Finite Group Databasebeta

← Group #144078

Character table — Group #144078

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122222444444448888888844444444448888888888881616161616161616161616161616161622244488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ11222222-2-2222-2-2200000000-22222-2-2-2-2-20000000000002222−2−2−2−22222−2−2−2−200000000
χ12222222-2-2222-2-2200000000-22222-2-2-2-2-2000000000000−2−2−2−22222−2−2−2−2222200000000
χ13222222-2-2222-2-2200000000-2-2-2-2-22222-20000000000002222−2−2−2−2−2−2−2−2222200000000
χ14222222-2-2222-2-2200000000-2-2-2-2-22222-2000000000000−2−2−2−222222222−2−2−2−200000000
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
χ17222222-2-2-2-2-222-2-2-2-2-22222-2000000002-2-22200000000000000000000000000002-200
χ18222222-2-2-2-2-222-2-2-2-2-22222-2000000002-2-2220000000000000000000000000000-2200
χ192222-2-22222-222-222222222-200000000-2-2-2-2-2000000000000000000000000002-20000
χ202222-2-22222-222-222222222-200000000-2-2-2-2-200000000000000000000000000-220000
χ212222-2-22222-222-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000000000000000002i−2i
χ222222-2-22222-222-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000−2i2i
χ232222-2-222-2-22-2-2200000000-200000000200002222-2-2-2-222−2−222−2−222−2−222−2−200000000
χ242222-2-222-2-22-2-2200000000-200000000200002222-2-2-2-2−2−222−2−222−2−222−2−22200000000
χ252222-2-222-2-22-2-2200000000-20000000020000-2-2-2-2222222−2−222−2−2−2−222−2−22200000000
χ262222-2-222-2-22-2-2200000000-20000000020000-2-2-2-22222−2−222−2−22222−2−222−2−200000000
χ272222-2-2-2-2-2-222222222-2-2-2-2200000000-2-2-2220000000022-2-2-2-2220000000000000000
χ282222-2-2-2-2-2-222222222-2-2-2-2200000000-2-2-22200000000-2-22222-2-20000000000000000
χ292222-2-2-2-2-2-22222-2-2-2-22222200000000-222-2-2000000000000000022-2-2-2-22200000000
χ302222-2-2-2-2-2-22222-2-2-2-22222200000000-222-2-20000000000000000-2-22222-2-200000000
χ312-22-22-2002-2200-222−2−222−2−2000002i2i−2i−2i02−22−2i2i2−i2−i2i2i2−i2−i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ322-22-22-2002-2200-222−2−222−2−2000002i2i−2i−2i02−22−2i2i2−i2−i2i2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ332-22-22-2002-2200-222−2−222−2−200000−2i−2i2i2i02−22−2−i2−i2i2i2−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ342-22-22-2002-2200-222−2−222−2−200000−2i−2i2i2i02−22−2−i2−i2i2i2−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ352-22-22-2002-2200-2−2−222−2−222000002i2i−2i−2i0−22−22−i2−i2i2i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ362-22-22-2002-2200-2−2−222−2−222000002i2i−2i−2i0−22−22−i2−i2i2i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ372-22-22-2002-2200-2−2−222−2−22200000−2i−2i2i2i0−22−22i2i2−i2−i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ382-22-22-2002-2200-2−2−222−2−22200000−2i−2i2i2i0−22−22i2i2−i2−i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ392-22-2-2200-22200-222−2−2−2−22202i2i−2i−2i00000−222−2i2i2−i2−i2−i2−i2i2i2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ402-22-2-2200-22200-222−2−2−2−22202i2i−2i−2i00000−222−2i2i2−i2−i2−i2−i2i2i2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ412-22-2-2200-22200-222−2−2−2−2220−2i−2i2i2i00000−222−2−i2−i2i2i2i2i2−i2−i2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ700000000
χ422-22-2-2200-22200-222−2−2−2−2220−2i−2i2i2i00000−222−2−i2−i2i2i2i2i2−i2−i2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ700000000
χ432-22-2-2200-22200-2−2−22222−2−202i2i−2i−2i000002−2−22−i2−i2i2i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ442-22-2-2200-22200-2−2−22222−2−202i2i−2i−2i000002−2−22−i2−i2i2i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ452-22-2-2200-22200-2−2−22222−2−20−2i−2i2i2i000002−2−22i2i2−i2−i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ500000000
χ462-22-2-2200-22200-2−2−22222−2−20−2i−2i2i2i000002−2−22i2i2−i2−i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ500000000
χ4744444444-4-4-4-4-4-400000000400000000-4000000000000000000000000000000000000
χ484444-4-4-4-444-4-4-4-4000000004000000004000000000000000000000000000000000000
χ4944-4-4004-400000022−2222−2222−2222−2202i−2i2i−2i2i−2i2i−2i0000000002i2−2i22i2−2i2000000000000000000000000
χ5044-4-4004-400000022−2222−2222−2222−220−2i2i−2i2i−2i2i−2i2i000000000−2i22i2−2i22i2000000000000000000000000
χ5144-4-4004-4000000−2222−2222−2222−222202i−2i2i−2i2i−2i2i−2i000000000−2i22i2−2i22i2000000000000000000000000
χ5244-4-4004-4000000−2222−2222−2222−22220−2i2i−2i2i−2i2i−2i2i0000000002i2−2i22i2−2i2000000000000000000000000
χ5344-4-400-4400000022−2222−22−2222−222202i−2i2i−2i−2i2i−2i2i000002i2−2i22i2−2i20000000000000000000000000000
χ5444-4-400-4400000022−2222−22−2222−22220−2i2i−2i2i2i−2i2i−2i00000−2i22i2−2i22i20000000000000000000000000000
χ5544-4-400-44000000−2222−222222−2222−2202i−2i2i−2i−2i2i−2i2i00000−2i22i2−2i22i20000000000000000000000000000
χ5644-4-400-44000000−2222−222222−2222−220−2i2i−2i2i2i−2i2i−2i000002i2−2i22i2−2i20000000000000000000000000000
χ574-44-44-400-44-40042222−22−22−22−222222000000000022−22−222200000000000000000000000000000000
χ584-44-44-400-44-4004−22−2222222222−22−220000000000−222222−2200000000000000000000000000000000
χ594-44-4-44004-4-40042222−22−222222−22−220000000000−2222−222200000000000000000000000000000000
χ604-44-4-44004-4-4004−22−222222−22−222222000000000022−2222−2200000000000000000000000000000000
χ614-4-4400000004-4000004-4-4402-2-222-2-22000002-2-222-2-22000000000000000000000000
χ624-4-4400000004-4000004-4-440-222-2-222-200000-222-2-222-2000000000000000000000000
χ634-4-4400000004-400000-444-402-2-222-2-2200000-222-2-222-2000000000000000000000000
χ644-4-4400000004-400000-444-40-222-2-222-2000002-2-222-2-22000000000000000000000000
χ654-4-440000000-4404-4-44000002-2-22-222-2000002-2-22-222-2000000000000000000000000
χ664-4-440000000-4404-4-4400000-222-22-2-2200000-222-22-2-22000000000000000000000000
χ674-4-440000000-440-444-4000002-2-22-222-200000-222-22-2-22000000000000000000000000
χ684-4-440000000-440-444-400000-222-22-2-22000002-2-22-222-2000000000000000000000000

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