Finite Group Databasebeta

← Group #500736

Character table — Group #500736

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order1244222444888888884444888816161616161616161616161616161616222244442224448888881616161688
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
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
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-111-1-111-1-1-1-111
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
χ91111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1111-1111-1-11-1-11-11-1-1-11111-1-11-1
χ101111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-111-1111-11-1-11-1-11-11-1-111-1-111-11
χ111111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-11-1-1-11-11-111-111-111-1-111-1-1-11
χ121111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-111-1-1111-1-1-1-1111-1
χ131111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111111-1111-111-111-11-1-1-1-1-1-1-111-11
χ141111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1111-111-111-11-11-1-1-1-111-1-11-1
χ151111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-11-1-1-11-1-1-11-1-111-11111-1-1111-1
χ161111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-11-1-1-11-11-1-11-1-11111111-1-1-11
χ1722222222222222-2-2-2-2-2-2-2-2-222-2000000000000000000220022000000-2-20000000000
χ1822222222222222-2-2-2-2-2-2-2-2-222-2000000000000000000-2-200-2-2000000220000000000
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
χ2122222-2-22-2-20000-2-2-2-2000020022i2i2i2i−2i−2i−2i−2i000000002-2002-20000000000002i−2i000000
χ2222222-2-22-2-20000-2-2-2-2000020022i2i2i2i−2i−2i−2i−2i00000000-2200-22000000000000−2i2i000000
χ2322222-2-22-2-20000-2-2-2-200002002−2i−2i−2i−2i2i2i2i2i000000002-2002-2000000000000−2i2i000000
χ2422222-2-22-2-20000-2-2-2-200002002−2i−2i−2i−2i2i2i2i2i00000000-2200-220000000000002i−2i000000
χ2522-2-22-2-2-22222-2-20000000002-2022−2−222−2−22222−2−2−2−2002200-2-20000000000002−22−200
χ2622-2-22-2-2-22222-2-20000000002-2022−2−222−2−22222−2−2−2−200-2-20022000000000000−22−2200
χ2722-2-22-2-2-22222-2-20000000002-20−2−222−2−222−2−2−2−22222002200-2-2000000000000−22−2200
χ2822-2-22-2-2-22222-2-20000000002-20−2−222−2−222−2−2−2−2222200-2-200220000000000002−22−200
χ2922-2-22-2-2-222-2-222000000000-22022−2−222−2−2−2−2−2−22222002-200-220000000000002−2−2200
χ3022-2-22-2-2-222-2-222000000000-22022−2−222−2−2−2−2−2−2222200-22002-2000000000000−222−200
χ3122-2-22-2-2-222-2-222000000000-220−2−222−2−2222222−2−2−2−2002-200-22000000000000−222−200
χ3222-2-22-2-2-222-2-222000000000-220−2−222−2−2222222−2−2−2−200-22002-20000000000002−2−2200
χ3322-2-2-22-222-20000-2-2220000-20020000000022-2-222-2-22200-2-200200-200000000000000
χ3422-2-2-22-222-20000-2-2220000-20020000000022-2-222-2-2-2-2002200-200200000000000000
χ3522-2-2-22-222-20000-2-2220000-200200000000-2-222-2-2222200-2-200-200200000000000000
χ3622-2-2-22-222-20000-2-2220000-200200000000-2-222-2-222-2-2002200200-200000000000000
χ3722-2-2-2-222-2222-2-222-2-222-2-2-2-22200000000000000002-200-2200000000002-200000000
χ3822-2-2-2-222-2222-2-222-2-222-2-2-2-2220000000000000000-22002-20000000000-2200000000
χ3922-2-2-2-222-2222-2-2-2-222-2-2222-22-20000000000000000000000000220-2-2000000000000
χ4022-2-2-2-222-2222-2-2-2-222-2-2222-22-20000000000000000000000000-2-2022000000000000
χ4122-2-2-2-222-22-2-22222-2-2-2-222-22-2200000000000000002-200-220000000000-2200000000
χ4222-2-2-2-222-22-2-22222-2-2-2-222-22-220000000000000000-22002-200000000002-200000000
χ4322-2-2-2-222-22-2-222-2-22222-2-222-2-200000000000000000000000002-20-22000000000000
χ4422-2-2-2-222-22-2-222-2-22222-2-222-2-20000000000000000000000000-2202-2000000000000
χ4544444-4-44-4-4000044440000-400-4000000000000000000000000000000000000000000
χ464444-44-4-4-444444000000000-4-40000000000000000000000000000000000000000000
χ474444-44-4-4-44-4-4-4-4000000000440000000000000000000000000000000000000000000
χ484444-4-44-44-40000000000000000000000002222−22−22−22−22222200000000000000000000000000
χ494444-4-44-44-4000000000000000000000000−22−2222222222−22−2200000000000000000000000000
χ5044-4-4444-4-4-400000000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000
χ5144-4-4444-4-4-40000000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000
χ5244-4-4-44-444-4000044-4-40000400-4000000000000000000000000000000000000000000
χ534-44i−4i00000022−222i2−2i22i2−2i222−222i−2i2-200002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ3ζ+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
χ544-44i−4i00000022−222i2−2i22i2−2i222−222i−2i2-20000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ3−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
χ554-44i−4i00000022−222i2−2i2−2i22i2−2222−2i2i-2200002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ7−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
χ564-44i−4i00000022−222i2−2i2−2i22i2−2222−2i2i-220000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ7ζ−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
χ574-44i−4i000000−2222−2i22i22i2−2i222−22−2i2i-2200002ζ−2ζ2ζ5−2ζ52ζ7−2ζ72ζ3−2ζ3−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
χ584-44i−4i000000−2222−2i22i22i2−2i222−22−2i2i-220000−2ζ2ζ−2ζ52ζ5−2ζ72ζ7−2ζ32ζ3ζ+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
χ594-44i−4i000000−2222−2i22i2−2i22i2−22222i−2i2-200002ζ5−2ζ5−2ζ2ζ2ζ3−2ζ3−2ζ72ζ7ζ−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
χ604-44i−4i000000−2222−2i22i2−2i22i2−22222i−2i2-20000−2ζ52ζ52ζ−2ζ−2ζ32ζ32ζ7−2ζ7−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
χ614-4−4i4i00000022−22−2i22i22i2−2i2−22222i−2i-2200002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζζ−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
χ624-4−4i4i00000022−22−2i22i22i2−2i2−22222i−2i-220000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζ−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
χ634-4−4i4i00000022−22−2i22i2−2i22i222−22−2i2i2-200002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ5−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
χ644-4−4i4i00000022−22−2i22i2−2i22i222−22−2i2i2-20000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ5ζ+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
χ654-4−4i4i000000−22222i2−2i22i2−2i2−2222−2i2i2-200002ζ3−2ζ3−2ζ72ζ72ζ5−2ζ5−2ζ2ζ−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
χ664-4−4i4i000000−22222i2−2i22i2−2i2−2222−2i2i2-20000−2ζ32ζ32ζ7−2ζ7−2ζ52ζ52ζ−2ζζ−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
χ674-4−4i4i000000−22222i2−2i2−2i22i222−222i−2i-2200002ζ7−2ζ72ζ3−2ζ32ζ−2ζ2ζ5−2ζ5ζ+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
χ684-4−4i4i000000−22222i2−2i2−2i22i222−222i−2i-220000−2ζ72ζ7−2ζ32ζ3−2ζ2ζ−2ζ52ζ5−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

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