Finite Group Databasebeta

← Group #419442

Character table — Group #419442

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422224444444444448888888888884444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ41111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ511111111111111111111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111-1-1
χ9111111111111111111-1-11111-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-111-1-1
χ10111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ11111111111111111111-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ12111111111111111111-1-111-1-111-1-111-1-111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111
χ13111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ14111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1111111
χ172222222222-2-2-2-2-2-2-2-22-200000000002-20000002i2i−2i−2i0000000000002i−2i000000
χ182222222222-2-2-2-2-2-2-2-22-200000000002-2000000−2i−2i2i2i000000000000−2i2i000000
χ192222222222-2-2-2-2-2-2-2-2-220000000000-220000002i2i−2i−2i000000000000−2i2i000000
χ202222222222-2-2-2-2-2-2-2-2-220000000000-22000000−2i−2i2i2i0000000000002i−2i000000
χ21222222-2-2-2-22-22-2-2-222002-2002200-2-2002-20000000000000000002-200000000
χ22222222-2-2-2-22-22-2-2-222002-200-2-20022002-2000000000000000000-2200000000
χ23222222-2-2-2-22-22-2-2-22200-22002200-2-200-22000000000000000000-2200000000
χ24222222-2-2-2-22-22-2-2-22200-2200-2-2002200-220000000000000000002-200000000
χ252222-2-222-2-2-2-2222-22-2002-22200-2-20000-220000000000000000000000002-200
χ262222-2-222-2-2-2-2222-22-2002-2-2-200220000-22000000000000000000000000-2200
χ272222-2-222-2-2-2-2222-22-200-222200-2-200002-2000000000000000000000000-2200
χ282222-2-222-2-2-2-2222-22-200-22-2-2002200002-20000000000000000000000002-200
χ292222-2-2-2-2222-2-222-2-22220000000000-2-2000000000022-2-200000000002-20000
χ302222-2-2-2-2222-2-222-2-22220000000000-2-20000000000-2-2220000000000-220000
χ312222-2-2-2-2222-2-222-2-22-2-2000000000022000000000022-2-20000000000-220000
χ322222-2-2-2-2222-2-222-2-22-2-20000000000220000000000-2-22200000000002-20000
χ332222-2-2-2-222-222-2-222-22-22200000000-22-2-20000000000002-200000000000000
χ342222-2-2-2-222-222-2-222-22-2-2-200000000-2222000000000000-2200000000000000
χ352222-2-2-2-222-222-2-222-2-2222000000002-2-2-2000000000000-2200000000000000
χ362222-2-2-2-222-222-2-222-2-22-2-2000000002-2220000000000002-200000000000000
χ372-2-222-22-22-22-2-22-222-20000002i−2i002i−2i000000002i−2i2i−2i0000000000000000002-2
χ382-2-222-22-22-22-2-22-222-20000002i−2i002i−2i00000000−2i2i−2i2i000000000000000000-22
χ392-2-222-22-22-22-2-22-222-2000000−2i2i00−2i2i000000002i−2i2i−2i000000000000000000-22
χ402-2-222-22-22-22-2-22-222-2000000−2i2i00−2i2i00000000−2i2i−2i2i0000000000000000002-2
χ412-2-222-22-22-2-222-22-2-2200002i−2i002i−2i0000002i2i−2i−2i2-2-2200000000000000000000
χ422-2-222-22-22-2-222-22-2-2200002i−2i002i−2i000000−2i−2i2i2i-222-200000000000000000000
χ432-2-222-22-22-2-222-22-2-220000−2i2i00−2i2i0000002i2i−2i−2i-222-200000000000000000000
χ442-2-222-22-22-2-222-22-2-220000−2i2i00−2i2i000000−2i−2i2i2i2-2-2200000000000000000000
χ452-2-222-2-22-2222-2-22-22-20000002i−2i00−2i2i0000000000002i−2i2i−2i002-2000000000000
χ462-2-222-2-22-2222-2-22-22-20000002i−2i00−2i2i000000000000−2i2i−2i2i00-22000000000000
χ472-2-222-2-22-2222-2-22-22-2000000−2i2i002i−2i0000000000002i−2i2i−2i00-22000000000000
χ482-2-222-2-22-2222-2-22-22-2000000−2i2i002i−2i000000000000−2i2i−2i2i002-2000000000000
χ492-2-22-222-2-222-22-222-2-200002i−2i00−2i2i000000000000002i−2i−2i2i00002-20000000000
χ502-2-22-222-2-222-22-222-2-200002i−2i00−2i2i00000000000000−2i2i2i−2i0000-220000000000
χ512-2-22-222-2-222-22-222-2-20000−2i2i002i−2i000000000000002i−2i−2i2i0000-220000000000
χ522-2-22-222-2-222-22-222-2-20000−2i2i002i−2i00000000000000−2i2i2i−2i00002-20000000000
χ53444444-4-4-4-4-44-4444-4-400000000000000000000000000000000000000000000
χ544444-4-444-4-444-4-4-44-4400000000000000000000000000000000000000000000
χ554-4-444-4-44-44-4-444-44-4400000000000000000000000000000000000000000000
χ564-4-44-444-4-44-44-44-4-44400000000000000000000000000000000000000000000
χ574-4-44-44-444-44444-4-4-4-400000000000000000000000000000000000000000000
χ584-4-44-44-444-4-4-4-4-4444400000000000000000000000000000000000000000000
χ5988-8-800000000000000000000000000000022−2222−22000000000000000000000000
χ6088-8-8000000000000000000000000000000−2222−2222000000000000000000000000
χ618-88-80000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ628-88-8000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000

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