Finite Group Databasebeta

← Group #278138

Character table — Group #278138

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244444444888844448888888888888888888888888844882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-11-1
χ91111111111111111-1-111-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ101111111111111111-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ121111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-111-1-11-1-11
χ172222222222-22-2-2-2222-2-222-2-2-2-2000022-2-2000000000000000000000000002-2000000
χ182222222222-22-2-2-2222-2-222-2-2-2-20000-2-22200000000000000000000000000-22000000
χ192222222222-22-2-2-22-2-2-2-2-2-22222000022-2-200000000000000000000000000-22000000
χ202222222222-22-2-2-22-2-2-2-2-2-222220000-2-222000000000000000000000000002-2000000
χ2122222222-2-22-2222-222-2-2-2-2-2-222222200002200000000-2-2-2-200000000000000000000
χ2222222222-2-22-2222-222-2-2-2-2-2-222-2-2-2-20000-2-200000000222200000000000000000000
χ2322222222-2-22-2222-2-2-2-2-22222-2-222220000-2-200000000-2-22200000000000000000000
χ2422222222-2-22-2222-2-2-2-2-22222-2-2-2-2-2-20000220000000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-2-200000000002i2i−2i−2i00000000000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-2-20000000000−2i−2i2i2i0000000000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-22200000000002i2i−2i−2i0000000000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000−2i−2i2i2i00000000000000000000002i−2i0000
χ2922-2-2-2-22200202-2-202-20000002-222-2-200002-20000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ3022-2-2-2-22200202-2-202-20000002-222-2-200002-20000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ3122-2-2-2-22200202-2-202-20000002-2-2-2220000-220000i2i2−i2−i20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ3222-2-2-2-22200202-2-202-20000002-2-2-2220000-220000−i2−i2i2i20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ3322-2-2-2-22200202-2-20-22000000-2222-2-20000-220000i2i2−i2−i20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ3422-2-2-2-22200202-2-20-22000000-2222-2-20000-220000−i2−i2i2i20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ3522-2-2-2-22200202-2-20-22000000-22-2-22200002-20000i2i2−i2−i20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ3622-2-2-2-22200202-2-20-22000000-22-2-22200002-20000−i2−i2i2i20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ372-222-2-22-200-2022-2000002i−2i2i−2i002-22-200000000002−22−2002i−2ii2−i2i2−i22−22−2i2−i2i2−i200000000
χ382-222-2-22-200-2022-2000002i−2i2i−2i002-22-20000000000−22−22002i−2i−i2i2−i2i2−22−22−i2i2−i2i200000000
χ392-222-2-22-200-2022-2000002i−2i2i−2i00-22-2200000000002−22−200−2i2ii2−i2i2−i2−22−22−i2i2−i2i200000000
χ402-222-2-22-200-2022-2000002i−2i2i−2i00-22-220000000000−22−2200−2i2i−i2i2−i2i22−22−2i2−i2i2−i200000000
χ412-222-2-22-200-2022-200000−2i2i−2i2i002-22-200000000002−22−200−2i2i−i2i2−i2i22−22−2−i2i2−i2i200000000
χ422-222-2-22-200-2022-200000−2i2i−2i2i002-22-20000000000−22−2200−2i2ii2−i2i2−i2−22−22i2−i2i2−i200000000
χ432-222-2-22-200-2022-200000−2i2i−2i2i00-22-2200000000002−22−2002i−2i−i2i2−i2i2−22−22i2−i2i2−i200000000
χ442-222-2-22-200-2022-200000−2i2i−2i2i00-22-220000000000−22−22002i−2ii2−i2i2−i22−22−2−i2i2−i2i200000000
χ452-2-2-2222-222-2-22-22-2002-20000002-2-2200000000002i−2i−2i2i2-20000002i−2i−2i2i000000000000
χ462-2-2-2222-222-2-22-22-2002-20000002-2-220000000000−2i2i2i−2i2-2000000−2i2i2i−2i000000000000
χ472-2-2-2222-222-2-22-22-2002-2000000-222-200000000002i−2i−2i2i-22000000−2i2i2i−2i000000000000
χ482-2-2-2222-222-2-22-22-2002-2000000-222-20000000000−2i2i2i−2i-220000002i−2i−2i2i000000000000
χ492-2-2-2222-2-2-2-222-22200-220000002-2-2200000000000000-22002-2-2200002-2-2200000000
χ502-2-2-2222-2-2-2-222-22200-220000002-2-2200000000000000-2200-222-20000-222-200000000
χ512-2-2-2222-2-2-2-222-22200-22000000-222-2000000000000002-2002-2-220000-222-200000000
χ522-2-2-2222-2-2-2-222-22200-22000000-222-2000000000000002-200-222-200002-2-2200000000
χ53444-44-4-4-44-404000-400000000000000004-40000000000000000000000000000000000
χ54444-44-4-4-44-404000-40000000000000000-440000000000000000000000000000000000
χ55444-44-4-4-4-440-40004000000000000004i−4i000000000000000000000000000000000000
χ56444-44-4-4-4-440-4000400000000000000−4i4i000000000000000000000000000000000000
χ5744-4-4-4-44400-40-44404-4000000-44000000000000000000000000000000000000000000
χ5844-4-4-4-44400-40-4440-440000004-4000000000000000000000000000000000000000000
χ594-444-4-44-40040-4-44000004i−4i−4i4i00000000000000000000000000000000000000000000
χ604-444-4-44-40040-4-4400000−4i4i4i−4i00000000000000000000000000000000000000000000
χ614-4-444-4-444-40-400040000000000000000000022−2222−220000000000000000000000000000
χ624-4-444-4-444-40-4000400000000000000000000−2222−22220000000000000000000000000000
χ634-4-444-4-44-4404000-4000000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ644-4-444-4-44-4404000-400000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ654-4-4-4444-4444-4-44-4-400-44000000000000000000000000000000000000000000000000
χ664-4-4-4444-4-4-444-44-44004-4000000000000000000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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