Finite Group Databasebeta

← Group #336743

Character table — Group #336743

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111-1-111111111-1-1-1-11111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-11111-1-1-1-11111111111-1-11-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111
χ51111111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-111111-111
χ71111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-111-1-1-1-1111-1-1
χ9111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11-1
χ11111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-111-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111111-11
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-11-1-11111-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-111-1
χ172222222222-2-2-2-222-2-2000022222200-2-2002200000000-2-200000000000-20000000
χ182222222222-2-2-2-222-2-200002222-2-2002200-2-200000000-2-20000000000020000000
χ192222222222-2-2-2-222-2-20000-2-2-2-222002200-2-2000000002200000000000-20000000
χ202222222222-2-2-2-222-2-20000-2-2-2-2-2-200-2-2002200000000220000000000020000000
χ2122222222-2-22222-2-2-2-2222200000022002200-2-2-2-20000000000000000-200000000
χ2222222222-2-22222-2-2-2-22222000000-2-200-2-20022-2-20000000000000000200000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000002200-2-200-2-2220000000000000000200000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2000000-2-200220022220000000000000000-200000000
χ2522-2-22-2-22002-22-200002i2i−2i−2ii2i2−i2−i2002i−2i002-20000000000i2−i222−2−222−2−2000000i2−i2000
χ2622-2-22-2-22002-22-200002i2i−2i−2ii2i2−i2−i200−2i2i00-220000000000i2−i2−2−22222−2−2000000−i2i2000
χ2722-2-22-2-22002-22-200002i2i−2i−2i−i2−i2i2i2002i−2i002-20000000000−i2i2−2−222−2−222000000−i2i2000
χ2822-2-22-2-22002-22-200002i2i−2i−2i−i2−i2i2i200−2i2i00-220000000000−i2i222−2−2−2−222000000i2−i2000
χ2922-2-22-2-22002-22-20000−2i−2i2i2ii2i2−i2−i2002i−2i00-220000000000i2−i222−2−2−2−222000000−i2i2000
χ3022-2-22-2-22002-22-20000−2i−2i2i2ii2i2−i2−i200−2i2i002-20000000000i2−i2−2−222−2−222000000i2−i2000
χ3122-2-22-2-22002-22-20000−2i−2i2i2i−i2−i2i2i2002i−2i00-220000000000−i2i2−2−22222−2−2000000i2−i2000
χ3222-2-22-2-22002-22-20000−2i−2i2i2i−i2−i2i2i200−2i2i002-20000000000−i2i222−2−222−2−2000000−i2i2000
χ332-222-2-2-22-2-222-2-2222-200000000000000000000002i2i−2i−2i002-22-200002i−2i000000000
χ342-222-2-2-22-2-222-2-2222-200000000000000000000002i2i−2i−2i00-22-220000−2i2i000000000
χ352-222-2-2-22-2-222-2-2222-20000000000000000000000−2i−2i2i2i002-22-20000−2i2i000000000
χ362-222-2-2-22-2-222-2-2222-20000000000000000000000−2i−2i2i2i00-22-2200002i−2i000000000
χ372-22-22-22-22-200002-200i2−i2i2−i22-22-22-20000002-200i2−i2i2−i2i2−i2000000i2−i2i2−i20000i2−i200000
χ382-22-22-22-22-200002-200i2−i2i2−i22-22-2-22000000-2200i2−i2−i2i2−i2i2000000i2−i2i2−i20000−i2i200000
χ392-22-22-22-22-200002-200i2−i2i2−i2-22-222-2000000-2200i2−i2−i2i2−i2i2000000−i2i2−i2i20000i2−i200000
χ402-22-22-22-22-200002-200i2−i2i2−i2-22-22-220000002-200i2−i2i2−i2i2−i2000000−i2i2−i2i20000−i2i200000
χ412-22-22-22-22-200002-200−i2i2−i2i22-22-22-20000002-200−i2i2−i2i2−i2i2000000−i2i2−i2i20000−i2i200000
χ422-22-22-22-22-200002-200−i2i2−i2i22-22-2-22000000-2200−i2i2i2−i2i2−i2000000−i2i2−i2i20000i2−i200000
χ432-22-22-22-22-200002-200−i2i2−i2i2-22-222-2000000-2200−i2i2i2−i2i2−i2000000i2−i2i2−i20000−i2i200000
χ442-22-22-22-22-200002-200−i2i2−i2i2-22-22-220000002-200−i2i2−i2i2−i2i2000000i2−i2i2−i20000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-44-4-44-40000-44000000000000004-4000000000000000000000000000000000
χ47444-4-44-4-44-40000-4400000000000000-44000000000000000000000000000000000
χ48444-4-44-4-4-4400004-400000000000000000000000022−22−2222000000000000000000000
χ49444-4-44-4-4-4400004-4000000000000000000000000−222222−22000000000000000000000
χ5044-4-44-4-4400-44-44000000002i22i2−2i2−2i2000000000000000000−2i22i20000000000000000000
χ5144-4-44-4-4400-44-4400000000−2i2−2i22i22i20000000000000000002i2−2i20000000000000000000
χ524-444-4-4-444444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ534-444-4-4-4444-4-444-4-44-400000000000000000000000000000000000000000000000
χ544-444-4-4-44-4-4-4-44444-4400000000000000000000000000000000000000000000000
χ554-44-44-44-4-440000-44002i2−2i22i2−2i20000000000000000−2i22i20000000000000000000000000
χ564-44-44-44-4-440000-4400−2i22i2−2i22i200000000000000002i2−2i20000000000000000000000000
χ574-4-4444-4-4000000000022−22−22222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ584-4-4444-4-4000000000022−22−2222−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ594-4-4444-4-40000000000−222222−222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ604-4-4444-4-40000000000−222222−22−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ614-4-4-4-4444004-4-440000000000000000000000000000000022−22−2222000000000000000
χ624-4-4-4-4444004-4-4400000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4-444400-444-400000000000000000000004-4000000000000000000000000000
χ644-4-4-4-444400-444-40000000000000000000000-44000000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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