Finite Group Databasebeta

← Group #500871

Character table — Group #500871

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ511111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-111
χ811111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1
χ91111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111
χ101111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ121111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ131111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1
χ141111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111
χ151111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111
χ161111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-222222222-2-200000000-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−20000000000000000
χ2222222222-2-222222222-2-200000000-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−2220000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-22222-2-200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-22222-2-2000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2522222222-2-2-2-2-2-22222-2-2000000002222-2-2-2-200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-22222-2-2000000002222-2-2-2-2000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2922-22-22-2-22-222-2-200002-22222-2-2-2-22-200000022-2-20000000000000000000000002-2002-20000000000
χ3022-22-22-2-22-222-2-200002-22222-2-2-2-22-200000022-2-2000000000000000000000000-2200-220000000000
χ3122-22-22-2-22-222-2-200002-2-2-2-2-222222-2000000-2-222000000000000000000000000002i−2i0000002i−2i0000
χ3222-22-22-2-22-222-2-200002-2-2-2-2-222222-2000000-2-22200000000000000000000000000−2i2i000000−2i2i0000
χ3322-22-22-2-22-2-2-22200002-22222-2-2-2-2-22000000-2-2220000000000000000000000002-200-220000000000
χ3422-22-22-2-22-2-2-22200002-22222-2-2-2-2-22000000-2-222000000000000000000000000-22002-20000000000
χ3522-22-22-2-22-2-2-22200002-2-2-2-2-22222-2200000022-2-2000000000000000000000000002i−2i000000−2i2i0000
χ3622-22-22-2-22-2-2-22200002-2-2-2-2-22222-2200000022-2-200000000000000000000000000−2i2i0000002i−2i0000
χ372-222-2-2-22002i−2i2i−2i2i2i−2i−2i0022−2−222−2−20000002-2i2−i2i2−i2i2i2−i2−i222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ382-222-2-2-22002i−2i2i−2i2i2i−2i−2i0022−2−222−2−20000002-2i2−i2i2−i2i2i2−i2−i222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ392-222-2-2-22002i−2i2i−2i2i2i−2i−2i00−2−222−2−2220000002-2−i2i2−i2i2−i2−i2i2i2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ402-222-2-2-22002i−2i2i−2i2i2i−2i−2i00−2−222−2−2220000002-2−i2i2−i2i2−i2−i2i2i2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ412-222-2-2-22002i−2i2i−2i−2i−2i2i2i0022−2−222−2−2000000-22i2−i2i2−i2−i2−i2i2i2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ422-222-2-2-22002i−2i2i−2i−2i−2i2i2i0022−2−222−2−2000000-22i2−i2i2−i2−i2−i2i2i2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ432-222-2-2-22002i−2i2i−2i−2i−2i2i2i00−2−222−2−222000000-22−i2i2−i2i2i2i2−i2−i222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ442-222-2-2-22002i−2i2i−2i−2i−2i2i2i00−2−222−2−222000000-22−i2i2−i2i2i2i2−i2−i222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ452-222-2-2-2200−2i2i−2i2i2i2i−2i−2i0022−2−222−2−2000000-22−i2i2−i2i2i2i2−i2−i2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ462-222-2-2-2200−2i2i−2i2i2i2i−2i−2i0022−2−222−2−2000000-22−i2i2−i2i2i2i2−i2−i2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ472-222-2-2-2200−2i2i−2i2i2i2i−2i−2i00−2−222−2−222000000-22i2−i2i2−i2−i2−i2i2i222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ482-222-2-2-2200−2i2i−2i2i2i2i−2i−2i00−2−222−2−222000000-22i2−i2i2−i2−i2−i2i2i222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ492-222-2-2-2200−2i2i−2i2i−2i−2i2i2i0022−2−222−2−20000002-2−i2i2−i2i2−i2−i2i2i222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ502-222-2-2-2200−2i2i−2i2i−2i−2i2i2i0022−2−222−2−20000002-2−i2i2−i2i2−i2−i2i2i222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ512-222-2-2-2200−2i2i−2i2i−2i−2i2i2i00−2−222−2−2220000002-2i2−i2i2−i2i2i2−i2−i2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ522-222-2-2-2200−2i2i−2i2i−2i−2i2i2i00−2−222−2−2220000002-2i2−i2i2−i2i2i2−i2−i2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ532-2-2-2-2222-2-200002-22-2222-22-22-22-200002-20000002-22-200000000000000000000000000002-2002-200
χ542-2-2-2-2222-2-200002-22-2222-22-22-22-200002-20000002-22-20000000000000000000000000000-2200-2200
χ552-2-2-2-2222-2-200002-22-222-22-22-22-2200002-2000000-22-22000000000000000000000000002-20000002-2
χ562-2-2-2-2222-2-200002-22-222-22-22-22-2200002-2000000-22-2200000000000000000000000000-22000000-22
χ572-2-2-2-2222-2-20000-22-22222-22-22-22-20000-22000000-22-2200000000000000000000000000002-200-2200
χ582-2-2-2-2222-2-20000-22-22222-22-22-22-20000-22000000-22-220000000000000000000000000000-22002-200
χ592-2-2-2-2222-2-20000-22-2222-22-22-22-220000-220000002-22-2000000000000000000000000002-2000000-22
χ602-2-2-2-2222-2-20000-22-2222-22-22-22-220000-220000002-22-200000000000000000000000000-220000002-2
χ61444-4-4-44-400000000000022−22−2222−222222−22004-400000000000022−2222−2200000000000000000000000000000000
χ62444-4-4-44-400000000000022−22−2222−222222−2200-44000000000000−2222−222200000000000000000000000000000000
χ63444-4-4-44-4000000000000−222222−2222−22−2222004-4000000000000−2222−222200000000000000000000000000000000
χ64444-4-4-44-4000000000000−222222−2222−22−222200-4400000000000022−2222−2200000000000000000000000000000000
χ6544-44-44-4-4-4444-4-40000-4400000000-4400000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-44-4-4440000-44000000004-400000000000000000000000000000000000000000000000000
χ6744-4-44-4-440000004i−4i−4i4i0022−22−222222−22−22220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ6844-4-44-4-440000004i−4i−4i4i00−222222−22−222222−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ6944-4-44-4-44000000−4i4i4i−4i0022−22−222222−22−2222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ7044-4-44-4-44000000−4i4i4i−4i00−222222−22−222222−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ714-44-444-4-44-400000000-440000000000000000000000004-4-4400000000000000000000000000000000
χ724-44-444-4-44-400000000-44000000000000000000000000-444-400000000000000000000000000000000
χ734-44-444-4-4-44000000004-44-44-4-44-440000000000000000000000000000000000000000000000000000
χ744-44-444-4-4-44000000004-4-44-444-44-40000000000000000000000000000000000000000000000000000
χ754-4-444-44-4004i−4i−4i4i0000002222−22−22−22−222222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ764-4-444-44-4004i−4i−4i4i000000−22−2222222222−22−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ774-4-444-44-400−4i4i4i−4i0000002222−22−22−22−22222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ784-4-444-44-400−4i4i4i−4i000000−22−2222222222−22−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ794-4-4-4-44444400004-44-4-4-4000000000000-440000000000000000000000000000000000000000000000
χ804-4-4-4-4444440000-44-44-4-40000000000004-40000000000000000000000000000000000000000000000

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