Finite Group Databasebeta

← Group #490088

Character table — Group #490088

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444444444888888888888888161616161616161616161616161616163232
order12224444448888244444448888248888816161616161616162224444488881616161624
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1-1-11111-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111-1-11-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1
χ7111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1
χ8111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111
χ911111-1-11111111-11-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-11-1-11-111-1-111-1-11-1
χ1011111-1-11111111-11-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-11-111-11-1-11111-1-1-11
χ1111111-1-11111111-11-1-111-1-1-1-1111-1-111-1-1-1-1-1-1111111-11-1-11-1-1-111-1-111-11
χ1211111-1-11111111-11-1-111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-11-111-1111-1-1-1-1111-1
χ1311111-1-11111111-11-1-1-1-111-1-111-11-1-1-1111111-1-1-1-1111-1-1-1-11-1-111-1-1111-1
χ1411111-1-11111111-11-1-1-1-111-1-111-11-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-111-11
χ1511111-1-11111111-11-1-1-1-111-1-111-11-1-1-111-1-1-1-11111111-1-1-1-1111-1-111-1-1-11
χ1611111-1-11111111-11-1-1-1-111-1-111-11-1-1-111-1-1-1-11111-1-1-11111-1-1-11111-1-11-1
χ172222222222-2-2-2-222222222-2-2-2-222-2-2-2-2-200000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ192222222-2-2200002-2-2-222-2-20000-220000022−2−222−2−20000000000002−22−200
χ202222222-2-2200002-2-2-222-2-20000-2200000−2−222−2−222000000000000−22−2200
χ212222222-2-2200002-2-2-2-2-22200002-20000022−2−222−2−2000000000000−22−2200
χ222222222-2-2200002-2-2-2-2-22200002-200000−2−222−2−2220000000000002−22−200
χ2322222-2-2222-2-2-2-2-22-2-222-2-222-2-22-22-2-22200000000000000000000000000
χ2422222-2-2222-2-2-2-2-22-2-2-2-22222-2-2-22222-2-200000000000000000000000000
χ2522222-2-2-2-220000-2-22222220000-2-20000022−2−2−2−2220000000000002−2−2200
χ2622222-2-2-2-220000-2-22222220000-2-200000−2−22222−2−2000000000000−222−200
χ2722222-2-2-2-220000-2-222-2-2-2-20000220000022−2−2−2−222000000000000−222−200
χ2822222-2-2-2-220000-2-222-2-2-2-200002200000−2−22222−2−20000000000002−2−2200
χ292222-22222-22222-2-22-2000022-2-200-2000000000000002-2002-20000000000
χ302222-22222-22222-2-22-2000022-2-200-200000000000000-2200-220000000000
χ312222-22222-2-2-2-2-2-2-22-20000-2-2220020000000000002-2002-2000000000000
χ322222-22222-2-2-2-2-2-2-22-20000-2-222002000000000000-2200-22000000000000
χ332222-2-2-222-222222-2-220000-2-2-2-2002000000000000002200-2-20000000000
χ342222-2-2-222-222222-2-220000-2-2-2-200200000000000000-2-200220000000000
χ352222-2-2-222-2-2-2-2-22-2-220000222200-20000000000002-200-22000000000000
χ362222-2-2-222-2-2-2-2-22-2-220000222200-2000000000000-22002-2000000000000
χ374444-444-4-4-40000-44-4400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-40000444-400000000000000000000000000000000000000000
χ3944-4-404i−4i00022−2222−22000000002i2−2i2000000000ζ+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
χ4044-4-404i−4i00022−2222−22000000002i2−2i2000000000−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
χ4144-4-404i−4i000−2222−222200000000−2i22i2000000000ζ−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
χ4244-4-404i−4i000−2222−222200000000−2i22i2000000000−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
χ4344-4-40−4i4i00022−2222−2200000000−2i22i2000000000ζ+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
χ4444-4-40−4i4i00022−2222−2200000000−2i22i2000000000−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
χ4544-4-40−4i4i000−2222−2222000000002i2−2i2000000000ζ−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
χ4644-4-40−4i4i000−2222−2222000000002i2−2i2000000000−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
χ474-44-40004-4044-4-400000000000000000000000000000000000002i2−2i2000000
χ484-44-40004-4044-4-40000000000000000000000000000000000000−2i22i2000000
χ494-44-40004-40-4-4440000000000000000000000000000000000022−2200000000
χ504-44-40004-40-4-44400000000000000000000000000000000000−222200000000
χ514-4-4440000-422−22−222200004i−4i000022−220002i2−2i20000000000000000000000000000
χ524-4-4440000-422−22−22220000−4i4i000022−22000−2i22i20000000000000000000000000000
χ534-4-4440000-4−222222−2200004i−4i0000−2222000−2i22i20000000000000000000000000000
χ544-4-4440000-4−222222−220000−4i4i0000−22220002i2−2i20000000000000000000000000000
χ554-4-44-40000422−22−22220000004-400−22220000022−2200000000000000000000000000
χ564-4-44-40000422−22−2222000000-4400−222200000−222200000000000000000000000000
χ574-4-44-400004−222222−220000004-40022−2200000−222200000000000000000000000000
χ584-4-44-400004−222222−22000000-440022−220000022−2200000000000000000000000000
χ598-88-8000-8800000000000000000000000000000000000000000000000000

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