Finite Group Databasebeta

← Group #144080

Character table — Group #144080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122222444444448888888844444444448888888888881616161616161616161616161616161622224488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-22-2-2-2-222222222000000000000000000000000
χ11222222222-2-2-2-2200000000-22222-2-2-2-2-20000000000002222−2−2−2−22222−2−2−2−200000000
χ12222222222-2-2-2-2200000000-22222-2-2-2-2-2000000000000−2−2−2−22222−2−2−2−2222200000000
χ13222222222-2-2-2-2200000000-2-2-2-2-22222-20000000000002222−2−2−2−2−2−2−2−2222200000000
χ14222222222-2-2-2-2200000000-2-2-2-2-22222-2000000000000−2−2−2−222222222−2−2−2−200000000
χ15222222-2-2-2-2-222-22222-2-2-2-2-200000000222-2-20000000000000000000000002-2000000
χ16222222-2-2-2-2-222-22222-2-2-2-2-200000000222-2-2000000000000000000000000-22000000
χ17222222-2-2-2-2-222-2-2-2-2-22222-2000000002-2-222000000000000000000000000002-20000
χ18222222-2-2-2-2-222-2-2-2-2-22222-2000000002-2-22200000000000000000000000000-220000
χ192222-2-222-22222-222222222-200000000-2-2-2-2-200000000000000000000000000002-200
χ202222-2-222-22222-222222222-200000000-2-2-2-2-20000000000000000000000000000-2200
χ212222-2-222-22222-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000000000000000002i−2i
χ222222-2-222-22222-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000−2i2i
χ232222-2-2-2-2222-2-2200000000-200000000200002222-2-2-2-222−2−222−2−222−2−222−2−200000000
χ242222-2-2-2-2222-2-2200000000-200000000200002222-2-2-2-2−2−222−2−222−2−222−2−22200000000
χ252222-2-2-2-2222-2-2200000000-20000000020000-2-2-2-2222222−2−222−2−2−2−222−2−22200000000
χ262222-2-2-2-2222-2-2200000000-20000000020000-2-2-2-22222−2−222−2−22222−2−222−2−200000000
χ272222-2-2-2-22-2-22222222-2-2-2-2200000000-2-2-2220000000022-2-2-2-2220000000000000000
χ282222-2-2-2-22-2-22222222-2-2-2-2200000000-2-2-22200000000-2-22222-2-20000000000000000
χ292222-2-2-2-22-2-2222-2-2-2-22222200000000-222-2-2000000000000000022-2-2-2-22200000000
χ302222-2-2-2-22-2-2222-2-2-2-22222200000000-222-2-20000000000000000-2-22222-2-200000000
χ3122-2-22-22-220000-222−2−222−2−20000022-2-202−22−222−2−222−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ3222-2-22-22-220000-222−2−222−2−20000022-2-202−22−222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ3322-2-22-22-220000-222−2−222−2−200000-2-22202−22−2−2−222−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ3422-2-22-22-220000-222−2−222−2−200000-2-22202−22−2−2−222−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ3522-2-22-22-220000-2−2−222−2−2220000022-2-20−22−22−2−222−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ3622-2-22-22-220000-2−2−222−2−2220000022-2-20−22−22−2−222−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ3722-2-22-22-220000-2−2−222−2−22200000-2-2220−22−2222−2−222−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ3822-2-22-22-220000-2−2−222−2−22200000-2-2220−22−2222−2−222−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ3922-2-2-22-2220000-222−2−2−2−222022-2-200000−222−222−2−2−2−222ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ4022-2-2-22-2220000-222−2−2−2−222022-2-200000−222−222−2−2−2−222−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ4122-2-2-22-2220000-222−2−2−2−2220-2-22200000−222−2−2−22222−2−2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ4222-2-2-22-2220000-222−2−2−2−2220-2-22200000−222−2−2−22222−2−2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ4322-2-2-22-2220000-2−2−22222−2−2022-2-2000002−2−22−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ4422-2-2-22-2220000-2−2−22222−2−2022-2-2000002−2−22−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ4522-2-2-22-2220000-2−2−22222−2−20-2-222000002−2−2222−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ4622-2-2-22-2220000-2−2−22222−2−20-2-222000002−2−2222−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ47444444-4-4-444-4-4-400000000400000000-4000000000000000000000000000000000000
χ484444-4-444-4-4-4-4-4-4000000004000000004000000000000000000000000000000000000
χ4944-4-44-4-44-4000042222−22−22−22−222222000000000022−22−222200000000000000000000000000000000
χ5044-4-44-4-44-400004−22−2222222222−22−220000000000−222222−2200000000000000000000000000000000
χ5144-4-4-444-4-4000042222−22−222222−22−220000000000−2222−222200000000000000000000000000000000
χ5244-4-4-444-4-400004−22−222222−22−222222000000000022−2222−2200000000000000000000000000000000
χ534-44-400000004-4000004-44-402-22-22-22-2000002-22-22-22-2000000000000000000000000
χ544-44-400000004-4000004-44-40-22-22-22-2200000-22-22-22-22000000000000000000000000
χ554-44-400000004-400000-44-4402-22-22-22-200000-22-22-22-22000000000000000000000000
χ564-44-400000004-400000-44-440-22-22-22-22000002-22-22-22-2000000000000000000000000
χ574-44-40000000-4404-44-4000002-22-2-22-22000002-22-2-22-22000000000000000000000000
χ584-44-40000000-4404-44-400000-22-222-22-200000-22-222-22-2000000000000000000000000
χ594-44-40000000-440-44-44000002-22-2-22-2200000-22-222-22-2000000000000000000000000
χ604-44-40000000-440-44-4400000-22-222-22-2000002-22-2-22-22000000000000000000000000
χ614-4-44000004-400022−22−222222−22−222202-2-222-2-2200000000022−22−2222000000000000000000000000
χ624-4-44000004-400022−22−222222−22−22220-222-2-222-2000000000−222222−22000000000000000000000000
χ634-4-44000004-4000−222222−22−222222−2202-2-222-2-22000000000−222222−22000000000000000000000000
χ644-4-44000004-4000−222222−22−222222−220-222-2-222-200000000022−22−2222000000000000000000000000
χ654-4-4400000-4400022−22−2222−222222−2202-2-22-222-20000022−22−22220000000000000000000000000000
χ664-4-4400000-4400022−22−2222−222222−220-222-22-2-2200000−222222−220000000000000000000000000000
χ674-4-4400000-44000−222222−2222−22−222202-2-22-222-200000−222222−220000000000000000000000000000
χ684-4-4400000-44000−222222−2222−22−22220-222-22-2-220000022−22−22220000000000000000000000000000

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