Finite Group Databasebeta

← Group #278984

Character table — Group #278984

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244448888888844444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-1-1-1111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-1111111111111-1-1-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-111111-11-1
χ91111111111111111-1-111-1-11111111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ121111111111111111-1-111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-111-1-1-1-11111111111-1-1-1-1-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-111-1-1-1-1111111-1-1-1-1111111-1-1-111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11-1-11
χ1722222222222-2-2-2-2222-2-2220000000022-222-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2222-2-22200000000-2-2-2-2-22222-20000000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-200000000222-2-222-2-220000000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-200000000-2-2222-2-22220000000000000000000000000000
χ2122222222-2-2-22222-222-2-2-2-22222-2-2-2-200-20000002-2-200002200000000000000000000
χ2222222222-2-2-22222-222-2-2-2-2-2-2-2-2222200-20000002220000-2-200000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2222222-2-2-2-2002000000-2220000-2-200000000000000000000
χ2422222222-2-2-22222-2-2-2-2-222-2-2-2-22222002000000-2-2-200002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000002000000-2002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000002000000-200−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000-20000002002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000-2000000200−2i−2i2i2i002i2i−2i−2i0000000000000000
χ292222-2-2-2-222-20000-22-2002-222−2−222−2−22-202-2000002−22−22−22−22−22−20000000000000000
χ302222-2-2-2-222-20000-22-2002-222−2−222−2−2-220-22000002−2−22−222−2−22−220000000000000000
χ312222-2-2-2-222-20000-22-2002-2−2−222−2−2222-202-200000−22−22−22−22−22−220000000000000000
χ322222-2-2-2-222-20000-22-2002-2−2−222−2−222-220-2200000−222−22−2−222−22−20000000000000000
χ332222-2-2-2-222-20000-2-2200-2222−2−222−2−22-20-2200000−222−22−2−22−22−220000000000000000
χ342222-2-2-2-222-20000-2-2200-2222−2−222−2−2-2202-200000−22−22−22−222−22−20000000000000000
χ352222-2-2-2-222-20000-2-2200-22−2−222−2−2222-20-22000002−2−22−222−22−22−20000000000000000
χ362222-2-2-2-222-20000-2-2200-22−2−222−2−222-2202-2000002−22−22−22−2−22−220000000000000000
χ372222-2-2-2-2-2-22000022-200-2222−2−2−2−222000002i−2i2i−2i0−22i2−i2−i2i22−2i2−i2−i2i20000000000000000
χ382222-2-2-2-2-2-22000022-200-2222−2−2−2−22200000−2i2i−2i2i0−22−i2i2i2−i22−2−i2i2i2−i20000000000000000
χ392222-2-2-2-2-2-22000022-200-22−2−22222−2−2000002i−2i2i−2i02−2−i2i2i2−i2−22−i2i2i2−i20000000000000000
χ402222-2-2-2-2-2-22000022-200-22−2−22222−2−200000−2i2i−2i2i02−2i2−i2−i2i2−22i2−i2−i2i20000000000000000
χ412222-2-2-2-2-2-2200002-22002-222−2−2−2−222000002i−2i−2i2i02−2−i2i2i2−i2−22i2−i2−i2i20000000000000000
χ422222-2-2-2-2-2-2200002-22002-222−2−2−2−22200000−2i2i2i−2i02−2i2−i2−i2i2−22−i2i2i2−i20000000000000000
χ432222-2-2-2-2-2-2200002-22002-2−2−22222−2−2000002i−2i−2i2i0−22i2−i2−i2i22−2−i2i2i2−i20000000000000000
χ442222-2-2-2-2-2-2200002-22002-2−2−22222−2−200000−2i2i2i−2i0−22−i2i2i2−i22−2i2−i2−i2i20000000000000000
χ452-2-222-2-222-22-22-22-2002-2002-22-22-22-2000000000000000000000000002i2i−2i−2i002i−2i0000
χ462-2-222-2-222-22-22-22-2002-2002-22-22-22-200000000000000000000000000−2i−2i2i2i00−2i2i0000
χ472-2-222-2-222-22-22-22-2002-200-22-22-22-22000000000000000000000000002i2i−2i−2i00−2i2i0000
χ482-2-222-2-222-22-22-22-2002-200-22-22-22-2200000000000000000000000000−2i−2i2i2i002i−2i0000
χ492-2-222-2-22-22-2-22-22200-22002-22-2-22-22000000000000000000000022-2-200002-2000000
χ502-2-222-2-22-22-2-22-22200-22002-22-2-22-220000000000000000000000-2-2220000-22000000
χ512-2-222-2-22-22-2-22-22200-2200-22-222-22-2000000000000000000000022-2-20000-22000000
χ522-2-222-2-22-22-2-22-22200-2200-22-222-22-20000000000000000000000-2-22200002-2000000
χ5344-4-4-44-440004-4-44000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ5444-4-4-44-440004-4-4400000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ5544-4-4-44-44000-444-400000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ5644-4-4-44-44000-444-40000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ574-44-4-4-44400044-4-400000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ584-44-4-4-44400044-4-40000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ594-44-4-4-444000-4-4440000000000000000000000000000000000000000022−22−222200000000
χ604-44-4-4-444000-4-44400000000000000000000000000000000000000000−222222−2200000000
χ614-4-444-4-444-444-44-4-400-44000000000000000000000000000000000000000000000000
χ624-4-444-4-44-44-44-44-44004-4000000000000000000000000000000000000000000000000
χ634-4-44-444-44-4-40000400000022−22−222222−22−222200000000000000000000000000000000000000
χ644-4-44-444-44-4-400004000000−222222−22−222222−2200000000000000000000000000000000000000
χ654-4-44-444-4-4440000-400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-44-444-4-4440000-4000000−222222−2222−22−222200000000000000000000000000000000000000
χ6788-8-88-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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