Finite Group Databasebeta

← Group #145980

Character table — Group #145980

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888816161616161616161616161616161616444488881616161616161616888888884444
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
χ112222222222-2-2-2-22200000000-2-200002222−2−2−2−22222−2−2−2−222-2-200002222−2−2−2−2000000000000
χ122222222222-2-2-2-22200000000-2-200002222−2−2−2−22222−2−2−2−2-2-2220000−2−2−2−22222000000000000
χ132222222222-2-2-2-22200000000-2-20000−2−2−2−22222−2−2−2−2222222-2-20000−2−2−2−22222000000000000
χ142222222222-2-2-2-22200000000-2-20000−2−2−2−22222−2−2−2−22222-2-22200002222−2−2−2−2000000000000
χ1522222222-2-22222-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1622222222-2-22222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1722222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ1822222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ1922222222-2-2-2-2-2-2-2-2000000002200002222−2−2−2−2−2−2−2−2222200002i2i−2i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ2022222222-2-2-2-2-2-2-2-2000000002200002222−2−2−2−2−2−2−2−222220000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ2122222222-2-2-2-2-2-2-2-200000000220000−2−2−2−222222222−2−2−2−200002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ2222222222-2-2-2-2-2-2-2-200000000220000−2−2−2−222222222−2−2−2−20000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ23222-2-2-22-20022-2-20022-2-2-2-2220000002i2i−2i−2i2i2i−2i−2i000000000000000000000000i2i2−i2−i222−2−20000
χ24222-2-2-22-20022-2-20022-2-2-2-2220000002i2i−2i−2i2i2i−2i−2i000000000000000000000000−i2−i2i2i2−2−2220000
χ25222-2-2-22-20022-2-20022-2-2-2-222000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000i2i2−i2−i2−2−2220000
χ26222-2-2-22-20022-2-20022-2-2-2-222000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000−i2−i2i2i222−2−20000
χ272-222-2-2-2222-222-2-2-22222-2-2-2-22-222-2-20000000000000000000000000000000000000000002-2
χ282-222-2-2-2222-222-2-2-22222-2-2-2-22-222-2-2000000000000000000000000000000000000000000-22
χ292-222-2-2-2222-222-2-2-2-2-2-2-222222-2-2-2220000000000000000000000000000000000002i−2i2i−2i0000
χ302-222-2-2-2222-222-2-2-2-2-2-2-222222-2-2-222000000000000000000000000000000000000−2i2i−2i2i0000
χ312-222-2-2-22-2-2-222-2222222-2-2-2-2-22-2-22200000000000000000000000000000000000000002i−2i00
χ322-222-2-2-22-2-2-222-2222222-2-2-2-2-22-2-2220000000000000000000000000000000000000000−2i2i00
χ332-222-2-2-22-2-2-222-222-2-2-2-22222-2222-2-2000000000000000000000000000000002-22-200000000
χ342-222-2-2-22-2-2-222-222-2-2-2-22222-2222-2-200000000000000000000000000000000-22-2200000000
χ352-22-222-2-200-22-2200-2-222-2-2220000000000000022-2-222-2-20000000000000000i2−i2−i2i2i2−i2−i2i20000
χ362-22-222-2-200-22-2200-2-222-2-2220000000000000022-2-222-2-20000000000000000−i2i2i2−i2−i2i2i2−i20000
χ372-22-222-2-200-22-2200-2-222-2-22200000000000000-2-222-2-2220000000000000000i2−i2−i2i2−i2i2i2−i20000
χ382-22-222-2-200-22-2200-2-222-2-22200000000000000-2-222-2-2220000000000000000−i2i2i2−i2i2−i2−i2i20000
χ392-2-222-22-22-200002-22−22−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5002i−2ii2−i2i2−i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000000000000
χ402-2-222-22-22-200002-22−22−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500−2i2i−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000000000000
χ412-2-222-22-22-200002-22−22−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5002i−2ii2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5000000000000
χ422-2-222-22-22-200002-22−22−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500−2i2i−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5000000000000
χ432-2-222-22-22-200002-2−22−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7002i−2i−i2i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000000000000
χ442-2-222-22-22-200002-2−22−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700−2i2ii2−i2i2−i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000000000000
χ452-2-222-22-22-200002-2−22−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7002i−2i−i2i2−i2i2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7000000000000
χ462-2-222-22-22-200002-2−22−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700−2i2ii2−i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7000000000000
χ472-2-222-22-2-220000-222−22−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ52-2002−2−22ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ482-2-222-22-2-220000-222−22−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5-2200−222−2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ492-2-222-22-2-220000-222−22−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ52-2002−2−22−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5000000000000
χ502-2-222-22-2-220000-222−22−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5-2200−222−2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5000000000000
χ512-2-222-22-2-220000-22−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ72-200−222−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7000000000000
χ522-2-222-22-2-220000-22−22−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7-22002−2−22−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7000000000000
χ532-2-222-22-2-220000-22−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ72-200−222−2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7000000000000
χ542-2-222-22-2-220000-22−22−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7-22002−2−22ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7000000000000
χ55444-4-4-44-40044-4-400-4-44444-4-400000000000000000000000000000000000000000000000000
χ56444-4-4-44-400-4-44400000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000
χ57444-4-4-44-400-4-4440000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000000000
χ5844-44-44-4-44-40000-4422−2222−22−2222−22220022−22−222200000000000000000000000000000000000000000000
χ5944-44-44-4-44-40000-44−2222−222222−2222−2200−222222−2200000000000000000000000000000000000000000000
χ6044-44-44-4-4-4400004-422−2222−22−2222−222200−222222−2200000000000000000000000000000000000000000000
χ6144-44-44-4-4-4400004-4−2222−222222−2222−220022−22−222200000000000000000000000000000000000000000000
χ6244-4-44-4-440000000022−22−222222−22−2222000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ70000000000000000000000000000
χ6344-4-44-4-440000000022−22−222222−22−222200000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ70000000000000000000000000000
χ6444-4-44-4-4400000000−222222−22−222222−22000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000
χ6544-4-44-4-4400000000−222222−22−222222−2200000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000
χ664-444-4-4-44444-4-44-4-400000000-44000000000000000000000000000000000000000000000000
χ674-444-4-4-44-4-44-4-4444000000004-4000000000000000000000000000000000000000000000000
χ684-44-444-4-4004-44-40000000000000000000000002222−22−22−22−2222220000000000000000000000000000
χ694-44-444-4-4004-44-4000000000000000000000000−22−2222222222−22−220000000000000000000000000000
χ704-44-444-4-400-44-440044-4-444-4-400000000000000000000000000000000000000000000000000
χ714-4-4-4-44440000000022−22−2222−222222−220000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000000
χ724-4-4-4-44440000000022−22−2222−222222−22000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000000
χ734-4-4-4-444400000000−222222−2222−22−22220000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000000
χ744-4-4-4-444400000000−222222−2222−22−2222000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000000

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