Finite Group Databasebeta

← Group #419721

Character table — Group #419721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422444444444444444444444488882224444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-11111-1-1-1-1-1-1
χ511111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-111-1-111-1-111-1-1
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111111-1-1-1-1-1-111
χ9111111111111111111-1-11111-1-1-1-1-1-11111111111111111-111-1-1-1-1-1-1-1-1-1-1-111
χ10111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-111-1-1
χ12111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-11111-1-1111111111111-1-1-1-11-1-1111-1-111-1-1-1-1-1-1
χ14111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ172222222222-2-2-2-2-2-2-2-200000022-2-2000000000022-2-20000000000002-2000000
χ182222222222-2-2-2-2-2-2-2-200000022-2-20000000000-2-222000000000000-22000000
χ192222222222-2-2-2-2-2-2-2-2000000-2-222000000000022-2-2000000000000-22000000
χ202222222222-2-2-2-2-2-2-2-2000000-2-2220000000000-2-2220000000000002-2000000
χ2122222-22-2-2-22222-2-2-2-20000002-22-20000002i2i−2i−2i0000000000002i−2i0000000000
χ2222222-22-2-2-22222-2-2-2-20000002-22-2000000−2i−2i2i2i000000000000−2i2i0000000000
χ2322222-22-2-2-22222-2-2-2-2000000-22-220000002i2i−2i−2i000000000000−2i2i0000000000
χ2422222-22-2-2-22222-2-2-2-2000000-22-22000000−2i−2i2i2i0000000000002i−2i0000000000
χ2522222-22-2-2-2-2-2-2-222220000002-2-220022-2-2000000000000200-2000000000000
χ2622222-22-2-2-2-2-2-2-222220000002-2-2200-2-222000000000000-2002000000000000
χ2722222-22-2-2-2-2-2-2-22222000000-222-20022-2-2000000000000-2002000000000000
χ2822222-22-2-2-2-2-2-2-22222000000-222-200-2-222000000000000200-2000000000000
χ292222-22-2-2-2222-2-2-22-220022-2-20000002-22-2000000000000000000000000002-2
χ302222-22-2-2-2222-2-2-22-220022-2-2000000-22-2200000000000000000000000000-22
χ312222-22-2-2-2222-2-2-22-2200-2-2220000002-22-200000000000000000000000000-22
χ322222-22-2-2-2222-2-2-22-2200-2-222000000-22-22000000000000000000000000002-2
χ332222-2-2-222-2-2-222-22-222200000000-2-22-2-220000000000000000000000002-200
χ342222-2-2-222-2-2-222-22-222200000000-2-2-222-2000000000000000000000000-2200
χ352222-2-2-222-2-2-222-22-22-2-200000000222-2-22000000000000000000000000-2200
χ362222-2-2-222-2-2-222-22-22-2-20000000022-222-20000000000000000000000002-200
χ372-2-2222-22-2-22-22-22-2-222-2000000002-2000000002i−2i2i−2i00000000002i−2i00000000
χ382-2-2222-22-2-22-22-22-2-222-2000000002-200000000−2i2i−2i2i0000000000−2i2i00000000
χ392-2-2222-22-2-22-22-22-2-22-2200000000-22000000002i−2i2i−2i0000000000−2i2i00000000
χ402-2-2222-22-2-22-22-22-2-22-2200000000-2200000000−2i2i−2i2i00000000002i−2i00000000
χ412-2-2222-22-2-2-22-22-222-2002i−2i2i−2i000000000000002i−2i−2i2i000002-20000000000000
χ422-2-2222-22-2-2-22-22-222-2002i−2i2i−2i00000000000000−2i2i2i−2i00000-220000000000000
χ432-2-2222-22-2-2-22-22-222-200−2i2i−2i2i000000000000002i−2i−2i2i00000-220000000000000
χ442-2-2222-22-2-2-22-22-222-200−2i2i−2i2i00000000000000−2i2i2i−2i000002-20000000000000
χ452-2-22-222-22-2-222-222-2-2002i−2i−2i2i00000000002i−2i2i−2i000022-2-20000000000000000
χ462-2-22-222-22-2-222-222-2-2002i−2i−2i2i0000000000−2i2i−2i2i0000-2-2220000000000000000
χ472-2-22-222-22-2-222-222-2-200−2i2i2i−2i00000000002i−2i2i−2i0000-2-2220000000000000000
χ482-2-22-222-22-2-222-222-2-200−2i2i2i−2i0000000000−2i2i−2i2i000022-2-20000000000000000
χ492-2-22-2-222-22-222-2-2-2222-200000000-2200002-2-220000000000000000002-20000
χ502-2-22-2-222-22-222-2-2-2222-200000000-220000-222-2000000000000000000-220000
χ512-2-22-2-222-22-222-2-2-222-22000000002-200002-2-22000000000000000000-220000
χ522-2-22-2-222-22-222-2-2-222-22000000002-20000-222-20000000000000000002-20000
χ534444-44-4-4-44-4-4444-44-400000000000000000000000000000000000000000000
χ544444-4-4-444-444-4-44-44-400000000000000000000000000000000000000000000
χ554-4-444-4-4-4444-44-4-444-400000000000000000000000000000000000000000000
χ564-4-444-4-4-444-44-444-4-4400000000000000000000000000000000000000000000
χ574-4-44-444-44-44-4-44-4-44400000000000000000000000000000000000000000000
χ584-4-44-4-444-444-4-4444-4-400000000000000000000000000000000000000000000
χ5988-8-8000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ6088-8-800000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ618-88-8000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ628-88-800000000000000000000000000000000000000−2i22i22i2−2i20000000000000000

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