Finite Group Databasebeta

← Group #143402

Character table — Group #143402

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888816161616161616161616161616161616444488881616161616161616224488882244
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ92222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ102222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ11222222222-2-2-2222-222222222-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ12222222222-2-2-2222-222222222-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ13222222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002-200
χ14222222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000-2200
χ1522222222-2222-2-2-2200000000-2-2000022222222−2−2−2−2−2−2−2−222-2-200002222−2−2−2−2000000000000
χ1622222222-2222-2-2-2200000000-2-2000022222222−2−2−2−2−2−2−2−2-2-2220000−2−2−2−22222000000000000
χ1722222222-2222-2-2-2200000000-2-20000−2−2−2−2−2−2−2−22222222222-2-20000−2−2−2−22222000000000000
χ1822222222-2222-2-2-2200000000-2-20000−2−2−2−2−2−2−2−222222222-2-22200002222−2−2−2−2000000000000
χ192222-2-2-2-220002-2-2022-2-2-2-222000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000002i−2i22−2−20000
χ202222-2-2-2-220002-2-2022-2-2-2-222000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000000000−2i2i−2−2220000
χ212222-2-2-2-220002-2-2022-2-2-2-222000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000002i−2i−2−2220000
χ222222-2-2-2-220002-2-2022-2-2-2-222000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000−2i2i22−2−20000
χ2322-2-22-22-2022-2000-22−222−2−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5002-222−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000000000
χ2422-2-22-22-2022-2000-22−222−2−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500-22−2−222−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000000000
χ2522-2-22-22-2022-2000-22−222−2−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5002-222−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000000000
χ2622-2-22-22-2022-2000-22−222−2−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500-22−2−222ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000000000
χ2722-2-22-22-2022-2000-2−22−2−222−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7002-2−2−222−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000000000
χ2822-2-22-22-2022-2000-2−22−2−222−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700-2222−2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000000000
χ2922-2-22-22-2022-2000-2−22−2−222−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7002-2−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000000000
χ3022-2-22-22-2022-2000-2−22−2−222−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700-2222−2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000000000
χ312-22-2-222-202-22000-22−22−22−2−2200−222−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ52-2002−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ322-22-2-222-202-22000-22−22−22−2−2200−222−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5-2200−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ332-22-2-222-202-22000-22−22−22−2−2200−222−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ52-2002−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ342-22-2-222-202-22000-22−22−22−2−2200−222−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5-2200−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ352-22-2-222-202-22000-2−22−22−222−2002−2−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ72-200−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000000000
χ362-22-2-222-202-22000-2−22−22−222−2002−2−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7-22002−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000000000
χ372-22-2-222-202-22000-2−22−22−222−2002−2−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ72-200−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000000000
χ382-22-2-222-202-22000-2−22−22−222−2002−2−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7-22002−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000000000
χ392-2-2222-2-2-20002-22022-222-2-2-2000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000002-200i2−i2i2−i20000
χ402-2-2222-2-2-20002-22022-222-2-2-2000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000-2200−i2i2−i2i20000
χ412-2-2222-2-2-20002-22022-222-2-2-2000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000002-200−i2i2−i2i20000
χ422-2-2222-2-2-20002-22022-222-2-2-2000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000-2200i2−i2i2−i20000
χ432-2-22-2-22222-2-2-2-222000000002-200002−2−222−2−22−222−2−222−200002-2-22−222−2−222−2000000000000
χ442-2-22-2-22222-2-2-2-222000000002-200002−2−222−2−22−222−2−222−20000-222-22−2−222−2−22000000000000
χ452-2-22-2-22222-2-2-2-222000000002-20000−222−2−222−22−2−222−2−2200002-2-222−2−222−2−22000000000000
χ462-2-22-2-22222-2-2-2-222000000002-20000−222−2−222−22−2−222−2−220000-222-2−222−2−222−2000000000000
χ472-2-22-2-222-22-2-222-22222-2-22-2-2-22-2-2222-2-222-2-222-2-222-2-220000000000000000000000000000
χ482-2-22-2-222-22-2-222-22222-2-22-2-2-22-2-222-222-2-222-2-222-2-222-20000000000000000000000000000
χ492-2-22-2-222-22-2-222-22-2-2-222-222-2222-2-20000000000000000000000002-2-22-222-2000000000000
χ502-2-22-2-222-22-2-222-22-2-2-222-222-2222-2-2000000000000000000000000-222-22-2-22000000000000
χ512-2-22-2-222-2-22222-2-2222-2-22-2-22-222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ522-2-22-2-222-2-22222-2-2222-2-22-2-22-222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ532-2-22-2-222-2-22222-2-2-2-2-222-2222-2-2-2220000000000000000000000000000000000000000002-2
χ542-2-22-2-222-2-22222-2-2-2-2-222-2222-2-2-222000000000000000000000000000000000000000000-22
χ5544444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ564444-4-4-4-440004-4-40-4-44444-4-400000000000000000000000000000000000000000000000000
χ574444-4-4-4-4-4000-4440000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ584444-4-4-4-4-4000-444000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ5944-4-44-44-40-4-44000422−222222−22−2222−2200−2222−222200000000000000000000000000000000000000000000
χ6044-4-44-44-40-4-440004−2222−22−222222−22220022−2222−2200000000000000000000000000000000000000000000
χ6144-4-4-44-440000000022−22−22−22222222−22000000ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ70000000000000000000000000000
χ6244-4-4-44-440000000022−22−22−22222222−22000000−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ70000000000000000000000000000
χ6344-4-4-44-4400000000−22222222−22−22−2222000000ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−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−ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ70000000000000000000000000000
χ6444-4-4-44-4400000000−22222222−22−22−2222000000−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+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+ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ70000000000000000000000000000
χ654-44-44-4-440000000022−22−2222−2222−2222000000ζ−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−ζ70000000000000000000000000000
χ664-44-44-4-440000000022−22−2222−2222−2222000000−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+ζ70000000000000000000000000000
χ674-44-44-4-4400000000−222222−2222−2222−22000000ζ+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+ζ70000000000000000000000000000
χ684-44-44-4-4400000000−222222−2222−2222−22000000−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−ζ70000000000000000000000000000
χ694-44-4-444-40-44-4000422−2222−2222−22−22220022−22−222200000000000000000000000000000000000000000000
χ704-44-4-444-40-44-40004−2222−2222−222222−2200−222222−2200000000000000000000000000000000000000000000
χ714-4-4444-4-44000-44-40000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ724-4-4444-4-44000-44-4000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ734-4-4444-4-4-40004-440-4-44-4-444400000000000000000000000000000000000000000000000000
χ744-4-44-4-4444-444-4-44-400000000-44000000000000000000000000000000000000000000000000

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