Finite Group Databasebeta

← Group #144147

Character table — Group #144147

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222244444444888888884488881616161616161616161616161616161688888888161616161616161622244488
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ112222222-2-222-2-222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ122222222-2-222-2-222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ132222222-2-222-2-22-2-2-2-22222-2-222-2-20000000000000000000000002222-2-2-2-200000000
χ142222222-2-222-2-22-2-2-2-22222-2-222-2-2000000000000000000000000-2-2-2-2222200000000
χ152222-2-2222-2-2-2-2200000000-2200002222−2−2−2−22222−2−2−2−2000022-2-222−2−222−2−200000000
χ162222-2-2222-2-2-2-2200000000-2200002222−2−2−2−22222−2−2−2−20000-2-222−2−222−2−22200000000
χ172222-2-2222-2-2-2-2200000000-220000−2−2−2−22222−2−2−2−22222000022-2-2−2−222−2−22200000000
χ182222-2-2222-2-2-2-2200000000-220000−2−2−2−22222−2−2−2−222220000-2-22222−2−222−2−200000000
χ192222-2-22-2-2-2-2222000000002-200002222−2−2−2−2−2−2−2−2222222-2-2000022−2−2−2−22200000000
χ202222-2-22-2-2-2-2222000000002-200002222−2−2−2−2−2−2−2−22222-2-2220000−2−22222−2−200000000
χ212222-2-22-2-2-2-2222000000002-20000−2−2−2−222222222−2−2−2−222-2-20000−2−22222−2−200000000
χ222222-2-22-2-2-2-2222000000002-20000−2−2−2−222222222−2−2−2−2-2-222000022−2−2−2−22200000000
χ232222-2-2-2222222-222222222-2-2-2-2-2-200000000000000000000000000000000002-20000
χ242222-2-2-2222222-222222222-2-2-2-2-2-20000000000000000000000000000000000-220000
χ252222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002-200
χ262222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000-2200
χ272222-2-2-2-2-222-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000002i−2i
χ282222-2-2-2-2-222-2-2-22222-2-2-2-22222-2-200000000000000000000000000000000000000−2i2i
χ292222-2-2-2-2-222-2-2-2-2-2-2-2222222-2-222000000000000000000000000000000002-2000000
χ302222-2-2-2-2-222-2-2-2-2-2-2-2222222-2-22200000000000000000000000000000000-22000000
χ312-22-22-22002-200-2000022-2-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i200002-22-200000000
χ322-22-22-22002-200-2000022-2-2002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i20000-22-2200000000
χ332-22-22-22002-200-2000022-2-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i20000-22-2200000000
χ342-22-22-22002-200-2000022-2-2002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i200002-22-200000000
χ352-22-22-22002-200-20000-2-22200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i22-22-2000000000000
χ362-22-22-22002-200-20000-2-22200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i2-22-22000000000000
χ372-22-22-22002-200-20000-2-22200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i2-22-22000000000000
χ382-22-22-22002-200-20000-2-22200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i22-22-2000000000000
χ392-22-2-22200-2200-222-2-2000000002-2000000002i2i−2i−2i−2i−2i2i2ii2−i2−i2i2i2−i2−i2i22−2−222−2−2200000000
χ402-22-2-22200-2200-222-2-2000000002-2000000002i2i−2i−2i−2i−2i2i2i−i2i2i2−i2−i2i2i2−i2−222−2−222−200000000
χ412-22-2-22200-2200-222-2-2000000002-200000000−2i−2i2i2i2i2i−2i−2ii2−i2−i2i2i2−i2−i2i2−222−2−222−200000000
χ422-22-2-22200-2200-222-2-2000000002-200000000−2i−2i2i2i2i2i−2i−2i−i2i2i2−i2−i2i2i2−i22−2−222−2−2200000000
χ432-22-2-22200-2200-2-2-22200000000-222i2i−2i−2i−2i−2i2i2i00000000i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000
χ442-22-2-22200-2200-2-2-22200000000-222i2i−2i−2i−2i−2i2i2i00000000−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000
χ452-22-2-22200-2200-2-2-22200000000-22−2i−2i2i2i2i2i−2i−2i00000000i2−i2−i2i2−i2i2i2−i2−222−22−2−2200000000
χ462-22-2-22200-2200-2-2-22200000000-22−2i−2i2i2i2i2i−2i−2i00000000−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000
χ47444444-444-4-4-4-4-4000000004-400000000000000000000000000000000000000000000
χ48444444-4-4-4-4-444-400000000-4400000000000000000000000000000000000000000000
χ4944-4-40004-40000022−2222−2222−2222−22000000ζ+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−ζ7ζ+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−ζ7000000000000000000000000
χ5044-4-40004-40000022−2222−2222−2222−22000000−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+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−ζ7ζ−ζ3−ζ5+ζ7000000000000000000000000
χ5144-4-40004-400000−2222−2222−2222−2222000000ζ−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+ζ7ζ−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+ζ7000000000000000000000000
χ5244-4-40004-400000−2222−2222−2222−2222000000−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−ζ7−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−ζ7000000000000000000000000
χ5344-4-4000-440000022−2222−22−2222−2222000000ζ+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−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−ζ7ζ−ζ3−ζ5+ζ7000000000000000000000000
χ5444-4-4000-440000022−2222−22−2222−2222000000−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+ζ7ζ+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−ζ7000000000000000000000000
χ5544-4-4000-4400000−2222−222222−2222−22000000ζ−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+ζ7−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−ζ7000000000000000000000000
χ5644-4-4000-4400000−2222−222222−2222−22000000−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−ζ7ζ−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+ζ7000000000000000000000000
χ574-44-44-4-400-4400444-4-400000000-440000000000000000000000000000000000000000
χ584-44-44-4-400-44004-4-444000000004-40000000000000000000000000000000000000000
χ594-44-4-44-4004-4004000044-4-400-44000000000000000000000000000000000000000000
χ604-44-4-44-4004-40040000-4-444004-4000000000000000000000000000000000000000000
χ614-4-4400000004-4022−22−222222−22−2222000000ζ−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+ζ7ζ+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−ζ7000000000000000000000000
χ624-4-4400000004-4022−22−222222−22−2222000000−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−ζ7−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+ζ7000000000000000000000000
χ634-4-4400000004-40−222222−22−222222−22000000ζ+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−ζ7−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−ζ7000000000000000000000000
χ644-4-4400000004-40−222222−22−222222−22000000−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+ζ7ζ−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+ζ7000000000000000000000000
χ654-4-440000000-44022−22−2222−222222−22000000ζ−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+ζ7−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+ζ7000000000000000000000000
χ664-4-440000000-44022−22−2222−222222−22000000−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−ζ7ζ+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−ζ7000000000000000000000000
χ674-4-440000000-440−222222−2222−22−2222000000ζ+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−ζ7ζ−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+ζ7000000000000000000000000
χ684-4-440000000-440−222222−2222−22−2222000000−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+ζ7−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−ζ7000000000000000000000000

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