Finite Group Databasebeta

← Group #318570

Character table — Group #318570

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444448888888888882244444488888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ101111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-11-11
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-11111-1-11-1-11
χ172222222-2-22-22-22-2-20000222200002222-2-2-2-2-2-2000000000000000000000000
χ182222222-2-22-22-22-2-2000022220000-2-2-2-22222-2-2000000000000000000000000
χ192222222-2-22-22-22-2-20000-2-2-2-2000022-2-2-2-22222000000000000000000000000
χ202222222-2-22-22-22-2-20000-2-2-2-20000-2-22222-2-222000000000000000000000000
χ21222222-222-22-22-2-2-222220000-2-2-2-2000000000000000000000000002i−2i2i−2i0000
χ22222222-222-22-22-2-2-222220000-2-2-2-200000000000000000000000000−2i2i−2i2i0000
χ23222222-222-22-22-2-2-2-2-2-2-200002222000000000000000000000000002i−2i−2i2i0000
χ24222222-222-22-22-2-2-2-2-2-2-20000222200000000000000000000000000−2i2i2i−2i0000
χ252222-2-22-2-2-22-2222-222-2-2000022-2-200000000000000000000002-22-200000000
χ262222-2-22-2-2-22-2222-222-2-2000022-2-20000000000000000000000-22-2200000000
χ272222-2-22-2-2-22-2222-2-2-2220000-2-22200000000000000000000002-2-2200000000
χ282222-2-22-2-2-22-2222-2-2-2220000-2-2220000000000000000000000-222-200000000
χ292222-2-2-2222-22-2-22-2000022-2-20000000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000
χ302222-2-2-2222-22-2-22-2000022-2-20000000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-2-2222-22-2-22-20000-2-222000000000000-222i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2222-22-2-22-20000-2-222000000000000-22−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2-22222-2-2222-2-222-2-2-2-22200000000-220000000022-2-2000000000000
χ342222-2-2-2-2-22222-2-2222-2-2-2-222-2-222000000002-200000000-2-222000000000000
χ352222-2-2-2-2-22222-2-22-2-22222-2-222-2-200000000-2200000000-2-222000000000000
χ362222-2-2-2-2-22222-2-22-2-222-2-22222-2-2000000002-20000000022-2-2000000000000
χ3722-2-22-220020-20-2002−22−22-22-22−22−22-22-20000002−22−22−22−22−22−2000000000000
χ3822-2-22-220020-20-2002−22−22-22-22−22−2-22-22000000−22−22−22−222−22−2000000000000
χ3922-2-22-220020-20-2002−22−2-22-222−22−22-2-220000002−22−2−22−22−22−22000000000000
χ4022-2-22-220020-20-2002−22−2-22-222−22−2-222-2000000−22−222−22−2−22−22000000000000
χ4122-2-22-220020-20-200−22−222-22-2−22−222-22-2000000−22−22−22−22−22−22000000000000
χ4222-2-22-220020-20-200−22−222-22-2−22−22-22-220000002−22−22−22−2−22−22000000000000
χ4322-2-22-220020-20-200−22−22-22-22−22−222-2-22000000−22−222−22−22−22−2000000000000
χ4422-2-22-220020-20-200−22−22-22-22−22−22-222-20000002−22−2−22−222−22−2000000000000
χ4522-2-2-22-20020-202002−2−222-2-22−222−200002i−2i2i−2i00i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ4622-2-2-22-20020-202002−2−222-2-22−222−20000−2i2i−2i2i00−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ4722-2-2-22-20020-202002−2−22-222-2−222−200002i−2i−2i2i00i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ4822-2-2-22-20020-202002−2−22-222-2−222−20000−2i2i2i−2i00−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ4922-2-2-22-20020-20200−222−22-2-222−2−2200002i−2i2i−2i00−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ5022-2-2-22-20020-20200−222−22-2-222−2−220000−2i2i−2i2i00i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ5122-2-2-22-20020-20200−222−2-222-22−2−2200002i−2i−2i2i00−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ5222-2-2-22-20020-20200−222−2-222-22−2−220000−2i2i2i−2i00i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ53444444-4-4-4-4-4-4-4-4440000000000000000000000000000000000000000000000
χ544444-4-4444-4-4-4-44-440000000000000000000000000000000000000000000000
χ5544-4-44-4-400-404040022−2222−220000−2222−22220000000000000000000000000000000000
χ5644-4-44-4-400-4040400−2222−2222000022−2222−220000000000000000000000000000000000
χ5744-4-4-44400-4040-40022−22−2222000022−22−22220000000000000000000000000000000000
χ5844-4-4-44400-4040-400−222222−220000−222222−220000000000000000000000000000000000
χ598-88-800000080-80000000000000000000000000000000000000000000000000
χ608-88-8000000-8080000000000000000000000000000000000000000000000000
χ618-8-880008i−8i00000000000000000000000000000000000000000000000000000
χ628-8-88000−8i8i00000000000000000000000000000000000000000000000000000

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