Finite Group Databasebeta

← Group #272199

Character table — Group #272199

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422224444488882444444888888888824444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1111111111-1-11-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-1-1-11111
χ511111111111111-1-1111111111-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-111-1-1
χ611111111111111-1-1111111111-111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111-1-1-1-1-111
χ711111111111111-1-111111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111-1-111
χ811111111111111-1-111111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-111-11111111-1-1
χ9111111111111-1-1111-1-11111111-1-11111-1-11111-1-1-1-1-111-1111-1-1-11-1-1-1-11-1
χ10111111111111-1-1111-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ11111111111111-1-1111-1-111-1-1-1-11-1-11111-1-1-1-1-1-11111-111-11-1-1-1-1-1-11111-11
χ12111111111111-1-1111-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-111-1-11-1
χ13111111111111-1-1-1-11-1-1111111-1-1-111-1-1-1-1-1-111-1-1-1-11-1-11111-111-111-1-1-11
χ14111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-11-1-1-111111-1
χ15111111111111-1-1-1-11-1-111-1-1-1-1-1-1-111-1-1-1-111-1-111111-1-111-1-1-1111-1-1111-1
χ16111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1111-1-11-1-1-1-1-11
χ172222222-22-2-2-20022200-2-2000020000-2-20000002i2i−2i−2i000000000002i−2i0000
χ182222222-22-2-2-20022200-2-2000020000-2-2000000−2i−2i2i2i00000000000−2i2i0000
χ192222222-22-2-2-200-2-2200-2-20000-20000220000002i2i−2i−2i00000000000−2i2i0000
χ202222222-22-2-2-200-2-2200-2-20000-2000022000000−2i−2i2i2i000000000002i−2i0000
χ21222222-22-22222200-222-2-200000-2-2220022000000000000-200-2000000000
χ22222222-22-22222200-222-2-200000-2-2-2-200-2-20000000000002002000000000
χ23222222-22-2222-2-200-2-2-2-2-200000222200-2-2000000000000-2002000000000
χ24222222-22-2222-2-200-2-2-2-2-20000022-2-20022000000000000200-2000000000
χ252222-2-2222-2-220022-200-222222-200002-20022-2-200000000000000-2000000
χ262222-2-2222-2-220022-200-22-2-2-2-2-200002-200-2-222000000000000002000000
χ272222-2-2222-2-2200-2-2-200-22222220000-2200-2-2-2-2000000000000002000000
χ282222-2-2222-2-2200-2-2-200-22-2-2-2-220000-2200222200000000000000-2000000
χ292222-2-22-2222-22222-2-2-22-20000-22-200-220000000000200-20000000000000
χ302222-2-22-2222-222-2-2-2-2-22-2000022-2002-20000000000-20020000000000000
χ312222-2-22-2222-2-2-222-2222-20000-2-2200-220000000000-20020000000000000
χ322222-2-22-2222-2-2-2-2-2-2222-200002-22002-20000000000200-20000000000000
χ332222-2-2-2-2-222-222002-2-2-2200000-220000000000000002-2000002-20000000
χ342222-2-2-2-2-222-222002-2-2-2200000-22000000000000000-2200000-220000000
χ352222-2-2-2-2-222-2-2-200222-22000002-20000000000000002-200000-220000000
χ362222-2-2-2-2-222-2-2-200222-22000002-2000000000000000-22000002-20000000
χ372-2-222-20202-2-22-20002-200i2i2−i2−i20002i−2i002i−2i00i2−i2i2−i2i2−i2000002−20000002−200
χ382-2-222-20202-2-22-20002-200i2i2−i2−i2000−2i2i00−2i2i00i2−i2i2−i2i2−i200000−22000000−2200
χ392-2-222-20202-2-22-20002-200−i2−i2i2i20002i−2i002i−2i00−i2i2−i2i2−i2i200000−22000000−2200
χ402-2-222-20202-2-22-20002-200−i2−i2i2i2000−2i2i00−2i2i00−i2i2−i2i2−i2i2000002−20000002−200
χ412-2-222-20202-2-2-22000-2200i2i2−i2−i20002i−2i00−2i2i00i2−i2−i2i2−i2i2000002−2000000−2200
χ422-2-222-20202-2-2-22000-2200i2i2−i2−i2000−2i2i002i−2i00i2−i2−i2i2−i2i200000−220000002−200
χ432-2-222-20202-2-2-22000-2200−i2−i2i2i20002i−2i00−2i2i00−i2i2i2−i2i2−i200000−220000002−200
χ442-2-222-20202-2-2-22000-2200−i2−i2i2i2000−2i2i002i−2i00−i2i2i2−i2i2−i2000002−2000000−2200
χ45444444-4-4-4-4-4-40000-4004400000000000000000000000000000000000000
χ464444-4-4-44-4-4-4400004004-400000000000000000000000000000000000000
χ4744-4-40040-4000004-40000022−2222−2200000000022−2200000000000000000000000
χ4844-4-40040-4000004-400000−2222−2222000000000−222200000000000000000000000
χ4944-4-40040-400000-440000022−2222−22000000000−222200000000000000000000000
χ5044-4-40040-400000-4400000−2222−222200000000022−2200000000000000000000000
χ514-4-444-40-40-4440000000000000000000000000022−22−222200000000000000000
χ524-4-444-40-40-44400000000000000000000000000−222222−2200000000000000000
χ534-4-44-44040-44-40000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ544-4-44-44040-44-4000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ554-4-44-440-404-444-4000-440000000000000000000000000000000000000000
χ564-4-44-440-404-44-440004-40000000000000000000000000000000000000000
χ5788-8-800-80800000000000000000000000000000000000000000000000000
χ588-88-8000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ598-88-800000000000000000−4i4i4i−4i0000000000000000000000000000000000

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