Finite Group Databasebeta

← Group #270656

Character table — Group #270656

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444488888888888888888888161616161616161616161616163232
order12222244444422224444444444424444444448888888888222244888888848
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-11-1111-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1111111
χ511111111111111-1-11111-1-1111111-1-11111111-1-11111-1-1-1-1-111-1-1-1-1-1-111-1-11-1
χ611111111111111-1-11111-1-1111111-1-11111111-1-1-1-1-1-11111-1-1-11-11-1-1-1-1-111-11
χ711111111111111-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1111-1-111-11
χ811111111111111-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-11-1111111-1-11-1
χ9111111111111-1-11111-1-11111111-111-111-1-1-1-11111111111-1-1-1-1-1-11-1-11111-1-1
χ10111111111111-1-11111-1-11111111-111-111-1-1-1-111-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-111
χ11111111111111-1-11111-1-111-1-1-1-11-111-1-1-11111-1-111111111-1-1-1-1-1-1-111-1-1-1-111
χ12111111111111-1-11111-1-111-1-1-1-11-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11-1111111-1-1
χ13111111111111-1-1-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1111-11111-1-1-11
χ14111111111111-1-1-1-111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-11-1-111-1-1111-1
χ15111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111-1-1-1-11-1-11111-1-1-1-1111-1
χ16111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-11111111-11-11-1-111-1-1-11
χ17222222222-2-220022-2-200222222-20-2-20-2-200002200000000000000-200000000
χ18222222222-2-220022-2-20022-2-2-2-2-20-2-20220000-2-200000000000000200000000
χ19222222222-2-2200-2-2-2-200-2-22222-20220-2-20000-2-200000000000000200000000
χ20222222222-2-2200-2-2-2-200-2-2-2-2-2-2-202202200002200000000000000-200000000
χ21222222-2-2-222-222002-2-2-2000000-2200-20000000022-2-2000002-2000000000000
χ22222222-2-2-222-222002-2-2-2000000-2200-200000000-2-22200000-22000000000000
χ23222222-2-2-222-2-2-2002-222000000-2-20020000000022-2-200000-22000000000000
χ24222222-2-2-222-2-2-2002-222000000-2-200200000000-2-222000002-2000000000000
χ252222-2-22-2222-22222-2-2-2-2-2-200002-22-2200000000000000002000-20000000000
χ262222-2-22-2222-222-2-2-2-2-2-22200002-2-2220000000000000000-200020000000000
χ272222-2-22-2222-2-2-222-2-222-2-20000222-2-20000000000000000-200020000000000
χ282222-2-22-2222-2-2-2-2-2-2-22222000022-22-200000000000000002000-20000000000
χ292222-2-22-22-2-2-200222200-2-20000-20-220002i2i−2i−2i000000000000000002i−2i000000
χ302222-2-22-22-2-2-200222200-2-20000-20-22000−2i−2i2i2i00000000000000000−2i2i000000
χ312222-2-22-22-2-2-200-2-22200220000-202-20002i2i−2i−2i00000000000000000−2i2i000000
χ322222-2-22-22-2-2-200-2-22200220000-202-2000−2i−2i2i2i000000000000000002i−2i000000
χ332222-2-2-22-22222200-2222000000-2-200-200000000000022-2-200020-2000000000
χ342222-2-2-22-22222200-2222000000-2-200-2000000000000-2-222000-202000000000
χ352222-2-2-22-2222-2-200-22-2-2000000-2200200000000000022-2-2000-202000000000
χ362222-2-2-22-2222-2-200-22-2-2000000-22002000000000000-2-22200020-2000000000
χ372-2-222-222-200-2002-200002-22i2i−2i−2i000000000002i−2i2−22−22−22−2000000000i2−i2i2−i200
χ382-2-222-222-200-2002-200002-22i2i−2i−2i000000000002i−2i−22−22−22−22000000000−i2i2−i2i200
χ392-2-222-222-200-2002-200002-2−2i−2i2i2i00000000000−2i2i2−22−22−22−2000000000−i2i2−i2i200
χ402-2-222-222-200-2002-200002-2−2i−2i2i2i00000000000−2i2i−22−22−22−22000000000i2−i2i2−i200
χ412-2-222-222-200-200-220000-222i2i−2i−2i00000000000−2i2i2−22−2−22−22000000000i2−i2−i2i200
χ422-2-222-222-200-200-220000-222i2i−2i−2i00000000000−2i2i−22−222−22−2000000000−i2i2i2−i200
χ432-2-222-222-200-200-220000-22−2i−2i2i2i000000000002i−2i2−22−2−22−22000000000−i2i2i2−i200
χ442-2-222-222-200-200-220000-22−2i−2i2i2i000000000002i−2i−22−222−22−2000000000i2−i2−i2i200
χ45444444-4-4-4-4-4-40000-4400000000400000000000000000000000000000000000
χ464444-4-4-44-4-4-4400004-400000000400000000000000000000000000000000000
χ4744-4-4000004-400000004i−4i002i−2i2i−2i000002i−2i2-22-20000000000000000000000000
χ4844-4-4000004-400000004i−4i00−2i2i−2i2i00000−2i2i-22-220000000000000000000000000
χ4944-4-4000004-40000000−4i4i002i−2i2i−2i000002i−2i-22-220000000000000000000000000
χ5044-4-4000004-40000000−4i4i00−2i2i−2i2i00000−2i2i2-22-20000000000000000000000000
χ5144-4-400000-4404-4000000002i−2i2i−2i00000−2i2i2i−2i−2i2i0000000000000000000000000
χ5244-4-400000-4404-400000000−2i2i−2i2i000002i−2i−2i2i2i−2i0000000000000000000000000
χ5344-4-400000-440-44000000002i−2i2i−2i00000−2i2i−2i2i2i−2i0000000000000000000000000
χ5444-4-400000-440-4400000000−2i2i−2i2i000002i−2i2i−2i−2i2i0000000000000000000000000
χ554-4-444-4-4-4400400000000000000000000000000022−22−22220000000000000000000
χ564-4-444-4-4-44004000000000000000000000000000−222222−220000000000000000000
χ574-4-44-444-4-4004004-40000-440000000000000000000000000000000000000000
χ584-4-44-444-4-400400-4400004-40000000000000000000000000000000000000000
χ594-4-44-44-44400-4000000000000000000000000000000022−22−2222000000000000000
χ604-4-44-44-44400-40000000000000000000000000000000−222222−22000000000000000
χ618-88-80000000000000000004-4-44000000000000000000000000000000000000
χ628-88-8000000000000000000-444-4000000000000000000000000000000000000

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