Finite Group Databasebeta

← Group #504166

Character table — Group #504166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444888888888888888888888161616161616161616161616163232
order122222444488884444888816161616224444448881616161616161616161644444444888161648
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111
χ51111111111111111111-1-1111111111-1-1-1-111-1111111-1-1-1-111111-1-11-1-1-1-1-1-1-1
χ61111111111111111111-1-111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-11111
χ81111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111111-1-1111-11111-1-1
χ911111111111111-1-1-1-1111111111111-1-111-1-11-1-1-1-1111111-1-11-1-1-1-11-111-1-1-11
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-111-1-11-1-1-1-111111111-11111-1-1-1-1-1-11-1
χ1111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1111111-1-1-111-11
χ1311111111111111-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111-1-1111-1
χ1411111111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-111-1-1-111111-11
χ1511111111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-11111-1-1111111-1-1-111-11-1-1-1-1-11
χ1611111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-1111-1-11111-1-11-1
χ172222222222-2-2-2-22222-222-20000000022-2-2-2-22000000000000000000-2000000
χ182222222222-2-2-2-22222-2-2-2-200000000-2-222-2-2-20000000000000000002000000
χ192222222222-2-2-2-2-2-2-2-2-222-200000000-2-2-2-22220000000000000000002000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2000000000000000000-2000000
χ212222-2-22-2-22000022-2-2022022−2−200002-20000-222−2−22−222−2−2000000000002−200
χ222222-2-22-2-22000022-2-20220−2−22200002-20000-2−2−222−22−2−22200000000000−2200
χ232222-2-22-2-22000022-2-20-2-2022−2−20000-220000222−2−22−2−2−22200000000000−2200
χ242222-2-22-2-22000022-2-20-2-20−2−2220000-2200002−2−222−2222−2−2000000000002−200
χ252222-2-22-2-220000-2-222022022−2−20000-220000-2−2−2222−222−2−200000000000−2200
χ262222-2-22-2-220000-2-2220220−2−2220000-220000-222−2−2−22−2−222000000000002−200
χ272222-2-22-2-220000-2-2220-2-2022−2−200002-200002−2−2222−2−2−222000000000002−200
χ282222-2-22-2-220000-2-2220-2-20−2−22200002-20000222−2−2−2222−2−200000000000−2200
χ292222-2-2-222-222220000-200-2222222-2-200000000000-2-200000020000-20000000
χ302222-2-2-222-222220000-200-22222-2-22200000000000-2-2000000-2000020000000
χ312222-2-2-222-222220000-200-2-2-2-2-222-2-20000000000022000000-2000020000000
χ322222-2-2-222-222220000-200-2-2-2-2-2-2-222000000000002200000020000-20000000
χ3322-2-22-222-2-222-2-20000200-200002-22-200000002-22-20000002-20000000000000
χ3422-2-22-222-2-222-2-20000200-200002-22-20000000-22-22000000-220000000000000
χ3522-2-22-222-2-222-2-20000200-20000-22-2200000002-22-2000000-220000000000000
χ3622-2-22-222-2-222-2-20000200-20000-22-220000000-22-220000002-20000000000000
χ3722-2-2-22-22-2222-2-22i−2i2i−2i-200200002-2-2200002i−2i000000000000002i−2i0000000000
χ3822-2-2-22-22-2222-2-22i−2i2i−2i-20020000-222-200002i−2i00000000000000−2i2i0000000000
χ3922-2-2-22-22-2222-2-2−2i2i−2i2i-200200002-2-220000−2i2i00000000000000−2i2i0000000000
χ4022-2-2-22-22-2222-2-2−2i2i−2i2i-20020000-222-20000−2i2i000000000000002i−2i0000000000
χ4122-2-2-22-22-22-2-2222i−2i2i−2i200-2000000000000−2i2i00000000000000002i−2i002-20000
χ4222-2-2-22-22-22-2-2222i−2i2i−2i200-2000000000000−2i2i0000000000000000−2i2i00-220000
χ4322-2-2-22-22-22-2-222−2i2i−2i2i200-20000000000002i−2i00000000000000002i−2i00-220000
χ4422-2-2-22-22-22-2-222−2i2i−2i2i200-20000000000002i−2i0000000000000000−2i2i002-20000
χ45444444-4-4-4-40000000000002222−22−22000000000000000−22220000000000000000000
χ46444444-4-4-4-4000000000000−22−22222200000000000000022−220000000000000000000
χ474444-4-4-444-4-4-4-4-4000040040000000000000000000000000000000000000000
χ4844-4-44-444-4-4-4-4440000-40040000000000000000000000000000000000000000
χ4944-4-44-4-4-44400004i−4i−4i4i00000000000000000000000000000000000000000000
χ5044-4-44-4-4-4440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5144-4-4-444-44-400000000000000000000000000022−22−2222000000000000000000000
χ5244-4-4-444-44-4000000000000000000000000000−222222−22000000000000000000000
χ534-4-4400000022−2222−220000022−2202ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000002-2000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ544-4-4400000022−2222−220000022−220−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000002-2000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ554-4-4400000022−2222−2200000−222202ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000-22000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ564-4-4400000022−2222−2200000−22220−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000-22000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ574-4-44000000−2222−22220000022−2202ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000-22000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ584-4-44000000−2222−22220000022−220−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000-22000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ594-4-44000000−2222−222200000−222202ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000002-2000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ604-4-44000000−2222−222200000−22220−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000002-2000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ618-88-800000042−42−4242000000000000000000000000000000000000000000000000
χ628-88-8000000−424242−42000000000000000000000000000000000000000000000000

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