Finite Group Databasebeta

← Group #492586

Character table — Group #492586

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444488888888888888888888816161616161616161632323232
order122244448888224888888161616162222444888816161616161616161616448888816162244
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-111111111111111111-1-11-1-1-1-111-1-1-1-1
χ3111111111111111111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11-11-1
χ4111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11-11
χ5111111111111111-1-1-1-111111111111-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-111-1-1
χ6111111111111111-1-1-1-1111111-1-1-1-11-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-111-1-1-1-111-1-11-1-111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-11
χ8111111111111111-1-1-1-111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111-11-111-1-111-111-1
χ9111111111111-1-1111111111111111-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1-1
χ10111111111111-1-111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-11111
χ11111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111-11-11
χ12111111111111-1-11111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-11-1-1-111111-11-1
χ13111111111111-1-11-1-1-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-111-1-111
χ14111111111111-1-11-1-1-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ15111111111111-1-11-1-1-1-111-1-1-1-111-1-1-111-1-1-1-1-1-1111111111-11-1-111-1-1-111-1
χ16111111111111-1-11-1-1-1-111-1-1-1-1-1-111-111-1-1-1-1-1-111111111-11111-1-1-1-11-1-11
χ1722222222-2-2-2-22222222-2-200000000222-2-2-2-2000000000000-20000000000
χ1822222222-2-2-2-2222-2-2-2-2-2-2000000002-2-2-2-22200000000000020000000000
χ1922222222-2-2-2-2-2-222222-2-200000000-2-2-222-2-200000000000020000000000
χ2022222222-2-2-2-2-2-22-2-2-2-2-2-200000000-2222222000000000000-20000000000
χ21222222-2-2222200-20000-2-2222222220000000-2-200000000-2-200000000000
χ22222222-2-2222200-20000-2-22222-2-2-2-20000000-2-2000000002200000000000
χ23222222-2-2222200-20000-2-2-2-2-2-222-2-200000002200000000-2200000000000
χ24222222-2-2222200-20000-2-2-2-2-2-2-2-222000000022000000002-200000000000
χ252222-2-222000022-222-2-20022−2−20000-22-200002−222−2−222−2−200000002−20000
χ262222-2-222000022-222-2-200−2−2220000-22-20000−22−2−222−2−2220000000−220000
χ272222-2-222000022-2-2-2220022−2−20000-2-2200002−222−2−2−2−2220000000−220000
χ282222-2-222000022-2-2-22200−2−2220000-2-220000−22−2−22222−2−200000002−20000
χ292222-2-2220000-2-2-222-2-20022−2−200002-2200002−2−2−22222−2−20000000−220000
χ302222-2-2220000-2-2-222-2-200−2−22200002-220000−2222−2−2−2−22200000002−20000
χ312222-2-2220000-2-2-2-2-2220022−2−2000022-200002−2−2−222−2−22200000002−20000
χ322222-2-2220000-2-2-2-2-22200−2−222000022-20000−2222−2−222−2−20000000−220000
χ3322-2-22-20022-2-2000i2−i2i2−i2002-22-22-22-200000i2−i2000000i2−i2i2−i2000i2−i2i2−i2000000
χ3422-2-22-20022-2-2000i2−i2i2−i2002-22-2-22-2200000i2−i2000000i2−i2i2−i2000−i2i2−i2i2000000
χ3522-2-22-20022-2-2000i2−i2i2−i200-22-222-2-2200000i2−i2000000−i2i2−i2i2000i2−i2−i2i2000000
χ3622-2-22-20022-2-2000i2−i2i2−i200-22-22-222-200000i2−i2000000−i2i2−i2i2000−i2i2i2−i2000000
χ3722-2-22-20022-2-2000−i2i2−i2i2002-22-22-22-200000−i2i2000000−i2i2−i2i2000−i2i2−i2i2000000
χ3822-2-22-20022-2-2000−i2i2−i2i2002-22-2-22-2200000−i2i2000000−i2i2−i2i2000i2−i2i2−i2000000
χ3922-2-22-20022-2-2000−i2i2−i2i200-22-222-2-2200000−i2i2000000i2−i2i2−i2000−i2i2i2−i2000000
χ4022-2-22-20022-2-2000−i2i2−i2i200-22-22-222-200000−i2i2000000i2−i2i2−i2000i2−i2−i2i2000000
χ41444444-4-4-4-4-4-400-400004400000000000000000000000000000000000000
χ424444-4-4-4-400000040000002222−22−2200000000000−2222000000000000000000000
χ434444-4-4-4-40000004000000−22−2222220000000000022−22000000000000000000000
χ4444-4-44-400-4-4440002i2−2i22i2−2i2000000000000000−2i22i200000000000000000000000
χ4544-4-44-400-4-444000−2i22i2−2i22i20000000000000002i2−2i200000000000000000000000
χ4644-4-4-440000000002i2−2i2−2i22i20022−22−2222000000000000000002i−2i−2i2i0000000000000
χ4744-4-4-440000000002i2−2i2−2i22i200−222222−2200000000000000000−2i2i2i−2i0000000000000
χ4844-4-4-44000000000−2i22i22i2−2i20022−22−222200000000000000000−2i2i2i−2i0000000000000
χ4944-4-4-44000000000−2i22i22i2−2i200−222222−22000000000000000002i−2i−2i2i0000000000000
χ504-4-44004-422−2222−22000000022−22000000000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000
χ514-4-44004-422−2222−22000000022−2200000000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000
χ524-4-44004-4−2222−22220000000−2222000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000
χ534-4-44004-4−2222−22220000000−222200000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000
χ544-4-4400-4422−2222−224-400000−22220000000000022−220000000000000000000000000
χ554-4-4400-4422−2222−22-4400000−222200000000000−22220000000000000000000000000
χ564-4-4400-44−2222−22224-40000022−2200000000000−22220000000000000000000000000
χ574-4-4400-44−2222−2222-440000022−220000000000022−220000000000000000000000000
χ588-88-8000042−42−424200000000000000000000000000000000000000000000000
χ598-88-80000−424242−4200000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.