Finite Group Databasebeta

← Group #145115

Character table — Group #145115

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888816161616161616161616161616161616444488881616161616161616444488884444
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
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
χ1122222222222-2-2-2-2200000000-2-2000022222222−2−2−2−2−2−2−2−222-2-200002222−2−2−2−2000000000000
χ1222222222222-2-2-2-2200000000-2-2000022222222−2−2−2−2−2−2−2−2-2-2220000−2−2−2−22222000000000000
χ1322222222222-2-2-2-2200000000-2-20000−2−2−2−2−2−2−2−22222222222-2-20000−2−2−2−22222000000000000
χ1422222222222-2-2-2-2200000000-2-20000−2−2−2−2−2−2−2−222222222-2-22200002222−2−2−2−2000000000000
χ1522222222-2-2-22222-222222222-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ1622222222-2-2-22222-222222222-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ1722222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000002-2
χ1822222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000-22
χ19222-2-22-2-200022-2-202222-2-2-2-20000002222−2−2−2−22222−2−2−2−200000000000000002-20022−2−20000
χ20222-2-22-2-200022-2-202222-2-2-2-20000002222−2−2−2−22222−2−2−2−20000000000000000-2200−2−2220000
χ21222-2-22-2-200022-2-202222-2-2-2-2000000−2−2−2−22222−2−2−2−2222200000000000000002-200−2−2220000
χ22222-2-22-2-200022-2-202222-2-2-2-2000000−2−2−2−22222−2−2−2−222220000000000000000-220022−2−20000
χ2322-222-2-2-222-20000-222−2−22−22−2002−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ52-20022−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000
χ2422-222-2-2-222-20000-222−2−22−22−2002−22−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5-2200−2−222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000
χ2522-222-2-2-222-20000-222−2−22−22−2002−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ52-20022−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5000000000000
χ2622-222-2-2-222-20000-222−2−22−22−2002−22−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5-2200−2−222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5000000000000
χ2722-222-2-2-222-20000-2−2−222−22−2200−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ72-200−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000
χ2822-222-2-2-222-20000-2−2−222−22−2200−22−22ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7-220022−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000
χ2922-222-2-2-222-20000-2−2−222−22−2200−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ72-200−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7000000000000
χ3022-222-2-2-222-20000-2−2−222−22−2200−22−22−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7-220022−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7000000000000
χ312-222-2-22-22-2-2000022−22−22−2−2200−222−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5002-22−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000000000
χ322-222-2-22-22-2-2000022−22−22−2−2200−222−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500-22−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000000000
χ332-222-2-22-22-2-2000022−22−22−2−2200−222−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5002-22−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7000000000000
χ342-222-2-22-22-2-2000022−22−22−2−2200−222−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500-22−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7000000000000
χ352-222-2-22-22-2-200002−22−22−222−2002−2−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7002-2−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ362-222-2-22-22-2-200002−22−22−222−2002−2−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700-222−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ372-222-2-22-22-2-200002−22−22−222−2002−2−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7002-2−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ382-222-2-22-22-2-200002−22−22−222−2002−2−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700-222−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ392-2-22-22-222-222-2-22-2000000002-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200002-2-22i2−i2−i2i2−i2i2i2−i2000000000000
χ402-2-22-22-222-222-2-22-2000000002-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000-222-2−i2i2i2−i2i2−i2−i2i2000000000000
χ412-2-22-22-222-222-2-22-2000000002-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200002-2-22−i2i2i2−i2i2−i2−i2i2000000000000
χ422-2-22-22-222-222-2-22-2000000002-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000-222-2i2−i2−i2i2−i2i2i2−i2000000000000
χ432-2-22-22-222-22-222-2-22-2-2222-2-2-22-2-2220000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ442-2-22-22-222-22-222-2-22-2-2222-2-2-22-2-222000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ452-2-22-22-222-22-222-2-2-222-2-2-222-2222-2-22i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ462-2-22-22-222-22-222-2-2-222-2-2-222-2222-2-2−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ472-2-22-22-22-22-2-222-222-2-2222-2-22-222-2-200000000000000000000000000000000000000002i−2i00
χ482-2-22-22-22-22-2-222-222-2-2222-2-22-222-2-20000000000000000000000000000000000000000−2i2i00
χ492-2-22-22-22-22-2-222-22-222-2-2-2222-2-2-2220000000000000000000000000000000000002-22-20000
χ502-2-22-22-22-22-2-222-22-222-2-2-2222-2-2-222000000000000000000000000000000000000-22-220000
χ512-2-2-2222-2000-22-220-222-222-2-2000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000002i−2i2−2−220000
χ522-2-2-2222-2000-22-220-222-222-2-2000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000−2i2i−222−20000
χ532-2-2-2222-2000-22-220-222-222-2-2000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000002i−2i−222−20000
χ542-2-2-2222-2000-22-220-222-222-2-2000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000−2i2i2−2−220000
χ5544444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ56444-4-44-4-400044-4-40-4-4-4-4444400000000000000000000000000000000000000000000000000
χ57444-4-44-4-4000-4-4440000000000000002222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ58444-4-44-4-4000-4-444000000000000000-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ5944-444-4-4-4-4-44000042222−22−2222−2222−2200−2222−222200000000000000000000000000000000000000000000
χ6044-444-4-4-4-4-4400004−22−222222−2222−22220022−2222−2200000000000000000000000000000000000000000000
χ6144-4-4-4-444000000002222−22−22−2222−2222000000ζ+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−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
χ6244-4-4-4-444000000002222−22−22−2222−2222000000−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+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
χ6344-4-4-4-44400000000−22−22222222−2222−22000000ζ−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−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
χ6444-4-4-4-44400000000−22−22222222−2222−22000000−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+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
χ654-444-4-44-4-4440000-422−2222−2222−22−22220022−22−222200000000000000000000000000000000000000000000
χ664-444-4-44-4-4440000-4−2222−2222−222222−2200−222222−2200000000000000000000000000000000000000000000
χ674-44-44-4-440000000022−2222−22−222222−22000000ζ−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
χ684-44-44-4-440000000022−2222−22−222222−22000000−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
χ694-44-44-4-4400000000−2222−222222−22−2222000000ζ+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
χ704-44-44-4-4400000000−2222−222222−22−2222000000−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
χ714-4-44-44-44-44-44-4-44400000000-44000000000000000000000000000000000000000000000000
χ724-4-4-4444-40004-44-40000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ734-4-4-4444-40004-44-4000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ744-4-4-4444-4000-44-4404-4-44-4-44400000000000000000000000000000000000000000000000000

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