Finite Group Databasebeta

← Group #143641

Character table — Group #143641

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222222244444444888888888888888881616161616161616323232323232
order12224444448888244488888888888881616161616161616888816161616444444
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111
χ511111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ92222222222-2-2-2-22222-2-2-2-2-22222-2-2-2-20000000000000000000000
χ102222222222-2-2-2-22222-2-2-2-2-2-2-2-2-222220000000000000000000000
χ1122222222-2-20000-2-2-220000022-2-200002222−2−2−2−2000022−2−2000000
χ1222222222-2-20000-2-2-220000022-2-20000−2−2−2−222220000−2−222000000
χ1322222222-2-20000-2-2-2200000-2-22200002222−2−2−2−20000−2−222000000
χ1422222222-2-20000-2-2-2200000-2-2220000−2−2−2−22222000022−2−2000000
χ15222222-2-2222222-22-2-2-2-222-2000000000000000000000000020-200
χ16222222-2-2222222-22-2-2-2-222-20000000000000000000000000-20200
χ17222222-2-222-2-2-2-2-22-2-222-2-2200000000000000002i2i−2i−2i0000000000
χ18222222-2-222-2-2-2-2-22-2-222-2-220000000000000000−2i−2i2i2i0000000000
χ192222-2-222222222-2-22-222-2-2-200000000000000000000000020-2000
χ202222-2-222222222-2-22-222-2-2-2000000000000000000000000-202000
χ212222-2-22222-2-2-2-2-2-22-2-2-222200000000000000000000000000002-2
χ222222-2-22222-2-2-2-2-2-22-2-2-22220000000000000000000000000000-22
χ232222-2-2-2-22222222-2-22-2-2-2-22000000000000000000002-22-2000000
χ242222-2-2-2-22222222-2-22-2-2-2-2200000000000000000000-22-22000000
χ252222-2-2-2-222-2-2-2-22-2-222222-20000000022-2-222-2-200000000000000
χ262222-2-2-2-222-2-2-2-22-2-222222-200000000-2-222-2-22200000000000000
χ272222-2-2-2-2-2-20000-222200000000022-2-222−2−2−2−22200002−2−22000000
χ282222-2-2-2-2-2-20000-222200000000022-2-2−2−22222−2−20000−222−2000000
χ292222-2-2-2-2-2-20000-2222000000000-2-22222−2−2−2−2220000−222−2000000
χ302222-2-2-2-2-2-20000-2222000000000-2-222−2−22222−2−200002−2−22000000
χ31444444-4-4-4-400004-44-400000000000000000000000000000000000
χ324444-4-444-4-4000044-4-400000000000000000000000000000000000
χ3344-4-4004-40022−2222−22000022−2200000000000ζ+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
χ3444-4-4004-40022−2222−22000022−2200000000000−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
χ3544-4-4004-400−2222−22220000−222200000000000ζ−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
χ3644-4-4004-400−2222−22220000−222200000000000−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
χ3744-4-400-440022−2222−220000−222200000000000ζ−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
χ3844-4-400-440022−2222−220000−222200000000000−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
χ3944-4-400-4400−2222−2222000022−2200000000000ζ+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
χ4044-4-400-4400−2222−2222000022−2200000000000−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
χ414-44-400004-444-4-400000000000000000000000002-22-20000000000
χ424-44-400004-444-4-40000000000000000000000000-22-220000000000
χ434-44-400004-4-4-44400000000000000000000000002i−2i−2i2i0000000000
χ444-44-400004-4-4-4440000000000000000000000000−2i2i2i−2i0000000000
χ454-4-444-4000022−22−222200000022−220002i2−2i22i−2i2i−2i0000000000000000000000
χ464-4-444-4000022−22−222200000022−22000−2i22i2−2i2i−2i2i0000000000000000000000
χ474-4-444-40000−222222−22000000−22220002i2−2i2−2i2i−2i2i0000000000000000000000
χ484-4-444-40000−222222−22000000−2222000−2i22i22i−2i2i−2i0000000000000000000000
χ494-4-44-44000022−22−2222000000−222202i2−2i2002i−2i−2i2i0000000000000000000000
χ504-4-44-44000022−22−2222000000−22220−2i22i200−2i2i2i−2i0000000000000000000000
χ514-4-44-440000−222222−2200000022−2202i2−2i200−2i2i2i−2i0000000000000000000000
χ524-4-44-440000−222222−2200000022−220−2i22i2002i−2i−2i2i0000000000000000000000
χ538-88-80000-880000000000000000000000000000000000000000000

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