Finite Group Databasebeta

← Group #143592

Character table — Group #143592

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222222244444444888888888888888881616161616161616323232323232
order122244444488882444888881616161616161616161616161616161644888888244488
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ611111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ92222222222-2-2-2-22222-2-2-2-2-20000000000000000220000-2-2000000
χ102222222222-2-2-2-22222-2-2-2-2-20000000000000000-2-2000022000000
χ11222222-2-2222222-2-2-2222-2-2-20000000000000000000000002-20000
χ12222222-2-2222222-2-2-2222-2-2-2000000000000000000000000-220000
χ13222222-2-222-2-2-2-2-2-2-22-2-222200000000000000000000000000002-2
χ14222222-2-222-2-2-2-2-2-2-22-2-22220000000000000000000000000000-22
χ1522222-222-220000-22-2-2000002222−2−2−2−22222−2−2−2−22-2000000000000
χ1622222-222-220000-22-2-2000002222−2−2−2−2−2−2−2−22222-22000000000000
χ1722222-222-220000-22-2-200000−2−2−2−222222222−2−2−2−2-22000000000000
χ1822222-222-220000-22-2-200000−2−2−2−22222−2−2−2−222222-2000000000000
χ192222-22222-22222-2-22-2-2-222-200000000000000000022-2-200000000
χ202222-22222-22222-2-22-2-2-222-2000000000000000000-2-22200000000
χ212222-22222-2-2-2-2-2-2-22-222-2-22000000000000000000000000002-200
χ222222-22222-2-2-2-2-2-2-22-222-2-2200000000000000000000000000-2200
χ232222-22-2-22-2222222-2-2-2-2-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ242222-22-2-22-2222222-2-2-2-2-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ252222-22-2-22-2-2-2-2-222-2-22222-20000000022-2-222-2-200000000000000
χ262222-22-2-22-2-2-2-2-222-2-22222-200000000-2-222-2-22200000000000000
χ272222-2-2-2-2-2-20000-222200000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000002i−2i000000
χ282222-2-2-2-2-2-20000-222200000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000−2i2i000000
χ292222-2-2-2-2-2-20000-222200000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000−2i2i000000
χ302222-2-2-2-2-2-20000-222200000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000002i−2i000000
χ3144444-4-4-4-4400004-44-400000000000000000000000000000000000
χ324444-4-444-4-400004-4-4400000000000000000000000000000000000
χ3344-4-40400-4044-4-40000000000000000000000000000022−2200000000
χ3444-4-40400-4044-4-400000000000000000000000000000−222200000000
χ3544-4-40400-40-4-44400000000000000000000000000022−220000000000
χ3644-4-40400-40-4-444000000000000000000000000000−22220000000000
χ374-44-440000-422−2222−22000022−22000ζ+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+ζ70000000000000000000000
χ384-44-440000-422−2222−22000022−22000−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−ζ70000000000000000000000
χ394-44-440000-4−2222−22220000−2222000ζ−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−ζ70000000000000000000000
χ404-44-440000-4−2222−22220000−2222000−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+ζ70000000000000000000000
χ414-44-4-40000422−2222−220000−2222000ζ+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−ζ70000000000000000000000
χ424-44-4-40000422−2222−220000−2222000−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+ζ70000000000000000000000
χ434-44-4-400004−2222−2222000022−22000ζ−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+ζ70000000000000000000000
χ444-44-4-400004−2222−2222000022−22000−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−ζ70000000000000000000000
χ454-4-44004-40022−22−222200000022−22000000000ζ−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
χ464-4-44004-40022−22−222200000022−22000000000−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
χ474-4-44004-400−222222−22000000−2222000000000ζ+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
χ484-4-44004-400−222222−22000000−2222000000000−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
χ494-4-4400-440022−22−2222000000−2222000000000ζ+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
χ504-4-4400-440022−22−2222000000−2222000000000−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
χ514-4-4400-4400−222222−2200000022−22000000000ζ−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
χ524-4-4400-4400−222222−2200000022−22000000000−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
χ5388-8-80-800800000000000000000000000000000000000000000000

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