Finite Group Databasebeta

← Group #488564

Character table — Group #488564

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222224444442444448888888844888816161616161616161616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ6111111111111111-1-11-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ7111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-111
χ8111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ91111-1-1111-1-1-1-11-1111-1-1-1-1-1-11111-1111-1-11111-1-1-1-11111-1-1-1-11-1-111-11-11-11-1
χ101111-1-1111-1-1-1-11-1111-1-1-1-1-1-11111-1111-1-11111-1-1-1-11111-1-1-1-1-111-1-11-11-11-11
χ111111-1-1111-1-1-1-11-1111-1-1-1-1-1-11111-1111-1-1-1-1-1-11111-1-1-1-111111-1-111-11-1-11-11
χ121111-1-1111-1-1-1-11-1111-1-1-1-1-1-11111-1111-1-1-1-1-1-11111-1-1-1-11111-111-1-11-111-11-1
χ131111-1-1111-1-1-1-11-1-1-1111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-11
χ141111-1-1111-1-1-1-11-1-1-1111-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-111-1
χ151111-1-1111-1-1-1-11-1-1-1111-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-11-111-1
χ161111-1-1111-1-1-1-11-1-1-1111-1-1-1-111111-1-1-111-1-1-1-111111111-1-1-1-1-1-111-111-11-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ18222222222222222-2-22-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-2-2-2-2-2222-2-2-2000000002-2000022−2−222−2−222−2−222−2−2000000000000
χ2022222222-2-2-2-2-2-2222-2-2-2000000002-20000−2−222−2−222−2−222−2−222000000000000
χ2122222222-2-2-2-2-2-22-2-2-22200000000-22000022−2−222−2−2−2−222−2−222000000000000
χ2222222222-2-2-2-2-2-22-2-2-22200000000-220000−2−222−2−22222−2−222−2−2000000000000
χ23222222-2-2222-2-22-200-20022-2-222-2-200000000000000000000002020-2-2000000
χ24222222-2-2222-2-22-200-20022-2-222-2-20000000000000000000000-20-2022000000
χ25222222-2-2222-2-22-200-200-2-222-2-2220000000000000000000000020200-2-20000
χ26222222-2-2222-2-22-200-200-2-222-2-22200000000000000000000000-20-200220000
χ272222-2-2222-2-2-2-22-2222-2-22222-2-2-2-2-22-2-2220000000000000000000000000000
χ282222-2-2222-2-2-2-22-2-2-22222222-2-2-2-22-222-2-20000000000000000000000000000
χ292222-2-222-22222-2-222-22200000000-2-2000022−2−2−2−22222−2−2−2−222000000000000
χ302222-2-222-22222-2-222-22200000000-2-20000−2−22222−2−2−2−22222−2−2000000000000
χ312222-2-222-22222-2-2-2-2-2-2-20000000022000022−2−2−2−222−2−22222−2−2000000000000
χ322222-2-222-22222-2-2-2-2-2-2-200000000220000−2−22222−2−222−2−2−2−222000000000000
χ332222-2-2-2-22-2-2222200-20022-2-2-2-2220000000000000000000000020-2002-20000
χ342222-2-2-2-22-2-2222200-20022-2-2-2-22200000000000000000000000-20200-220000
χ352222-2-2-2-22-2-2222200-200-2-22222-2-2000000000000000000000020-20-22000000
χ362222-2-2-2-22-2-2222200-200-2-22222-2-20000000000000000000000-20202-2000000
χ372-22-2002-202i−2i2i−2i002i−2i02-2i2−i2i2−i22−22−200i2−i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ382-22-2002-202i−2i2i−2i002i−2i02-2i2−i2i2−i22−22−200i2−i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ392-22-2002-202i−2i2i−2i002i−2i02-2−i2i2−i2i2−22−2200−i2i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ402-22-2002-202i−2i2i−2i002i−2i02-2−i2i2−i2i2−22−2200−i2i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ412-22-2002-202i−2i2i−2i00−2i2i0-22i2−i2i2−i22−22−200−i2i2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ422-22-2002-202i−2i2i−2i00−2i2i0-22i2−i2i2−i22−22−200−i2i2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ432-22-2002-202i−2i2i−2i00−2i2i0-22−i2i2−i2i2−22−2200i2−i22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ442-22-2002-202i−2i2i−2i00−2i2i0-22−i2i2−i2i2−22−2200i2−i22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ452-22-2002-20−2i2i−2i2i002i−2i0-22i2−i2i2−i2−22−2200−i2i22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ462-22-2002-20−2i2i−2i2i002i−2i0-22i2−i2i2−i2−22−2200−i2i22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ472-22-2002-20−2i2i−2i2i002i−2i0-22−i2i2−i2i22−22−200i2−i2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ482-22-2002-20−2i2i−2i2i002i−2i0-22−i2i2−i2i22−22−200i2−i2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ492-22-2002-20−2i2i−2i2i00−2i2i02-2i2−i2i2−i2−22−2200i2−i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ502-22-2002-20−2i2i−2i2i00−2i2i02-2i2−i2i2−i2−22−2200i2−i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ512-22-2002-20−2i2i−2i2i00−2i2i02-2−i2i2−i2i22−22−200−i2i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ522-22-2002-20−2i2i−2i2i00−2i2i02-2−i2i2−i2i22−22−200−i2i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ53444444-4-4-4-4-444-4-400400000000000000000000000000000000000000000000
χ544444-4-4-4-4-444-4-4-4400400000000000000000000000000000000000000000000
χ554-44-400-4404i−4i−4i4i00000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000
χ564-44-400-4404i−4i−4i4i0000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000
χ574-44-400-440−4i4i4i−4i00000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000
χ584-44-400-440−4i4i4i−4i0000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000
χ5988-8-88-800000000000000000000000000000000000000000000000000000000
χ6088-8-8-8800000000000000000000000000000000000000000000000000000000
χ618-8-88000080000-8000000000000000000000000000000000000000000000000
χ628-8-880000-800008000000000000000000000000000000000000000000000000

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