Finite Group Databasebeta

← Group #502516

Character table — Group #502516

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order122222444488888888161616161616161644448888161616161616161616161616244488881616161616161616224488882244
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111-11-1
χ91111111111-1-1-1-1111111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ101111111111-1-1-1-1111111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ111111111111-1-1-1-1111111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ121111111111-1-1-1-1111111111111-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111111-11-1-1-1111111-1-1-1-11-11-1-1-111-111-1
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111111-11-1-1-1111111-1-1-1-1-11-1111-1-11-1-11
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-11-1111-1-1-1-1-1-111111-11-1-1-1111-1-11
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111-11-1111-1-1-1-1-1-11111-11-1111-1-1-111-1
χ1722222222222222-2-2-2-200000000-2-2-2-2-222-20000000000002222-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-200000000-2-2-2-2-222-2000000000000-2-2-2-2222200000000000000000000
χ192222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000002-22-222-2-200000000000000000000
χ202222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000-22-22-2-22200000000000000000000
χ212222-2-22-2-22222200002222−2−2−2−200000-2-2022−2−22222−2−2−2−22-2-22000022−2−222−2−2000000000000
χ222222-2-22-2-22222200002222−2−2−2−200000-2-2022−2−22222−2−2−2−2-222-20000−2−222−2−222000000000000
χ232222-2-22-2-2222220000−2−2−2−2222200000-2-20−2−222−2−2−2−222222-2-220000−2−222−2−222000000000000
χ242222-2-22-2-2222220000−2−2−2−2222200000-2-20−2−222−2−2−2−22222-222-2000022−2−222−2−2000000000000
χ252222-2-22-2-22-2-2-2-200002222−2−2−2−20000022022−2−2−2−2−2−2222222-2-20000−2−22222−2−2000000000000
χ262222-2-22-2-22-2-2-2-200002222−2−2−2−20000022022−2−2−2−2−2−22222-2-222000022−2−2−2−222000000000000
χ272222-2-22-2-22-2-2-2-20000−2−2−2−2222200000220−2−2222222−2−2−2−222-2-2000022−2−2−2−222000000000000
χ282222-2-22-2-22-2-2-2-20000−2−2−2−2222200000220−2−2222222−2−2−2−2-2-2220000−2−22222−2−2000000000000
χ292222-2-2-222-200002222222222220000-200-2-2-2-2-200000000000000000000000022-2-200000000
χ302222-2-2-222-200002222222222220000-200-2-2-2-2-2000000000000000000000000-2-22200000000
χ312222-2-2-222-200002222-2-2-2-2-2-2-2-20000-200-222220000000000000000000000002-2-2200000000
χ322222-2-2-222-200002222-2-2-2-2-2-2-2-20000-200-22222000000000000000000000000-222-200000000
χ332-22-22-22-22-22i2i−2i−2i22-2-2000000002i2i−2i−2i-22i−2i2000000000000000000002-22-22i−2i2i−2i000000000000
χ342-22-22-22-22-22i2i−2i−2i22-2-2000000002i2i−2i−2i-22i−2i200000000000000000000-22-22−2i2i−2i2i000000000000
χ352-22-22-22-22-22i2i−2i−2i-2-22222-2-222-2-2−2i−2i2i2i22i−2i-22-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ362-22-22-22-22-22i2i−2i−2i-2-222-2-222-2-222−2i−2i2i2i22i−2i-2-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ372-22-22-22-22-2−2i−2i2i2i22-2-200000000−2i−2i2i2i-2−2i2i2000000000000000000002-22-2−2i2i−2i2i000000000000
χ382-22-22-22-22-2−2i−2i2i2i22-2-200000000−2i−2i2i2i-2−2i2i200000000000000000000-22-222i−2i2i−2i000000000000
χ392-22-22-22-22-2−2i−2i2i2i-2-22222-2-222-2-22i2i−2i−2i2−2i2i-22-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ402-22-22-22-22-2−2i−2i2i2i-2-222-2-222-2-2222i2i−2i−2i2−2i2i-2-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ412-22-2-2222-2-22i2i−2i−2i000022−2−2−2−22200000−2i2i02−2−22i2i2−i2−i2−i2−i2i2i200002-22i−2i2−2−22i2−i2−i2i2000000000000
χ422-22-2-2222-2-22i2i−2i−2i000022−2−2−2−22200000−2i2i02−2−22i2i2−i2−i2−i2−i2i2i20000-22−2i2i−222−2−i2i2i2−i2000000000000
χ432-22-2-2222-2-22i2i−2i−2i0000−2−22222−2−200000−2i2i0−222−2−i2−i2i2i2i2i2−i2−i200002-22i−2i−222−2−i2i2i2−i2000000000000
χ442-22-2-2222-2-22i2i−2i−2i0000−2−22222−2−200000−2i2i0−222−2−i2−i2i2i2i2i2−i2−i20000-22−2i2i2−2−22i2−i2−i2i2000000000000
χ452-22-2-2222-2-2−2i−2i2i2i000022−2−2−2−222000002i−2i02−2−22−i2−i2i2i2i2i2−i2−i200002-2−2i2i2−2−22−i2i2i2−i2000000000000
χ462-22-2-2222-2-2−2i−2i2i2i000022−2−2−2−222000002i−2i02−2−22−i2−i2i2i2i2i2−i2−i20000-222i−2i−222−2i2−i2−i2i2000000000000
χ472-22-2-2222-2-2−2i−2i2i2i0000−2−22222−2−2000002i−2i0−222−2i2i2−i2−i2−i2−i2i2i200002-2−2i2i−222−2i2−i2−i2i2000000000000
χ482-22-2-2222-2-2−2i−2i2i2i0000−2−22222−2−2000002i−2i0−222−2i2i2−i2−i2−i2−i2i2i20000-222i−2i2−2−22−i2i2i2−i2000000000000
χ492-22-2-22-2-2220000-2-22222-2-222-2-20000-2002-22-2200000000000000000000000000002-22-20000
χ502-22-2-22-2-2220000-2-22222-2-222-2-20000-2002-22-220000000000000000000000000000-22-220000
χ512-22-2-22-2-2220000-2-222-2-222-2-2220000-20022-22-200000000000000000000000000002-2-220000
χ522-22-2-22-2-2220000-2-222-2-222-2-2220000-20022-22-20000000000000000000000000000-222-20000
χ53444444-4-4-4-40000000022222222−22−22−22−2200000000−22−222222000000000000000000000000000000000000
χ54444444-4-4-4-400000000−22−22−22−2222222222000000002222−22−22000000000000000000000000000000000000
χ554444-4-4-444-40000-4-4-4-400000000000040040000000000000000000000000000000000000000
χ5644-4-40000002i2−2i22i2−2i222−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52i−2i2i−2i00000000ζ+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−ζ70000000000000000000000000000
χ5744-4-40000002i2−2i22i2−2i222−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52i−2i2i−2i00000000−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+ζ70000000000000000000000000000
χ5844-4-40000002i2−2i22i2−2i2−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2i2i−2i2i00000000−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
χ5944-4-40000002i2−2i22i2−2i2−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ7−2i2i−2i2i00000000ζ−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
χ6044-4-4000000−2i22i2−2i22i222−2222−222ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2i2i−2i2i00000000−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+ζ70000000000000000000000000000
χ6144-4-4000000−2i22i2−2i22i222−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2i2i−2i2i00000000ζ+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−ζ70000000000000000000000000000
χ6244-4-4000000−2i22i2−2i22i2−2222−22222ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ−2ζ72i−2i2i−2i00000000ζ−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
χ6344-4-4000000−2i22i2−2i22i2−2222−2222−2ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ+2ζ72i−2i2i−2i00000000−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
χ644-44-44-4-44-44000000002222−22−22−22−22222200000000−222222−22000000000000000000000000000000000000
χ654-44-44-4-44-4400000000−22−2222222222−22−220000000022−22−2222000000000000000000000000000000000000
χ664-44-4-44-4-444000044-4-4000000000000400-40000000000000000000000000000000000000000
χ674-4-4400000022−22−222222−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72-2-2200000000ζ−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−ζ70000000000000000000000000000
χ684-4-4400000022−22−222222−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72-2-2200000000−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+ζ70000000000000000000000000000
χ694-4-4400000022−22−2222−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5-222-200000000ζ+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+ζ70000000000000000000000000000
χ704-4-4400000022−22−2222−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5-222-200000000−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−ζ70000000000000000000000000000
χ714-4-44000000−222222−2222−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7-222-200000000−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+ζ70000000000000000000000000000
χ724-4-44000000−222222−2222−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7-222-200000000ζ−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−ζ70000000000000000000000000000
χ734-4-44000000−222222−22−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52-2-2200000000−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−ζ70000000000000000000000000000
χ744-4-44000000−222222−22−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52-2-2200000000ζ+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+ζ70000000000000000000000000000

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