Finite Group Databasebeta

← Group #259078

Character table — Group #259078

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ91111111111111111-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-1111-1-1-11-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-1-11-111-1-111-1-111
χ111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-111-1111-1-11111-1-1
χ121111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-11-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1111111-1-1111111-1-1-1-111-11-1-1-11-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-11-1-1-111111-1-111-1-1
χ151111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-11111-11111-1-1-1-111
χ161111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-11111-1-1-1-1-11111-1-1
χ172222222222-2-2-222-222-2-2-2-2-222222000000000000000000-2-200000000000000
χ182222222222-2-2-222-222-2-2-2-2-22-2-2-2-20000000000000000002200000000000000
χ192222222222-2-2-222-2-2-222-2-22-222-2-2000000000000000000-2200000000000000
χ202222222222-2-2-222-2-2-222-2-22-2-2-2220000000000000000002-200000000000000
χ2122222222-2-2222-2-222222-2-2-2-200000000222200000000000000-2-20000000000
χ2222222222-2-2222-2-222222-2-2-2-200000000-2-2-2-200000000000000220000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-2220000000022-2-200000000000000-220000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-22200000000-2-222000000000000002-20000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2222-2000022-2-200000000000000002-2000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2222-20000-2-2220000000000000000-22000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-22000022-2-20000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-220000-2-22200000000000000002-2000000000000
χ2922-2-2-222-2222-2-2-2-2200002-20000002i−2i2i−2i000000002i2i−2i−2i000000002-200000000
χ3022-2-2-222-2222-2-2-2-2200002-20000002i−2i2i−2i00000000−2i−2i2i2i00000000-2200000000
χ3122-2-2-222-2222-2-2-2-2200002-2000000−2i2i−2i2i000000002i2i−2i−2i00000000-2200000000
χ3222-2-2-222-2222-2-2-2-2200002-2000000−2i2i−2i2i00000000−2i−2i2i2i000000002-200000000
χ3322-2-2-222-2-2-2-22222-200002-20000002i−2i−2i2i000022-2-200002i−2i0000000000000000
χ3422-2-2-222-2-2-2-22222-200002-20000002i−2i−2i2i0000-2-2220000−2i2i0000000000000000
χ3522-2-2-222-2-2-2-22222-200002-2000000−2i2i2i−2i000022-2-20000−2i2i0000000000000000
χ3622-2-2-222-2-2-2-22222-200002-2000000−2i2i2i−2i0000-2-22200002i−2i0000000000000000
χ372-2-22-22-220022-200-22-22-20000000000002-22-2i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ382-2-22-22-220022-200-22-22-20000000000002-22-2−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ392-2-22-22-220022-200-22-22-2000000000000-22-22i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ402-2-22-22-220022-200-22-22-2000000000000-22-22−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ412-2-22-22-220022-200-2-22-220000000000002-2-22i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i20000
χ422-2-22-22-220022-200-2-22-220000000000002-2-22−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i20000
χ432-2-22-22-220022-200-2-22-22000000000000-222-2i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i20000
χ442-2-22-22-220022-200-2-22-22000000000000-222-2−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i20000
χ45444-4-4-4-444-40004-4000000000000000000000000000000000000000000022−2200
χ46444-4-4-4-444-40004-40000000000000000000000000000000000000000000−222200
χ47444-4-4-4-44-44000-4400000000000000000000000000000000000000000000022−22
χ48444-4-4-4-44-44000-44000000000000000000000000000000000000000000000−2222
χ4944-444-4-4-44-4000-44000000000004-40000000000000000000000000000000000
χ5044-444-4-4-44-4000-4400000000000-440000000000000000000000000000000000
χ5144-444-4-4-4-440004-40000000004-4000000000000000000000000000000000000
χ5244-444-4-4-4-440004-4000000000-44000000000000000000000000000000000000
χ5344-4-4-444-444-444-4-4-40000-440000000000000000000000000000000000000000
χ5444-4-4-444-4-4-44-4-44440000-440000000000000000000000000000000000000000
χ554-44-444-4-4004-4400-400000000000000000000000022−22−2222000000000000000000
χ564-44-444-4-4004-4400-4000000000000000000000000−222222−22000000000000000000
χ574-44-444-4-400-44-4004000000000000000000002i2−2i2−2i22i20000000000000000000000
χ584-44-444-4-400-44-400400000000000000000000−2i22i22i2−2i20000000000000000000000
χ594-4-44-44-4400-4-440044-4-44000000000000000000000000000000000000000000
χ604-4-44-44-4400-4-44004-444-4000000000000000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-88-888000000000000000000000000000000000000000000000000000000

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