Finite Group Databasebeta

← Group #489306

Character table — Group #489306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222444444488888888888888888888888881616161616161616161616163232
order122244444444888824488882224444481616161616161616161616161616161644444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111-1-1-111-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ511111111111111111111111-1-1111-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ911111-1-1-1-11111111-1-11-1-111111-11-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-111-1-11-1
χ1011111-1-1-1-11111111-1-11-1-111111-11-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-1-111-11
χ1111111-1-1-1-11111111-1-11-1-11111-11-1-1-11-11111-1-1-1-1-1-1-1-111111-1-1-111-11-1-1111-1
χ1211111-1-1-1-11111111-1-11-1-11111-11-1-1-11-1-1-1-1-111111111-1-1-1-11-1-1-111-1111-1-1-11
χ1311111-1-1-1-11111111-1-11-1-111-1-11-1111-1-11111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-111-11
χ1411111-1-1-1-11111111-1-11-1-111-1-11-1111-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-111-1-11-1
χ1511111-1-1-1-11111111-1-11-1-111-1-1-11-1111-11111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-11
χ1611111-1-1-1-11111111-1-11-1-111-1-1-11-1111-1-1-1-1-111111111-1-1-1-1-1111-1-1-11-1-1111-1
χ17222222222222-2-2-2-2222-2-2-2-200222002-20000000000000000000000-2-2000000
χ18222222222222-2-2-2-2222-2-2-2-200-2-2-200-2-2000000000000000000000022000000
χ192222222-2-2-2-2200002-2-20000002-2-2002022−2−222−2−222−2−222−2−200000000000000
χ202222222-2-2-2-2200002-2-20000002-2-20020−2−222−2−222−2−222−2−22200000000000000
χ212222222-2-2-2-2200002-2-2000000-22200-2022−2−222−2−2−2−222−2−22200000000000000
χ222222222-2-2-2-2200002-2-2000000-22200-20−2−222−2−22222−2−222−2−200000000000000
χ2322222-2-222-2-220000-22-200000022-200-2022−2−2−2−22222−2−2−2−22200000000000000
χ2422222-2-222-2-220000-22-200000022-200-20−2−22222−2−2−2−22222−2−200000000000000
χ2522222-2-222-2-220000-22-2000000-2-22002022−2−2−2−222−2−22222−2−200000000000000
χ2622222-2-222-2-220000-22-2000000-2-220020−2−22222−2−222−2−2−2−22200000000000000
χ2722222-2-2-2-2222-2-2-2-2-2-2222-2-2002-2200-220000000000000000000000-22000000
χ2822222-2-2-2-2222-2-2-2-2-2-2222-2-200-22-2002200000000000000000000002-2000000
χ292222-2222222-22222-2-2-222-2-222000220-20000000000000000-2-2000000000000
χ302222-2222222-22222-2-2-222-2-2-2-2000-2-20-2000000000000000022000000000000
χ312222-2222222-2-2-2-2-2-2-2-2-2-2220000000020000000000000000002-22-200000000
χ322222-2222222-2-2-2-2-2-2-2-2-2-222000000002000000000000000000-22-2200000000
χ332222-2-2-2-2-222-2222222-2-2-2-2-222000-2-2020000000000000000-22000000000000
χ342222-2-2-2-2-222-2222222-2-2-2-2-2-2-2000220200000000000000002-2000000000000
χ352222-2-2-2-2-222-2-2-2-2-222-2222200000000-20000000000000000002-2-2200000000
χ362222-2-2-2-2-222-2-2-2-2-222-2222200000000-2000000000000000000-222-200000000
χ372-22-202i−2i2i−2i2-2022-2-20002i−2i002-20002i−2i00000000002−22−2i2−i2i2−i2000000002−2i2−i200
χ382-22-202i−2i2i−2i2-2022-2-20002i−2i002-20002i−2i0000000000−22−22−i2i2−i2i200000000−22−i2i200
χ392-22-202i−2i2i−2i2-2022-2-20002i−2i00-22000−2i2i00000000002−22−2i2−i2i2−i200000000−22−i2i200
χ402-22-202i−2i2i−2i2-2022-2-20002i−2i00-22000−2i2i0000000000−22−22−i2i2−i2i2000000002−2i2−i200
χ412-22-20−2i2i−2i2i2-2022-2-2000−2i2i002-2000−2i2i00000000002−22−2−i2i2−i2i2000000002−2−i2i200
χ422-22-20−2i2i−2i2i2-2022-2-2000−2i2i002-2000−2i2i0000000000−22−22i2−i2i2−i200000000−22i2−i200
χ432-22-20−2i2i−2i2i2-2022-2-2000−2i2i00-220002i−2i00000000002−22−2−i2i2−i2i200000000−22i2−i200
χ442-22-20−2i2i−2i2i2-2022-2-2000−2i2i00-220002i−2i0000000000−22−22i2−i2i2−i2000000002−2−i2i200
χ454444-444-4-4-4-4-40000-4440000000000000000000000000000000000000000000
χ464444-4-4-444-4-4-400004-440000000000000000000000000000000000000000000
χ4744-4-44000000-422−2222−220000022−220000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ4844-4-44000000-422−2222−220000022−22000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ4944-4-44000000-4−2222−222200000−22220000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ5044-4-44000000-4−2222−222200000−2222000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ5144-4-4-4000000422−2222−2200000−222200000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000
χ5244-4-4-4000000422−2222−2200000−22220000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000
χ5344-4-4-40000004−2222−22220000022−2200000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000
χ5444-4-4-40000004−2222−22220000022−220000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000
χ554-44-404i−4i4i−4i4-40-4-444000−4i4i00000000000000000000000000000000000000000
χ564-44-404i−4i−4i4i-44000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ574-44-404i−4i−4i4i-4400000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ584-44-40−4i4i4i−4i-44000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ594-44-40−4i4i4i−4i-4400000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ604-44-40−4i4i−4i4i4-40-4-4440004i−4i00000000000000000000000000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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