2-2-2-222-2-222-2-20000-2-2200220000-2-2000000000000000020000-200000000
χ202222222222-2-2-2-2-2-222-2-222-2-20000-2-2200-2-20000220000000000000000-20000200000000
χ2122222222-2-2222222-2-22222-2-22222-2-2-2-2-200-2-22200000000000000000000000000000000
χ2222222222-2-2222222-2-22222-2-2-2-2-2-2-2-2-2220022-2-200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-200002220000000000000000000000000002-20002-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-20000222000000000000000000000000000-22000-22000000
χ2522222222-2-2-2-2-2-222-2-222-2-2222222-2-222200-2-2-2-200000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-222-2-2-2-2-2-22-2-200222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-20000000000000000000000000002-2000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2000000000000000000000000000-220002-2000000
χ2922-22-2-22-2002i2i−2i−2i2-2002-22i−2i0022-2-20000000002i−2i0000000000i2i2−i2−i222−2−20000000000i2−i22−2
χ3022-22-2-22-2002i2i−2i−2i2-2002-22i−2i0022-2-20000000002i−2i0000000000−i2−i2i2i2−2−2220000000000−i2i2−22
χ3122-22-2-22-2002i2i−2i−2i2-2002-22i−2i00-2-222000000000−2i2i0000000000i2i2−i2−i222−2−20000000000−i2i2−22
χ3222-22-2-22-2002i2i−2i−2i2-2002-22i−2i00-2-222000000000−2i2i0000000000−i2−i2i2i2−2−2220000000000i2−i22−2
χ3322-22-2-22-200−2i−2i2i2i2-2002-2−2i2i0022-2-2000000000−2i2i0000000000i2i2−i2−i2−2−2220000000000i2−i2−22
χ3422-22-2-22-200−2i−2i2i2i2-2002-2−2i2i0022-2-2000000000−2i2i0000000000−i2−i2i2i222−2−20000000000−i2i22−2
χ3522-22-2-22-200−2i−2i2i2i2-2002-2−2i2i00-2-2220000000002i−2i0000000000i2i2−i2−i2−2−2220000000000−i2i22−2
χ3622-22-2-22-200−2i−2i2i2i2-2002-2−2i2i00-2-2220000000002i−2i0000000000−i2−i2i2i222−2−20000000000i2−i2−22
χ372-2222-2-2-22-22i−2i2i−2i002-200002i−2i0000000002-200002i−2ii2i2−i2−i222−2−2i2−i2i2−i22−22−200000000000000
χ382-2222-2-2-22-22i−2i2i−2i002-200002i−2i0000000002-200002i−2i−i2−i2i2i2−2−222−i2i2−i2i2−22−2200000000000000
χ392-2222-2-2-22-22i−2i2i−2i002-200002i−2i000000000-220000−2i2ii2i2−i2−i222−2−2−i2i2−i2i2−22−2200000000000000
χ402-2222-2-2-22-22i−2i2i−2i002-200002i−2i000000000-220000−2i2i−i2−i2i2i2−2−222i2−i2i2−i22−22−200000000000000
χ412-2222-2-2-22-2−2i2i−2i2i002-20000−2i2i0000000002-20000−2i2ii2i2−i2−i2−2−222i2−i2i2−i2−22−2200000000000000
χ422-2222-2-2-22-2−2i2i−2i2i002-20000−2i2i0000000002-20000−2i2i−i2−i2i2i222−2−2−i2i2−i2i22−22−200000000000000
χ432-2222-2-2-22-2−2i2i−2i2i002-20000−2i2i000000000-2200002i−2ii2i2−i2−i2−2−222−i2i2−i2i22−22−200000000000000
χ442-2222-2-2-22-2−2i2i−2i2i002-20000−2i2i000000000-2200002i−2i−i2−i2i2i222−2−2i2−i2i2−i2−22−2200000000000000
χ452-2-2-2222-22-2000022-22-2-200002-22-22-2000002-2000000002i−2i2i−2i00000000000000002i−2i0000
χ462-2-2-2222-22-2000022-22-2-200002-22-22-2000002-200000000−2i2i−2i2i0000000000000000−2i2i0000
χ472-2-2-2222-22-2000022-22-2-20000-22-222-200000-22000000002i−2i2i−2i0000000000000000−2i2i0000
χ482-2-2-2222-22-2000022-22-2-20000-22-222-200000-2200000000−2i2i−2i2i00000000000000002i−2i0000
χ492-2-2-2222-2-220000222-2-2-200002-22-2-2200000-2200002i−2i2i−2i0000000000000002i−2i000000000
χ502-2-2-2222-2-220000222-2-2-200002-22-2-2200000-220000−2i2i−2i2i000000000000000−2i2i000000000
χ512-2-2-2222-2-220000222-2-2-20000-22-22-22000002-200002i−2i2i−2i000000000000000−2i2i000000000
χ522-2-2-2222-2-220000222-2-2-20000-22-22-22000002-20000−2i2i−2i2i0000000000000002i−2i000000000
χ5344-44-4-44-4004i4i−4i−4i-4400-44−4i4i0000000000000000000000000000000000000000000000000
χ5444-44-4-44-400−4i−4i4i4i-4400-444i−4i0000000000000000000000000000000000000000000000000
χ5544-4-44-4-4444000000-4-40000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5644-4-44-4-4444000000-4-4000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5744-4-44-4-44-4-4000000440000000000000000000000022−22−222200000000000000000000000000
χ5844-4-44-4-44-4-40000004400000000000000000000000−222222−2200000000000000000000000000
χ594-4444-4-4-4-444i−4i4i−4i00-440000−4i4i00000000000000000000000000000000000000000000000
χ604-4444-4-4-4-44−4i4i−4i4i00-4400004i−4i00000000000000000000000000000000000000000000000
χ614-44-4-4-4440000004-400-4400004-4-440000000000000000000000000000000000000000000
χ624-44-4-4-4440000004-400-440000-444-40000000000000000000000000000000000000000000
χ634-44-4-4-444000000-44004-4000000000004-400000000000000000000000000000000000000
χ644-44-4-4-444000000-44004-400000000000-4400000000000000000000000000000000000000
χ654-4-44-44-44004-4-44000000000000000000000000000000000002-2-222-2-2200000000000000
χ664-4-44-44-44004-4-4400000000000000000000000000000000000-222-2-222-200000000000000
χ674-4-44-44-4400-444-4000000000000000000000000000000000002-2-22-222-200000000000000
χ684-4-44-44-4400-444-400000000000000000000000000000000000-222-22-2-2200000000000000
χ694-4-4-4444-44-40000-4-4-444400000000-4400000000000000000000000000000000000000000
χ704-4-4-4444-4-440000-4-44-444000000004-400000000000000000000000000000000000000000
χ71888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000

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