Finite Group Databasebeta

← Group #33869

Character table — Group #33869

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55
size1111222222222222222222224444444444444444444448888161616161616
order122244444444888816161616161616162248888881616161616161616161616162244444444
χ11111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1
χ41111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ5111111-1-1-1-111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-11
χ6111111-1-1-1-111111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1
χ7111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1
χ8111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-111-1-1-1111
χ91111-1-111-1-1111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1
χ101111-1-111-1-1111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-111
χ111111-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-111-11
χ121111-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111-1-1-1-11111111111111111-11-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-11-1
χ141111-1-1-1-11111111111111111-11-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-11-11
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-1-1-111-1-1-11-1-111
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111-1-1-1-1-1-1111-111-1-1
χ17222222222222-2-2-2-200000000222-2-2-2-2-2-20000000000000000000000
χ182222222222-2-200002222−2−2−2−2-2-2-200000022−2−222−2−222−2−20000000000
χ192222222222-2-20000−2−2−2−22222-2-2-2000000−2−222−2−222−2−2220000000000
χ20222222-2-2-2-222-2-2-2-200000000-2-22-2-222220000000000000000000000
χ21222222-2-2-2-2-2-200002222−2−2−2−222-200000022−2−2−2−222−2−2220000000000
χ22222222-2-2-2-2-2-20000−2−2−2−2222222-2000000−2−22222−2−222−2−20000000000
χ232222-2-222-2-222-2-2-2-2000000002-2-222-2-2220000000000000000000000
χ242222-2-222-2-2-2-200002222−2−2−2−2-222000000−2−22222−2−2−2−2220000000000
χ252222-2-222-2-2-2-20000−2−2−2−22222-22200000022−2−2−2−22222−2−20000000000
χ262222-2-2-2-22222-2-2-2-200000000-22-22222-2-20000000000000000000000
χ272222-2-2-2-222-2-200002222−2−2−2−22-22000000−2−222−2−22222−2−20000000000
χ282222-2-2-2-222-2-20000−2−2−2−222222-2200000022−2−222−2−2−2−2220000000000
χ292-22-22-22i−2i2i−2i002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50002−2i2−i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000
χ302-22-22-22i−2i2i−2i002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50002−2i2−i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000
χ312-22-22-22i−2i2i−2i00−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000−22−i2i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000
χ322-22-22-22i−2i2i−2i00−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000−22−i2i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000
χ332-22-22-2−2i2i−2i2i002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50002−2−i2i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000
χ342-22-22-2−2i2i−2i2i002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50002−2−i2i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000
χ352-22-22-2−2i2i−2i2i00−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000−22i2−i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000
χ362-22-22-2−2i2i−2i2i00−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000−22i2−i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000
χ372-22-2-222i−2i−2i2i002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000−22i2−i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000
χ382-22-2-222i−2i−2i2i002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000−22i2−i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000
χ392-22-2-222i−2i−2i2i00−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70002−2−i2i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000
χ402-22-2-222i−2i−2i2i00−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70002−2−i2i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000
χ412-22-2-22−2i2i2i−2i002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000−22−i2i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000
χ422-22-2-22−2i2i2i−2i002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000−22−i2i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000
χ432-22-2-22−2i2i2i−2i00−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70002−2i2−i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000
χ442-22-2-22−2i2i2i−2i00−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70002−2i2−i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000
χ452-2-22000000-2222-2-22i−2i2i−2i2i−2i2i−2i0000000000000000000002-22i−2i000000
χ462-2-22000000-2222-2-22i−2i2i−2i2i−2i2i−2i000000000000000000000-22−2i2i000000
χ472-2-22000000-2222-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000002-2−2i2i000000
χ482-2-22000000-2222-2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000-222i−2i000000
χ4944-4-40000000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000
χ5044-4-40000000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000
χ5144-4-400000000−222222−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000
χ5244-4-400000000−222222−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000
χ534-4-440000004-400002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000
χ544-4-440000004-40000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000
χ554-4-44000000-44-4-444000000000000000000000000000000000000000

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