Finite Group Databasebeta

← Group #126427

Character table — Group #126427

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444448888888888888888888161616161616161616161632323232
order122222224444448888888844416161616161616161616161616161616444448888882444
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-111
χ511111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1
χ611111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-11-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-11111-11-1-1
χ922222222222222-2-2-2-2-2-2-2-2222000000000000000020000-2-200000000
χ1022222222222222-2-2-2-2-2-2-2-22-2-20000000000000000-200002200000000
χ11222222222222-2-222-2-222-2-2-2000000000000000000000220000000-200
χ12222222222222-2-222-2-222-2-2-2000000000000000000000-2-20000000200
χ13222222222222-2-2-2-222-2-222-200000000000000000002200000000-2000
χ14222222222222-2-2-2-222-2-222-20000000000000000000-2-2000000002000
χ1522222222-2-2-2-22200000000-2222222−2−2−2−22222−2−2−2−2-200000000000000
χ1622222222-2-2-2-22200000000-222−2−2−2−22222−2−2−2−22222-200000000000000
χ1722222222-2-2-2-22200000000-2-2-22222−2−2−2−2−2−2−2−22222200000000000000
χ1822222222-2-2-2-22200000000-2-2-2−2−2−2−222222222−2−2−2−2200000000000000
χ1922-222-2-2-20000-222−22−22−22−202i−2iζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700000i2−i200000000
χ2022-222-2-2-20000-222−22−22−22−202i−2i−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700000i2−i200000000
χ2122-222-2-2-20000-222−22−22−22−20−2i2iζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700000−i2i200000000
χ2222-222-2-2-20000-222−22−22−22−20−2i2i−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700000−i2i200000000
χ2322-222-2-2-20000-22−22−22−22−2202i−2iζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500000−i2i200000000
χ2422-222-2-2-20000-22−22−22−22−2202i−2i−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500000−i2i200000000
χ2522-222-2-2-20000-22−22−22−22−220−2i2iζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500000i2−i200000000
χ2622-222-2-2-20000-22−22−22−22−220−2i2i−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500000i2−i200000000
χ272-222-2-2-222-2-2200002200-2-2000i2−i2i2−i2i2−i2i2−i20000000002i−2i000022−2−20000
χ282-222-2-2-222-2-2200002200-2-2000i2−i2i2−i2i2−i2i2−i2000000000−2i2i0000−2−2220000
χ292-222-2-2-222-2-2200002200-2-2000−i2i2−i2i2−i2i2−i2i20000000002i−2i0000−2−2220000
χ302-222-2-2-222-2-2200002200-2-2000−i2i2−i2i2−i2i2−i2i2000000000−2i2i000022−2−20000
χ312-22-222-2-22-22-200-2-200220000000000000i2−i2i2−i2i2−i2i2−i20002i−2i002−22−20000
χ322-22-222-2-22-22-200-2-200220000000000000i2−i2i2−i2i2−i2i2−i2000−2i2i00−22−220000
χ332-22-222-2-22-22-200-2-200220000000000000−i2i2−i2i2−i2i2−i2i20002i−2i00−22−220000
χ342-22-222-2-22-22-200-2-200220000000000000−i2i2−i2i2−i2i2−i2i2000−2i2i002−22−20000
χ3544444444-4-4-4-4-4-4000000004000000000000000000000000000000000
χ36444-4-4-44-444-4-40000000000000000000000000000000000002-2-220000
χ37444-4-4-44-444-4-4000000000000000000000000000000000000-222-20000
χ38444-4-4-44-4-4-4440000000000000000000000000000000000000000002i−2i
χ39444-4-4-44-4-4-444000000000000000000000000000000000000000000−2i2i
χ4044-444-4-4-400004-422−22−222222−22−22220000000000000000000000000000000000
χ4144-444-4-4-400004-4−222222−22−222222−220000000000000000000000000000000000
χ424-444-4-4-444-4-440000-4-400440000000000000000000000000000000000
χ434-444-4-4-44-444-400000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000
χ444-444-4-4-44-444-40000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000
χ454-44-444-4-44-44-4004400-4-4000000000000000000000000000000000000
χ464-44-444-4-4-44-440000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000
χ474-44-444-4-4-44-44000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000
χ484-4-44-444-40000000022−2200−2222000ζ+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
χ494-4-44-444-40000000022−2200−2222000−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
χ504-4-44-444-400000000−22220022−22000ζ−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
χ514-4-44-444-400000000−22220022−22000−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
χ524-4-4-44-44400000022−2200−22220000000000000ζ−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
χ534-4-4-44-44400000022−2200−22220000000000000−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
χ544-4-4-44-444000000−22220022−220000000000000ζ+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
χ554-4-4-44-444000000−22220022−220000000000000−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
χ5688-8-8-88-88000000000000000000000000000000000000000000000000

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