Finite Group Databasebeta

← Group #504257

Character table — Group #504257

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1222224444888888884444888816161616161616161616161616161616444444442222448888881616161644
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1111-1111-111-1-1111-1-1-1-1-111-1-11-1
χ10111111111111-1-1-1-111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1111-11-1-11111-11-1-1-1-1-1-111-11
χ11111111111111-1-1-1-111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111-1-11-1111111-1-1-11
χ12111111111111-1-1-1-111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-111111-1-1111-1
χ13111111111111-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111111-1111-111-1-1-1-11-1-1-111-1-111-11
χ14111111111111-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1111-11-1-111-1-1-11-1-11111-1-11-1
χ15111111111111-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11-1-1-11-1-1-111111-111-1-1-1-1111-1
χ16111111111111-1-1-1-111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1111-1-111-1111-1-111-1-1-11
χ172222222222-2-22222-2-2-2-2-2-2-222-2000000000000000000220022000000-2-20000000000
χ182222222222-2-22222-2-2-2-2-2-2-222-2000000000000000000-2-200-2-2000000220000000000
χ192222222222-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000002-2002-2000000-220000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000-2200-220000002-20000000000
χ212222-2-22-22-2220000220000-200-22222-2-2-2-2000000002200-2-20000002-2000000000000
χ222222-2-22-22-2220000220000-200-22222-2-2-2-200000000-2-20022000000-22000000000000
χ232222-2-22-22-2220000220000-200-2-2-2-2-22222000000002200-2-2000000-22000000000000
χ242222-2-22-22-2220000220000-200-2-2-2-2-2222200000000-2-200220000002-2000000000000
χ252222-2-2-22-220022220000000-2-2022−2−222−2−22222−2−2−2−2002200-2-20000000000002−22−200
χ262222-2-2-22-220022220000000-2-2022−2−222−2−22222−2−2−2−200-2-20022000000000000−22−2200
χ272222-2-2-22-220022220000000-2-20−2−222−2−222−2−2−2−22222002200-2-2000000000000−22−2200
χ282222-2-2-22-220022220000000-2-20−2−222−2−222−2−2−2−2222200-2-200220000000000002−22−200
χ292222-2-2-22-2200-2-2-2-2000000022022−2−222−2−2−2−2−2−22222002-200-220000000000002−2−2200
χ302222-2-2-22-2200-2-2-2-2000000022022−2−222−2−2−2−2−2−2222200-22002-2000000000000−222−200
χ312222-2-2-22-2200-2-2-2-20000000220−2−222−2−2222222−2−2−2−2002-200-22000000000000−222−200
χ322222-2-2-22-2200-2-2-2-20000000220−2−222−2−2222222−2−2−2−200-22002-20000000000002−2−2200
χ3322-2-22-22-2-22-2-20000220000200-2000000002i2i−2i−2i2i2i−2i−2i2i−2i002i−2i0000000000002-2000000
χ3422-2-22-22-2-22-2-20000220000200-2000000002i2i−2i−2i2i2i−2i−2i−2i2i00−2i2i000000000000-22000000
χ3522-2-22-22-2-22-2-20000220000200-200000000−2i−2i2i2i−2i−2i2i2i2i−2i002i−2i000000000000-22000000
χ3622-2-22-22-2-22-2-20000220000200-200000000−2i−2i2i2i−2i−2i2i2i−2i2i00−2i2i0000000000002-2000000
χ3722-2-2-2222-2-22222-2-2-2-222-2-222-2-20000000000000000000000002-22-200000000000000
χ3822-2-2-2222-2-22222-2-2-2-222-2-222-2-2000000000000000000000000-22-2200000000000000
χ3922-2-2-2222-2-222-2-222-2-2-2-2222-22-20000000000000000000000002-2-2200000000000000
χ4022-2-2-2222-2-222-2-222-2-2-2-2222-22-2000000000000000000000000-222-200000000000000
χ4122-2-2-2222-2-2-2-222-2-222-2-222-22-2200000000000000002i−2i00−2i2i00000000002i−2i00000000
χ4222-2-2-2222-2-2-2-222-2-222-2-222-22-220000000000000000−2i2i002i−2i0000000000−2i2i00000000
χ4322-2-2-2222-2-2-2-2-2-2222222-2-2-2-22200000000000000002i−2i00−2i2i0000000000−2i2i00000000
χ4422-2-2-2222-2-2-2-2-2-2222222-2-2-2-2220000000000000000−2i2i002i−2i00000000002i−2i00000000
χ45444444-4-4-4-400000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ46444444-4-4-4-40000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ474444-4-44-44-4-4-40000-4-400004004000000000000000000000000000000000000000000
χ4844-4-44-44-4-44440000-4-40000-4004000000000000000000000000000000000000000000
χ4944-4-44-4-444-40044-4-40000000-440000000000000000000000000000000000000000000
χ5044-4-44-4-444-400-4-44400000004-40000000000000000000000000000000000000000000
χ5144-4-4-44-4-4440000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5244-4-4-44-4-444000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ534-44-400000022−2222−2222−2222−222-22-2000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7ζ+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−ζ700000000000000000000000000
χ544-44-400000022−2222−2222−2222−222-22-200000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−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+ζ700000000000000000000000000
χ554-44-400000022−22−2222−222222−22-22-22000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−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+ζ700000000000000000000000000
χ564-44-400000022−22−2222−222222−22-22-2200000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7ζ+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−ζ700000000000000000000000000
χ574-44-4000000−222222−2222−22−2222-22-22000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−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−ζ700000000000000000000000000
χ584-44-4000000−222222−2222−22−2222-22-2200000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5ζ−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+ζ700000000000000000000000000
χ594-44-4000000−2222−2222−2222−22222-22-2000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5ζ−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+ζ700000000000000000000000000
χ604-44-4000000−2222−2222−2222−22222-22-200000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−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−ζ700000000000000000000000000
χ614-4-4400000022−2222−22−2222−22222-2-2200002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ70000ζ−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−ζ700000000000000000000000000
χ624-4-4400000022−2222−22−2222−22222-2-220000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ70000−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+ζ700000000000000000000000000
χ634-4-4400000022−22−222222−22−2222-222-200002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ70000−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+ζ700000000000000000000000000
χ644-4-4400000022−22−222222−22−2222-222-20000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ70000ζ−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−ζ700000000000000000000000000
χ654-4-44000000−222222−22−222222−22-222-200002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ50000ζ+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+ζ700000000000000000000000000
χ664-4-44000000−222222−22−222222−22-222-20000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ50000−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−ζ700000000000000000000000000
χ674-4-44000000−2222−222222−2222−222-2-2200002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ50000−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−ζ700000000000000000000000000
χ684-4-44000000−2222−222222−2222−222-2-220000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ50000ζ+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+ζ700000000000000000000000000

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