Finite Group Databasebeta

← Group #505708

Character table — Group #505708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222444444448888888844444444888888888888161616161616161616161616161616162244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
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
χ19222222222222-2-22222-2-200000000-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-22222-2-200000000-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-2000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-20000000022-2-222-2-200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-22222-2-20000000022-2-222-2-2000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-22200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2922-22-22-2-222-2-22-200002-22222-2-2-2-22-200000022-2-20000000000000000000000002-22-2000000000000
χ3022-22-22-2-222-2-22-200002-22222-2-2-2-22-200000022-2-2000000000000000000000000-22-22000000000000
χ3122-22-22-2-222-2-22-200002-2-2-2-2-222222-2000000-2-22200000000000000000000000000002i−2i2i−2i00000000
χ3222-22-22-2-222-2-22-200002-2-2-2-2-222222-2000000-2-2220000000000000000000000000000−2i2i−2i2i00000000
χ3322-22-22-2-2-2-2222-200002-22222-2-2-2-2-22000000-2-2220000000000000000000000002-2-22000000000000
χ3422-22-22-2-2-2-2222-200002-22222-2-2-2-2-22000000-2-222000000000000000000000000-222-2000000000000
χ3522-22-22-2-2-2-2222-200002-2-2-2-2-22222-2200000022-2-200000000000000000000000000002i−2i−2i2i00000000
χ3622-22-22-2-2-2-2222-200002-2-2-2-2-22222-2200000022-2-20000000000000000000000000000−2i2i2i−2i00000000
χ372-2-222-22-20000-2-222-2-22222-2-222-2-2002-20000000022-2-20000000000000000000000000000002i−2i002i−2i
χ382-2-222-22-20000-2-222-2-22222-2-222-2-2002-20000000022-2-2000000000000000000000000000000−2i2i00−2i2i
χ392-2-222-22-20000-2-222-2-222-2-222-2-222002-200000000-2-22200000000000000000000000000002i−2i002i−2i00
χ402-2-222-22-20000-2-222-2-222-2-222-2-222002-200000000-2-2220000000000000000000000000000−2i2i00−2i2i00
χ412-2-222-22-20000-2-2-2-2222222-2-222-2-200-2200000000-2-2220000000000000000000000000000002i−2i00−2i2i
χ422-2-222-22-20000-2-2-2-2222222-2-222-2-200-2200000000-2-222000000000000000000000000000000−2i2i002i−2i
χ432-2-222-22-20000-2-2-2-22222-2-222-2-22200-220000000022-2-200000000000000000000000000002i−2i00−2i2i00
χ442-2-222-22-20000-2-2-2-22222-2-222-2-22200-220000000022-2-20000000000000000000000000000−2i2i002i−2i00
χ452-2-2-2-22222-22-2002-22-2002−22−22−22−20000002-22−22−22−22−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ462-2-2-2-22222-22-2002-22-2002−22−22−22−20000002-22−22−22−22−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ472-2-2-2-22222-22-2002-22-200−22−22−22−220000002-2−22−22−22−22−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ482-2-2-2-22222-22-2002-22-200−22−22−22−220000002-2−22−22−22−22−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ492-2-2-2-22222-22-200-22-22002−22−22−22−2000000-222−22−2−22−22−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ502-2-2-2-22222-22-200-22-22002−22−22−22−2000000-222−22−2−22−22−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ512-2-2-2-22222-22-200-22-2200−22−22−22−22000000-22−22−222−22−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ522-2-2-2-22222-22-200-22-2200−22−22−22−22000000-22−22−222−22−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ532-2-2-2-2222-22-22002-22-2002−22−22−22−2000000-22−22−222−22−2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ542-2-2-2-2222-22-22002-22-2002−22−22−22−2000000-22−22−222−22−2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ552-2-2-2-2222-22-22002-22-200−22−22−22−22000000-222−22−2−22−2222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ562-2-2-2-2222-22-22002-22-200−22−22−22−22000000-222−22−2−22−2222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ572-2-2-2-2222-22-2200-22-22002−22−22−22−20000002-2−22−22−22−2222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ582-2-2-2-2222-22-2200-22-22002−22−22−22−20000002-2−22−22−22−2222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ592-2-2-2-2222-22-2200-22-2200−22−22−22−220000002-22−22−22−22−2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ602-2-2-2-2222-22-2200-22-2200−22−22−22−220000002-22−22−22−22−2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ61444-4-4-44-40000004-4-440022−22−222222−22−222200000000000022−22−2222000000000000000000000000000000000000
χ62444-4-4-44-40000004-4-4400−222222−22−222222−22000000000000−222222−22000000000000000000000000000000000000
χ63444-4-4-44-4000000-444-40022−22−222222−22−2222000000000000−222222−22000000000000000000000000000000000000
χ64444-4-4-44-4000000-444-400−222222−22−222222−2200000000000022−22−2222000000000000000000000000000000000000
χ6544-44-44-4-444-4-4-440000-4400000000-4400000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-4-444-440000-44000000004-400000000000000000000000000000000000000000000000000
χ6744-4-44-4-4400000000000022−22−2222−222222−2200004-4000000000022−2222−2200000000000000000000000000000000
χ6844-4-44-4-4400000000000022−22−2222−222222−220000-440000000000−2222−222200000000000000000000000000000000
χ6944-4-44-4-44000000000000−222222−2222−22−222200004-40000000000−2222−222200000000000000000000000000000000
χ7044-4-44-4-44000000000000−222222−2222−22−22220000-44000000000022−2222−2200000000000000000000000000000000
χ714-444-4-4-4400004-40000-440000000000000000000000004-4-4400000000000000000000000000000000
χ724-444-4-4-4400004-40000-44000000000000000000000000-444-400000000000000000000000000000000
χ734-444-4-4-440000-4400004-444-4-4-4-4440000000000000000000000000000000000000000000000000000
χ744-444-4-4-440000-4400004-4-4-44444-4-40000000000000000000000000000000000000000000000000000
χ754-44-444-4-44-4-440000000022−2222−22−2222−22220000000022−22−22220000000000000000000000000000000000000000
χ764-44-444-4-44-4-4400000000−2222−222222−2222−2200000000−222222−220000000000000000000000000000000000000000
χ774-44-444-4-4-444-40000000022−2222−22−2222−222200000000−222222−220000000000000000000000000000000000000000
χ784-44-444-4-4-444-400000000−2222−222222−2222−220000000022−22−22220000000000000000000000000000000000000000
χ794-4-444-44-400004444-4-4-4-40000000000-44000000000000000000000000000000000000000000000000
χ804-4-444-44-4000044-4-444-4-400000000004-4000000000000000000000000000000000000000000000000

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