Finite Group Databasebeta

← Group #318576

Character table — Group #318576

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444448888888888882222444488888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-111-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-11-11-1-111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-11-111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-11-11-1-11111-1-1
χ91111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ101111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11-11
χ121111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111111-11-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-11-1111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111-11-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-11-1111-1-11-1-11
χ172222222-2-22-2-222-2-22222000000002222-2-2-2-200000000-2-20000000000000000
χ182222222-2-22-2-222-2-2222200000000-2-2-2-2222200000000-2-20000000000000000
χ192222222-2-22-2-222-2-2-2-2-2-20000000022-2-2-2-22200000000220000000000000000
χ202222222-2-22-2-222-2-2-2-2-2-200000000-2-22222-2-200000000220000000000000000
χ21222222-222-222-2-2-2-200002222-2-2-2-2000000000000000000000000002i−2i2i−2i0000
χ22222222-222-222-2-2-2-200002222-2-2-2-200000000000000000000000000−2i2i−2i2i0000
χ23222222-222-222-2-2-2-20000-2-2-2-22222000000000000000000000000002i−2i−2i2i0000
χ24222222-222-222-2-2-2-20000-2-2-2-2222200000000000000000000000000−2i2i2i−2i0000
χ252222-2-22-2-2-222-222-2000022-2-222-2-2000000000000000000000022-2-200000000
χ262222-2-22-2-2-222-222-2000022-2-222-2-20000000000000000000000-2-22200000000
χ272222-2-22-2-2-222-222-20000-2-222-2-22200000000000000000000002-2-2200000000
χ282222-2-22-2-2-222-222-20000-2-222-2-2220000000000000000000000-222-200000000
χ292222-2-2-2222-2-22-22-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i2-20000000000000000
χ302222-2-2-2222-2-22-22-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i2-20000000000000000
χ312222-2-2-2222-2-22-22-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i-220000000000000000
χ322222-2-2-2222-2-22-22-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i-220000000000000000
χ332222-2-2-2-2-22222-2-2222-2-222-2-2-2-2220000000000000000-2222-2-2000000000000
χ342222-2-2-2-2-22222-2-2222-2-2-2-22222-2-20000000000000000-22-2-222000000000000
χ352222-2-2-2-2-22222-2-22-2-22222-2-2-2-22200000000000000002-2-2-222000000000000
χ362222-2-2-2-2-22222-2-22-2-222-2-22222-2-200000000000000002-222-2-2000000000000
χ3722-2-22-2200200-2-2002-22-22−22−22−22−22-22-200002−22−22−22−2002−22−2000000000000
χ3822-2-22-2200200-2-2002-22-22−22−22−22−2-22-220000−22−22−22−22002−22−2000000000000
χ3922-2-22-2200200-2-2002-22-2−22−22−22−222-22-20000−22−22−22−2200−22−22000000000000
χ4022-2-22-2200200-2-2002-22-2−22−22−22−22-22-2200002−22−22−22−200−22−22000000000000
χ4122-2-22-2200200-2-200-22-222−22−22−22−22-2-2200002−22−2−22−2200−22−22000000000000
χ4222-2-22-2200200-2-200-22-222−22−22−22−2-222-20000−22−222−22−200−22−22000000000000
χ4322-2-22-2200200-2-200-22-22−22−22−22−222-2-220000−22−222−22−2002−22−2000000000000
χ4422-2-22-2200200-2-200-22-22−22−22−22−22-222-200002−22−2−22−22002−22−2000000000000
χ4522-2-2-22-200200-22002-2-222−2−22−222−200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2002−2−22000000000000
χ4622-2-2-22-200200-22002-2-222−2−22−222−20000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2002−2−22000000000000
χ4722-2-2-22-200200-22002-2-22−222−22−2−2200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200−222−2000000000000
χ4822-2-2-22-200200-22002-2-22−222−22−2−220000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200−222−2000000000000
χ4922-2-2-22-200200-2200-222-22−2−22−222−200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i200−222−2000000000000
χ5022-2-2-22-200200-2200-222-22−2−22−222−20000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i200−222−2000000000000
χ5122-2-2-22-200200-2200-222-2−222−22−2−2200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i2002−2−22000000000000
χ5222-2-2-22-200200-2200-222-2−222−22−2−220000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2002−2−22000000000000
χ53444444-4-4-4-4-4-4-4-4440000000000000000000000000000000000000000000000
χ544444-4-4444-4-4-4-44-440000000000000000000000000000000000000000000000
χ5544-4-44-4-400-4004400000022−2222−22−2222−22220000000000000000000000000000000000
χ5644-4-44-4-400-40044000000−2222−222222−2222−220000000000000000000000000000000000
χ5744-4-4-44400-4004-400000022−22−222222−22−22220000000000000000000000000000000000
χ5844-4-4-44400-4004-4000000−222222−22−222222−220000000000000000000000000000000000
χ598-88-80008i−8i00000000000000000000000000000000000000000000000000000
χ608-88-8000−8i8i00000000000000000000000000000000000000000000000000000
χ618-8-880000008-800000000000000000000000000000000000000000000000000
χ628-8-88000000-8800000000000000000000000000000000000000000000000000

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