Finite Group Databasebeta

← Group #126432

Character table — Group #126432

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444448888888888888888888161616161616161616161632323232
order122222224444448888888844416161616161616161616161616161616224448888884444
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111
χ511111111111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-1-1
χ611111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-111111-1-1-1
χ922222222222222-2-2-2-2-2-2-2-2222000000000000000000200-2-200000000
χ1022222222222222-2-2-2-2-2-2-2-22-2-2000000000000000000-2002200000000
χ11222222222222-2-222-2-222-2-2-200000000000000000000022000000-2000
χ12222222222222-2-222-2-222-2-2-2000000000000000000000-2-20000002000
χ13222222222222-2-2-2-222-2-222-2000000000000000000220000000000-200
χ14222222222222-2-2-2-222-2-222-2000000000000000000-2-20000000000200
χ1522222222-2-2-2-22200000000-2222222−2−2−2−22222−2−2−2−200-2000000000000
χ1622222222-2-2-2-22200000000-222−2−2−2−22222−2−2−2−2222200-2000000000000
χ1722222222-2-2-2-22200000000-2-2-22222−2−2−2−2−2−2−2−22222002000000000000
χ1822222222-2-2-2-22200000000-2-2-2−2−2−2−222222222−2−2−2−2002000000000000
χ1922-2-2-22-222-22-2002200-2-2000000000000022−2−222−2−20002i−2i00i2i2−i2−i20000
χ2022-2-2-22-222-22-2002200-2-2000000000000022−2−222−2−2000−2i2i00−i2−i2i2i20000
χ2122-2-2-22-222-22-2002200-2-20000000000000−2−222−2−2220002i−2i00−i2−i2i2i20000
χ2222-2-2-22-222-22-2002200-2-20000000000000−2−222−2−222000−2i2i00i2i2−i2−i20000
χ232-22-22-2-2200002-22−22−22−22−202i−2iζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000i2−i200000000
χ242-22-22-2-2200002-22−22−22−22−202i−2i−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000i2−i200000000
χ252-22-22-2-2200002-22−22−22−22−20−2i2iζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ700000−i2i200000000
χ262-22-22-2-2200002-22−22−22−22−20−2i2i−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ700000−i2i200000000
χ272-22-22-2-2200002-2−22−22−22−2202i−2iζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000−i2i200000000
χ282-22-22-2-2200002-2−22−22−22−2202i−2i−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000−i2i200000000
χ292-22-22-2-2200002-2−22−22−22−220−2i2iζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ500000i2−i200000000
χ302-22-22-2-2200002-2−22−22−22−220−2i2i−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ500000i2−i200000000
χ312-2-2-2222-22-2-2200002200-2-2000i2−i2i2−i2i2−i2i2−i2000000002-200000i2−i2i2−i20000
χ322-2-2-2222-22-2-2200002200-2-2000i2−i2i2−i2i2−i2i2−i200000000-2200000−i2i2−i2i20000
χ332-2-2-2222-22-2-2200002200-2-2000−i2i2−i2i2−i2i2−i2i2000000002-200000−i2i2−i2i20000
χ342-2-2-2222-22-2-2200002200-2-2000−i2i2−i2i2−i2i2−i2i200000000-2200000i2−i2i2−i20000
χ3544444444-4-4-4-4-4-4000000004000000000000000000000000000000000
χ3644-444-4-4-40000000022−2200−2222000ζ−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−ζ700000000000000000000000
χ3744-444-4-4-40000000022−2200−2222000−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+ζ700000000000000000000000
χ3844-444-4-4-400000000−22220022−22000ζ+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+ζ700000000000000000000000
χ3944-444-4-4-400000000−22220022−22000−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−ζ700000000000000000000000
χ4044-4-4-44-444-44-400-4-40044000000000000000000000000000000000000
χ4144-4-4-44-44-44-4400000000000000000000022-2-2-2-222000000000000000
χ4244-4-4-44-44-44-44000000000000000000000-2-22222-2-2000000000000000
χ434-444-44-4-444-4-40000000000000000000000000000000000002-2-220000
χ444-444-44-4-444-4-4000000000000000000000000000000000000-222-20000
χ454-444-44-4-4-4-4440000000000000000000000000000000000000000002i−2i
χ464-444-44-4-4-4-444000000000000000000000000000000000000000000−2i2i
χ474-44-44-4-440000-4422−22−222222−22−22220000000000000000000000000000000000
χ484-44-44-4-440000-44−222222−22−222222−220000000000000000000000000000000000
χ494-4-44-4-44400000022−2200−22220000000000000ζ−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−ζ7000000000000000
χ504-4-44-4-44400000022−2200−22220000000000000−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+ζ7000000000000000
χ514-4-44-4-444000000−22220022−220000000000000ζ+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+ζ7000000000000000
χ524-4-44-4-444000000−22220022−220000000000000−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−ζ7000000000000000
χ534-4-4-4444-44-4-440000-4-400440000000000000000000000000000000000
χ544-4-4-4444-4-444-400000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000
χ554-4-4-4444-4-444-40000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000
χ56888-8-8-88-8000000000000000000000000000000000000000000000000

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