Finite Group Databasebeta

← Group #500855

Character table — Group #500855

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222224444444444444444444444444488888888888888161616161616161632323232
order122222444488881616161616161616224444448888881616161616161616161616162488881616161616161616224444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111
χ911111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ1011111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111111-11-111-1-1-11-11
χ1211111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-11-11-1-1111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111-111-1
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-11-1-11
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1111111-1-1-1-11-11-1-1-1111-1-11
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1111111-1-1-1-1-11-1111-1-1-111-1
χ172222222222-2-2-2-20000000022222222-2-2-2-2-2-2000000000000-2-2-2-22200000000000000000000
χ182222222222-2-2-2-2000000002222-2-2-2-22222-2-200000000000022-2-2-2-200000000000000000000
χ192222222222-2-2-2-200000000-2-2-2-22222-2-2-2-2-2-20000000000002222-2-200000000000000000000
χ202222222222-2-2-2-200000000-2-2-2-2-2-2-2-22222-2-2000000000000-2-2222200000000000000000000
χ212222-2-22-22-2222222222222000000000000-2-2-2-2-2-2000000000000000000000022-2-200000000
χ222222-2-22-22-2222222222222000000000000-2-2-2-2-2-20000000000000000000000-2-22200000000
χ232222-2-22-22-22222-2-2-2-2-2-2-2-2000000000000-2-2222200000000000000000000002-2-2200000000
χ242222-2-22-22-22222-2-2-2-2-2-2-2-2000000000000-2-222220000000000000000000000-222-200000000
χ252222-2-2-22-2200002222−2−2−2−222-2-2000022-2-20022−2−22222−2−2−2−22-2000022−2−222−2−2000000000000
χ262222-2-2-22-2200002222−2−2−2−222-2-20000-2-2220022−2−2−2−2−2−22222-22000022−2−2−2−222000000000000
χ272222-2-2-22-2200002222−2−2−2−2-2-222000022-2-20022−2−22222−2−2−2−2-220000−2−222−2−222000000000000
χ282222-2-2-22-2200002222−2−2−2−2-2-2220000-2-2220022−2−2−2−2−2−222222-20000−2−22222−2−2000000000000
χ292222-2-2-22-220000−2−2−2−2222222-2-2000022-2-200−2−222−2−2−2−222222-20000−2−222−2−222000000000000
χ302222-2-2-22-220000−2−2−2−2222222-2-20000-2-22200−2−2222222−2−2−2−2-220000−2−22222−2−2000000000000
χ312222-2-2-22-220000−2−2−2−22222-2-222000022-2-200−2−222−2−2−2−22222-22000022−2−222−2−2000000000000
χ322222-2-2-22-220000−2−2−2−22222-2-2220000-2-22200−2−2222222−2−2−2−22-2000022−2−2−2−222000000000000
χ332-2-222-222-2-2000022−2−222−2−22-22-22i2i−2i−2i0000002−22−2i2i2−i2−i2i2i2−i2−i200002i−2i2−22−2i2−i2i2−i2000000000000
χ342-2-222-222-2-2000022−2−222−2−22-22-2−2i−2i2i2i0000002−22−2−i2−i2i2i2−i2−i2i2i20000−2i2i2−22−2−i2i2−i2i2000000000000
χ352-2-222-222-2-2000022−2−222−2−2-22-222i2i−2i−2i0000002−22−2i2i2−i2−i2i2i2−i2−i20000−2i2i−22−22−i2i2−i2i2000000000000
χ362-2-222-222-2-2000022−2−222−2−2-22-22−2i−2i2i2i0000002−22−2−i2−i2i2i2−i2−i2i2i200002i−2i−22−22i2−i2i2−i2000000000000
χ372-2-222-222-2-20000−2−222−2−2222-22-22i2i−2i−2i000000−22−22−i2−i2i2i2−i2−i2i2i200002i−2i−22−22−i2i2−i2i2000000000000
χ382-2-222-222-2-20000−2−222−2−2222-22-2−2i−2i2i2i000000−22−22i2i2−i2−i2i2i2−i2−i20000−2i2i−22−22i2−i2i2−i2000000000000
χ392-2-222-222-2-20000−2−222−2−222-22-222i2i−2i−2i000000−22−22−i2−i2i2i2−i2−i2i2i20000−2i2i2−22−2i2−i2i2−i2000000000000
χ402-2-222-222-2-20000−2−222−2−222-22-22−2i−2i2i2i000000−22−22i2i2−i2−i2i2i2−i2−i200002i−2i2−22−2−i2i2−i2i2000000000000
χ412-2-222-2-2-222-2-22222-2-2-2-2220000000000002-2-222-2000000000000000000000000002-22-20000
χ422-2-222-2-2-222-2-22222-2-2-2-2220000000000002-2-222-200000000000000000000000000-22-220000
χ432-2-222-2-2-222-2-222-2-22222-2-20000000000002-22-2-22000000000000000000000000002-2-220000
χ442-2-222-2-2-222-2-222-2-22222-2-20000000000002-22-2-2200000000000000000000000000-222-20000
χ452-2-22-22-222-222-2-2000000002-2-22000000002-200002i2i−2i−2i−2i−2i2i2i002-20000002i−2i−2i2i000000000000
χ462-2-22-22-222-222-2-2000000002-2-22000000002-20000−2i−2i2i2i2i2i−2i−2i002-2000000−2i2i2i−2i000000000000
χ472-2-22-22-222-222-2-200000000-222-2000000002-200002i2i−2i−2i−2i−2i2i2i00-22000000−2i2i2i−2i000000000000
χ482-2-22-22-222-222-2-200000000-222-2000000002-20000−2i−2i2i2i2i2i−2i−2i00-220000002i−2i−2i2i000000000000
χ492-2-22-22-222-2-2-22222-2-2-2-2222-2-2200000000-222-2-220000000000-22002-2-220000000000000000
χ502-2-22-22-222-2-2-22222-2-2-2-222-222-200000000-222-2-2200000000002-200-222-20000000000000000
χ512-2-22-22-222-2-2-222-2-22222-2-22-2-2200000000-22-222-20000000000-2200-222-20000000000000000
χ522-2-22-22-222-2-2-222-2-22222-2-2-222-200000000-22-222-200000000002-2002-2-220000000000000000
χ53444444-4-4-4-4000022222222−22−22−22−2200000000000000−22−2222220000000000000000000000000000000000
χ54444444-4-4-4-40000−22−22−22−2222222222000000000000002222−22−220000000000000000000000000000000000
χ554444-4-44-44-4-4-4-4-4000000000000000000004400000000000000000000000000000000000000
χ5644-4-400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ500002-22-222−2200000000ζ+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+ζ700000000000000000000000000
χ5744-4-400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ50000-22-22−222200000000−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−ζ700000000000000000000000000
χ5844-4-400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ500002-22-222−2200000000−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−ζ700000000000000000000000000
χ5944-4-400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ50000-22-22−222200000000ζ+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+ζ700000000000000000000000000
χ6044-4-4000000−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ700002-22-2−222200000000−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+ζ700000000000000000000000000
χ6144-4-4000000−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ70000-22-2222−2200000000ζ−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−ζ700000000000000000000000000
χ6244-4-4000000−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ700002-22-2−222200000000ζ−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−ζ700000000000000000000000000
χ6344-4-4000000−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ70000-22-2222−2200000000−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+ζ700000000000000000000000000
χ644-44-400000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700002i−2i−2i2i002i2−2i2000000ζ+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+ζ700000000000000000000000000
χ654-44-400000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000−2i2i2i−2i00−2i22i2000000−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−ζ700000000000000000000000000
χ664-44-400000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700002i−2i−2i2i002i2−2i2000000−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−ζ700000000000000000000000000
χ674-44-400000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000−2i2i2i−2i00−2i22i2000000ζ+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+ζ700000000000000000000000000
χ684-44-4000000−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500002i−2i−2i2i00−2i22i2000000−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+ζ700000000000000000000000000
χ694-44-4000000−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000−2i2i2i−2i002i2−2i2000000ζ−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−ζ700000000000000000000000000
χ704-44-4000000−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500002i−2i−2i2i00−2i22i2000000ζ−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−ζ700000000000000000000000000
χ714-44-4000000−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000−2i2i2i−2i002i2−2i2000000−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+ζ700000000000000000000000000
χ724-4-444-4-4-44444-4-400000000000000000000-4400000000000000000000000000000000000000
χ734-4-44-444-4-4400002222−22−222222−22−2200000000000000−2222−22220000000000000000000000000000000000
χ744-4-44-444-4-440000−22−222222−22−2222220000000000000022−2222−220000000000000000000000000000000000

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