Finite Group Databasebeta

← Group #145334

Character table — Group #145334

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111222222222244444444888888888888888881616161616161616323232323232
order122244444488882444888881616161616161616161616161616161644888888248888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ92222222222-2-2-2-22222-2-2-2-2-2000000000000000022-2-20000000000
χ102222222222-2-2-2-22222-2-2-2-2-20000000000000000-2-2220000000000
χ112222222-22-22222-22-2-222-2-2-200000000000000000000000000002i−2i
χ122222222-22-22222-22-2-222-2-2-20000000000000000000000000000−2i2i
χ132222222-22-2-2-2-2-2-22-2-2-2-2222000000000000000000002i2i−2i−2i000000
χ142222222-22-2-2-2-2-2-22-2-2-2-222200000000000000000000−2i−2i2i2i000000
χ15222222-2-2-2-20000-2-22200000i2i2i2i2−i2−i2−i2−i22222−2−2−2−2002i−2i0000000000
χ16222222-2-2-2-20000-2-22200000i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200−2i2i0000000000
χ17222222-2-2-2-20000-2-22200000−i2−i2−i2−i2i2i2i2i22222−2−2−2−200−2i2i0000000000
χ18222222-2-2-2-20000-2-22200000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222002i−2i0000000000
χ192222-2-222222222-2-22-2-2-222-2000000000000000000000000002-200
χ202222-2-222222222-2-22-2-2-222-200000000000000000000000000-2200
χ212222-2-22222-2-2-2-2-2-22-222-2-220000000000000000000000002-20000
χ222222-2-22222-2-2-2-2-2-22-222-2-22000000000000000000000000-220000
χ232222-2-22-22-222222-2-22-2-2-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ242222-2-22-22-222222-2-22-2-2-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ252222-2-22-22-2-2-2-2-22-2-222222-20000000022-2-222-2-200000000000000
χ262222-2-22-22-2-2-2-2-22-2-222222-200000000-2-222-2-22200000000000000
χ272222-2-2-22-220000-22-220000022−2−2−2−22222−2−2−2−2222-2000000000000
χ282222-2-2-22-220000-22-220000022−2−2−2−222−2−22222−2−2-22000000000000
χ292222-2-2-22-220000-22-2200000−2−22222−2−222−2−2−2−222-22000000000000
χ302222-2-2-22-220000-22-2200000−2−22222−2−2−2−22222−2−22-2000000000000
χ31444444-44-4400004-4-4-400000000000000000000000000000000000
χ324444-4-4-4-4-4-40000444-400000000000000000000000000000000000
χ3344-4-400-40404i4i−4i−4i000000000000000000000000000002ζ2−2ζ22ζ6−2ζ6000000
χ3444-4-400-40404i4i−4i−4i00000000000000000000000000000−2ζ22ζ2−2ζ62ζ6000000
χ3544-4-400-4040−4i−4i4i4i000000000000000000000000000002ζ6−2ζ62ζ2−2ζ2000000
χ3644-4-400-4040−4i−4i4i4i00000000000000000000000000000−2ζ62ζ6−2ζ22ζ2000000
χ374-44-44i−4i00002i2−2i22i2−2i2000022−2200000000000ζ+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
χ384-44-44i−4i00002i2−2i22i2−2i2000022−2200000000000−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
χ394-44-44i−4i0000−2i22i2−2i22i20000−222200000000000ζ−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
χ404-44-44i−4i0000−2i22i2−2i22i20000−222200000000000−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
χ414-44-4−4i4i00002i2−2i22i2−2i20000−222200000000000ζ−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
χ424-44-4−4i4i00002i2−2i22i2−2i20000−222200000000000−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
χ434-44-4−4i4i0000−2i22i2−2i22i2000022−2200000000000ζ+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
χ444-44-4−4i4i0000−2i22i2−2i22i2000022−2200000000000−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
χ454-4-4400040-422−22−222200000022−220ζ+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
χ464-4-4400040-422−22−222200000022−220−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
χ474-4-4400040-4−222222−22000000−22220ζ−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
χ484-4-4400040-4−222222−22000000−22220−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
χ494-4-44000-40422−22−2222000000−22220ζ+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
χ504-4-44000-40422−22−2222000000−22220−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
χ514-4-44000-404−222222−2200000022−220ζ−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
χ524-4-44000-404−222222−2200000022−220−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
χ5388-8-80080-800000000000000000000000000000000000000000000

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