Finite Group Databasebeta

← Group #144604

Character table — Group #144604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222224444444444888888888161616161616161616161616323232323232
order12222244442244888888816161616161616164444448816161616444488
χ111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111-1-11-1-11111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-111-111-1-1-1111111-1-1-1-1
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ922222222222222-2-2-2-2-2-2-200000000002002-2-20000000000
χ1022222222222222-2-2-2-2-2-2-20000000000-200-2220000000000
χ1122222222-2-2-2-2-222222-2-2-200000000220-2-20000000000000
χ1222222222-2-2-2-2-222222-2-2-200000000-2-20220000000000000
χ1322222222-2-2-2-2-22-2-2-2-222200000000000000000000002-200
χ1422222222-2-2-2-2-22-2-2-2-22220000000000000000000000-2200
χ15222222-2-222-2-22-200000002222−2−2−2−200200-20022−2−2000000
χ16222222-2-222-2-22-200000002222−2−2−2−200-200200−2−222000000
χ17222222-2-222-2-22-20000000−2−2−2−2222200200-200−2−222000000
χ18222222-2-222-2-22-20000000−2−2−2−2222200-20020022−2−2000000
χ192222-2-222222-2-2-222-2-222-200000000000000002i−2i2i−2i000000
χ202222-2-222222-2-2-222-2-222-20000000000000000−2i2i−2i2i000000
χ212222-2-222222-2-2-2-2-222-2-222i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222-2-222222-2-2-2-2-222-2-22−2i−2i2i2i−2i−2i2i2i000000000000000000
χ232222-2-222-2-2-222-222-2-2-2-22000000000000000000002-20000
χ242222-2-222-2-2-222-222-2-2-2-2200000000000000000000-220000
χ252222-2-222-2-2-222-2-2-22222-20000000000000000000000002i−2i
χ262222-2-222-2-2-222-2-2-22222-2000000000000000000000000−2i2i
χ272222-2-2-2-222-22-220000000i2i2−i2−i2−i2−i2i2i20000002-2i2−i2−i2i2000000
χ282222-2-2-2-222-22-220000000i2i2−i2−i2−i2−i2i2i2000000-22−i2i2i2−i2000000
χ292222-2-2-2-222-22-220000000−i2−i2i2i2i2i2−i2−i20000002-2−i2i2i2−i2000000
χ302222-2-2-2-222-22-220000000−i2−i2i2i2i2i2−i2−i2000000-22i2−i2−i2i2000000
χ31444444-4-4-4-444-4-4000000000000000000000000000000000
χ324444-4-4-4-4-4-44-444000000000000000000000000000000000
χ3344-4-44-40000000022−2222−22000ζ+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+ζ7000000000000000000
χ3444-4-44-40000000022−2222−22000−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−ζ7000000000000000000
χ3544-4-44-400000000−2222−2222000ζ−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−ζ7000000000000000000
χ3644-4-44-400000000−2222−2222000−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+ζ7000000000000000000
χ3744-4-4-440000000022−22−2222000ζ−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+ζ7000000000000000000
χ3844-4-4-440000000022−22−2222000−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−ζ7000000000000000000
χ3944-4-4-4400000000−222222−22000ζ+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−ζ7000000000000000000
χ4044-4-4-4400000000−222222−22000−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+ζ7000000000000000000
χ414-4-44004-400000000004i−4i0000000002i−2i02-20000000000000
χ424-4-44004-400000000004i−4i000000000−2i2i0-220000000000000
χ434-4-44004-40000000000−4i4i0000000002i−2i0-220000000000000
χ444-4-44004-40000000000−4i4i000000000−2i2i02-20000000000000
χ458-88-800008i−8i0000000000000000000000000000000000000
χ468-88-80000−8i8i0000000000000000000000000000000000000
χ478-8-8800-88000000000000000000000000000000000000000

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