Finite Group Databasebeta

← Group #139015

Character table — Group #139015

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12224444448888244488888888888888888881616161616161616444488161616164488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ811111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ91111-111-1-1-1-1-1-1-111-1-111ii−i−i11-1i−iii−i−iii−i−i1111-1-1-1-111-1-1i−iii−i−i1-1i−i
χ101111-111-1-1-1-1-1-1-111-1-111ii−i−i11-1i−iii−i−iii−i−i-1-1-1-1111111-1-1i−i−i−iii-11−ii
χ111111-111-1-1-1-1-1-1-111-1-111ii−i−i11-1i−i−i−iiiii−i−i1111-1-1-1-1-1-111−iiii−i−i-11−ii
χ121111-111-1-1-1-1-1-1-111-1-111ii−i−i11-1i−i−i−iiiii−i−i-1-1-1-11111-1-111−ii−i−iii1-1i−i
χ131111-111-1-1-1-1-1-1-111-1-111−i−iii11-1−iiii−i−i−i−iii1111-1-1-1-1-1-111i−i−i−iii-11i−i
χ141111-111-1-1-1-1-1-1-111-1-111−i−iii11-1−iiii−i−i−i−iii-1-1-1-11111-1-111i−iii−i−i1-1−ii
χ151111-111-1-1-1-1-1-1-111-1-111−i−iii11-1−ii−i−iii−i−iii1111-1-1-1-111-1-1−ii−i−iii1-1−ii
χ161111-111-1-1-1-1-1-1-111-1-111−i−iii11-1−ii−i−iii−i−iii-1-1-1-1111111-1-1−iiii−i−i-11i−i
χ172222222222-2-2-2-22222-2-22222-2-2-2220000-2-2-2-20000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ192222222-2-222222-2-22-2-2-2000022-20000000000000000002-22-20000000000
χ202222222-2-222222-2-22-2-2-2000022-2000000000000000000-22-220000000000
χ212222222-2-22-2-2-2-2-2-22-2220000-2-22002i2i−2i−2i0000000000000000−2i2i00000000
χ222222222-2-22-2-2-2-2-2-22-2220000-2-2200−2i−2i2i2i00000000000000002i−2i00000000
χ2322222-2-22220000-22-2-2002222000-2-20000000022−2−222−2−20000002−22−20000
χ2422222-2-22220000-22-2-2002222000-2-200000000−2−222−2−222000000−22−220000
χ2522222-2-22220000-22-2-200-2-2-2-2000220000000022−2−222−2−2000000−22−220000
χ2622222-2-22220000-22-2-200-2-2-2-20002200000000−2−222−2−2220000002−22−20000
χ272222-22222-22222-2-2-22220000-2-2-20022220000000000000000-2-200000000
χ282222-22222-22222-2-2-22220000-2-2-200-2-2-2-200000000000000002200000000
χ292222-22222-2-2-2-2-2-2-2-22-2-200002220000000000000000002-2-220000000000
χ302222-22222-2-2-2-2-2-2-2-22-2-20000222000000000000000000-222-20000000000
χ312222-222-2-2-2222222-2-2-2-22i2i−2i−2i-2-222i−2i0000−2i−2i2i2i0000000000000000000000
χ322222-222-2-2-2222222-2-2-2-2−2i−2i2i2i-2-22−2i2i00002i2i−2i−2i0000000000000000000000
χ332222-2-2-2-2-2-20000-2222002i2i−2i−2i000−2i2i0000000022−2−2−2−222000000i2−i2−i2i20000
χ342222-2-2-2-2-2-20000-2222002i2i−2i−2i000−2i2i00000000−2−22222−2−2000000−i2i2i2−i20000
χ352222-2-2-2-2-2-20000-222200−2i−2i2i2i0002i−2i0000000022−2−2−2−222000000−i2i2i2−i20000
χ362222-2-2-2-2-2-20000-222200−2i−2i2i2i0002i−2i00000000−2−22222−2−2000000i2−i2−i2i20000
χ3744444-4-4-4-4400004-4-4400000000000000000000000000000000000000000
χ384444-4-4-444-400004-44-400000000000000000000000000000000000000000
χ3944-4-404-400044-4-400000000000000022−2222−2200000000000000000000000000
χ4044-4-404-400044-4-4000000000000000−2222−222200000000000000000000000000
χ4144-4-404-4000-4-4440000000000000002i2−2i2−2i22i200000000000000000000000000
χ4244-4-404-4000-4-444000000000000000−2i22i22i2−2i200000000000000000000000000
χ434-44-440000-422−2222−2200000022−2222−2222−2200000002-22-20000000000000000000000
χ444-44-440000-422−2222−22000000−2222−222222−220000000-22-220000000000000000000000
χ454-44-440000-4−2222−222200000022−2222−22−22220000000-22-220000000000000000000000
χ464-44-440000-4−2222−2222000000−2222−2222−222200000002-22-20000000000000000000000
χ474-44-4-40000422−2222−220000002i2−2i2−2i22i2−22220000000−2i2i2i−2i0000000000000000000000
χ484-44-4-40000422−2222−22000000−2i22i22i2−2i2−222200000002i−2i−2i2i0000000000000000000000
χ494-44-4-400004−2222−22220000002i2−2i2−2i22i222−2200000002i−2i−2i2i0000000000000000000000
χ504-44-4-400004−2222−2222000000−2i22i22i2−2i222−220000000−2i2i2i−2i0000000000000000000000
χ514-4-440004-4022−22−2222000022−2200000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000
χ524-4-440004-4022−22−2222000022−2200000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000
χ534-4-440004-40−222222−220000−222200000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000
χ544-4-440004-40−222222−220000−222200000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000
χ554-4-44000-44022−22−22220000−222200000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000
χ564-4-44000-44022−22−22220000−222200000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000
χ574-4-44000-440−222222−22000022−2200000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000
χ584-4-44000-440−222222−22000022−2200000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000
χ5988-8-80-880000000000000000000000000000000000000000000000000000

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