Finite Group Databasebeta

← Group #492790

Character table — Group #492790

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444488888888888888888888816161616161616161632323232
order122244448888444888888161616164444444888816161616161616161616448888816164444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-111111111111111111-1-11-1-1-1-111-1-1-1-1
χ3111111111111111111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1
χ4111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ5111111111111111-1-1-1-11111111111-11-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1
χ6111111111111111-1-1-1-1111111-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1-11111-1-11-1-11
χ7111111111111111-1-1-1-111-1-1-1-111-1-1-11-111-1-1-1-1-1-1-1-111111-1-1-1-11111-11-11
χ8111111111111111-1-1-1-111-1-1-1-1-1-111-11-111-1-1-1-1-1-1-1-11111-11-111-1-1111-11-1
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
χ11111111111111-1-11111111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-111-1-111-1-111
χ12111111111111-1-11111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-11-1-1-1111111-1-1
χ13111111111111-1-11-1-1-1-111111111111-11-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11
χ14111111111111-1-11-1-1-1-1111111-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-111-1
χ15111111111111-1-11-1-1-1-111-1-1-1-111-1-11-11-1-1-1-1-1-1111111111-11-1-111-1-11-11-1
χ16111111111111-1-11-1-1-1-111-1-1-1-1-1-1111-11-1-1-1-1-1-111111111-11111-1-1-1-1-11-11
χ1722222222-2-2-2-22222222-2-200000000222-2-2-2-2000000000000-20000000000
χ1822222222-2-2-2-2222-2-2-2-2-2-200000000-22-2-2-22200000000000020000000000
χ1922222222-2-2-2-2-2-222222-2-200000000-2-2-222-2-200000000000020000000000
χ2022222222-2-2-2-2-2-22-2-2-2-2-2-2000000002-222222000000000000-20000000000
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
χ252222-2-222000022-222-2-20022−2−200002-2-200002−222−2−222−2−200000002−20000
χ262222-2-222000022-222-2-200−2−22200002-2-20000−22−2−222−2−2220000000−220000
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
χ292222-2-2220000-2-2-222-2-20022−2−20000-22200002−2−2−22222−2−20000000−220000
χ302222-2-2220000-2-2-222-2-200−2−2220000-2220000−2222−2−2−2−22200000002−20000
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
χ3322-2-22-20022-2-20002−22−2002-22-22-22-2000002−20000002−22−20002−22−2000000
χ3422-2-22-20022-2-20002−22−2002-22-2-22-22000002−20000002−22−2000−22−22000000
χ3522-2-22-20022-2-20002−22−200-22-222-2-22000002−2000000−22−220002−2−22000000
χ3622-2-22-20022-2-20002−22−200-22-22-222-2000002−2000000−22−22000−222−2000000
χ3722-2-22-20022-2-2000−22−22002-22-22-22-200000−22000000−22−22000−22−22000000
χ3822-2-22-20022-2-2000−22−22002-22-2-22-2200000−22000000−22−220002−22−2000000
χ3922-2-22-20022-2-2000−22−2200-22-222-2-2200000−220000002−22−2000−222−2000000
χ4022-2-22-20022-2-2000−22−2200-22-22-222-200000−220000002−22−20002−2−22000000
χ41444444-4-4-4-4-4-400-400004400000000000000000000000000000000000000
χ424444-4-4-4-400000040000002222−22−2200000000000−2222000000000000000000000
χ434444-4-4-4-40000004000000−22−2222220000000000022−22000000000000000000000
χ4444-4-44-400-4-44400022−2222−22000000000000000−222200000000000000000000000
χ4544-4-44-400-4-444000−2222−222200000000000000022−2200000000000000000000000
χ4644-4-4-4400000000022−22−22220022−22−2222000000000000000002-2-220000000000000
χ4744-4-4-4400000000022−22−222200−222222−2200000000000000000-222-20000000000000
χ4844-4-4-44000000000−222222−220022−22−222200000000000000000-222-20000000000000
χ4944-4-4-44000000000−222222−2200−222222−22000000000000000002-2-220000000000000
χ504-4-44004-422−2222−22000000022−22000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000
χ514-4-44004-422−2222−22000000022−2200000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000
χ524-4-44004-4−2222−22220000000−2222000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000
χ534-4-44004-4−2222−22220000000−222200000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000
χ544-4-4400-4422−2222−224i−4i00000−2222000000000002i2−2i20000000000000000000000000
χ554-4-4400-4422−2222−22−4i4i00000−222200000000000−2i22i20000000000000000000000000
χ564-4-4400-44−2222−22224i−4i0000022−2200000000000−2i22i20000000000000000000000000
χ574-4-4400-44−2222−2222−4i4i0000022−22000000000002i2−2i20000000000000000000000000
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.