Finite Group Databasebeta

← Group #491055

Character table — Group #491055

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122244444444888824488888888888888888888161616161616161616161616161616162444884444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1
χ61111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11-11
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-11-1
χ91111-1-1-1-111111111-1-1111-1-1-1-111-1-11-1111111-1-11111-1-1-1-11111-1-1-1-11-1-11-1-11-1-11
χ101111-1-1-1-111111111-1-1111-1-1-1-111-1-11-1111111-1-1-1-1-1-11111-1-1-1-111111-1-11-1-1-111-1
χ111111-1-1-1-111111111-1-1111-1-1-1-111-1-11-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-111-111-111-1
χ121111-1-1-1-111111111-1-1111-1-1-1-111-1-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1111-1-11
χ131111-1-1-1-111111111-1-1111-1-1-1-1-1-111-111111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1
χ141111-1-1-1-111111111-1-1111-1-1-1-1-1-111-111111-1-111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-111
χ151111-1-1-1-111111111-1-1111-1-1-1-1-1-111-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-111
χ161111-1-1-1-111111111-1-1111-1-1-1-1-1-111-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-111111-1-1
χ17222222222222-2-2-2-2222-2-2-2-2-2-22222220000-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ1922222222-2-2220000-2-2-20000002222-2-20000000022−2−222−2−222−2−222−2−20000000000
χ2022222222-2-2220000-2-2-20000002222-2-200000000−2−222−2−222−2−222−2−2220000000000
χ2122222222-2-2220000-2-2-2000000-2-2-2-2220000000022−2−222−2−2−2−222−2−2220000000000
χ2222222222-2-2220000-2-2-2000000-2-2-2-22200000000−2−222−2−22222−2−222−2−20000000000
χ23222222-2-222-2-222222-2-2-2-222-2-200000000000000000000000000000022-2-2000000
χ24222222-2-222-2-222222-2-2-2-222-2-2000000000000000000000000000000-2-222000000
χ25222222-2-222-2-2-2-2-2-22-2-222-2-2220000002i2i−2i−2i0000000000000000000000002i−2i0000
χ26222222-2-222-2-2-2-2-2-22-2-222-2-222000000−2i−2i2i2i000000000000000000000000−2i2i0000
χ272222-2-22222-2-22222-22-2-2-2-2-2220000000000000000000000000000002-22-2000000
χ282222-2-22222-2-22222-22-2-2-2-2-222000000000000000000000000000000-22-22000000
χ292222-2-22222-2-2-2-2-2-2-22-22222-2-20000002i2i−2i−2i000000000000000000000000−2i2i0000
χ302222-2-22222-2-2-2-2-2-2-22-22222-2-2000000−2i−2i2i2i0000000000000000000000002i−2i0000
χ312222-2-2-2-22222-2-2-2-2-2-22-2-2222222-2-22-20000-2-22200000000000000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-22-2-22222-2-222-22000022-2-200000000000000000000000000
χ332222-2-2-2-2-2-222000022-200000022-2-2-220000000022−2−2−2−22222−2−2−2−2220000000000
χ342222-2-2-2-2-2-222000022-200000022-2-2-2200000000−2−22222−2−2−2−22222−2−20000000000
χ352222-2-2-2-2-2-222000022-2000000-2-2222-20000000022−2−2−2−222−2−22222−2−20000000000
χ362222-2-2-2-2-2-222000022-2000000-2-2222-200000000−2−22222−2−222−2−2−2−2220000000000
χ372-2-222i−2i2i−2i002-22−22−20002−2i2−i2i2−i22i−2i2-2000000i2−i22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ382-2-222i−2i2i−2i002-22−22−20002−2i2−i2i2−i22i−2i2-2000000i2−i22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ392-2-222i−2i2i−2i002-22−22−20002−2i2−i2i2−i2−2i2i-22000000−i2i2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ402-2-222i−2i2i−2i002-22−22−20002−2i2−i2i2−i2−2i2i-22000000−i2i2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ412-2-222i−2i2i−2i002-2−22−22000−22−i2i2−i2i22i−2i2-2000000−i2i2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ422-2-222i−2i2i−2i002-2−22−22000−22−i2i2−i2i22i−2i2-2000000−i2i2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ432-2-222i−2i2i−2i002-2−22−22000−22−i2i2−i2i2−2i2i-22000000i2−i22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ442-2-222i−2i2i−2i002-2−22−22000−22−i2i2−i2i2−2i2i-22000000i2−i22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ452-2-22−2i2i−2i2i002-22−22−20002−2−i2i2−i2i22i−2i-22000000i2−i2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ462-2-22−2i2i−2i2i002-22−22−20002−2−i2i2−i2i22i−2i-22000000i2−i2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ472-2-22−2i2i−2i2i002-22−22−20002−2−i2i2−i2i2−2i2i2-2000000−i2i22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000
χ482-2-22−2i2i−2i2i002-22−22−20002−2−i2i2−i2i2−2i2i2-2000000−i2i22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000
χ492-2-22−2i2i−2i2i002-2−22−22000−22i2−i2i2−i22i−2i-22000000−i2i22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ502-2-22−2i2i−2i2i002-2−22−22000−22i2−i2i2−i22i−2i-22000000−i2i22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ512-2-22−2i2i−2i2i002-2−22−22000−22i2−i2i2−i2−2i2i2-2000000i2−i2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000
χ522-2-22−2i2i−2i2i002-2−22−22000−22i2−i2i2−i2−2i2i2-2000000i2−i2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000
χ53444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-400004-440000000000000000000000000000000000000000000000
χ5544-4-400004-40044-4-400000000000000022−2222−22000000000000000000000000000000
χ5644-4-400004-40044-4-4000000000000000−2222−2222000000000000000000000000000000
χ5744-4-400004-400-4-4440000000000000002i2−2i2−2i22i2000000000000000000000000000000
χ5844-4-400004-400-4-444000000000000000−2i22i22i2−2i2000000000000000000000000000000
χ594-4-444i−4i−4i4i00-4422−2222−22000−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ604-4-444i−4i−4i4i00-44−2222−222200022−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ614-4-44−4i4i4i−4i00-4422−2222−22000−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ624-4-44−4i4i4i−4i00-44−2222−222200022−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ6388-8-80000-880000000000000000000000000000000000000000000000000000000
χ648-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ658-88-800000000−424242−420000000000000000000000000000000000000000000000000

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