Finite Group Databasebeta

← Group #501460

Character table — Group #501460

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444488888888224444448888161616161616161616161616161616164488881616161616161616444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1
χ911111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ1011111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-111-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-11-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-1111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-11111-1-1-111-1
χ17222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-22200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000000000000000-2-2222200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-200000000000000000000
χ2122222222-2-2-2-20000000022-2-222-2-200002222−2−2−2−22222−2−2−2−2-22000022−2−222−2−2000000000000
χ2222222222-2-2-2-20000000022-2-222-2-20000−2−2−2−22222−2−2−2−22222-220000−2−222−2−222000000000000
χ2322222222-2-2-2-20000000022-2-2-2-22200002222−2−2−2−2−2−2−2−222222-2000022−2−2−2−222000000000000
χ2422222222-2-2-2-20000000022-2-2-2-2220000−2−2−2−222222222−2−2−2−22-20000−2−22222−2−2000000000000
χ2522222222-2-2-2-200000000-2-22222-2-200002222−2−2−2−22222−2−2−2−22-20000−2−222−2−222000000000000
χ2622222222-2-2-2-200000000-2-22222-2-20000−2−2−2−22222−2−2−2−222222-2000022−2−222−2−2000000000000
χ2722222222-2-2-2-200000000-2-222-2-22200002222−2−2−2−2−2−2−2−22222-220000−2−22222−2−2000000000000
χ2822222222-2-2-2-200000000-2-222-2-2220000−2−2−2−222222222−2−2−2−2-22000022−2−2−2−222000000000000
χ292-222-2-22-22-22-222-2-222-2-200002i−2i2i−2i2i2i−2i−2i000000000000000000000000000000002-2002i−2i0000
χ302-222-2-22-22-22-222-2-222-2-200002i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000-2200−2i2i0000
χ312-222-2-22-22-22-222-2-222-2-20000−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000002-200−2i2i0000
χ322-222-2-22-22-22-222-2-222-2-20000−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000-22002i−2i0000
χ332-222-2-22-22-22-2-2-222-2-22200002i−2i2i−2i−2i−2i2i2i0000000000000000000000000000002-2002i−2i000000
χ342-222-2-22-22-22-2-2-222-2-22200002i−2i2i−2i−2i−2i2i2i000000000000000000000000000000-2200−2i2i000000
χ352-222-2-22-22-22-2-2-222-2-2220000−2i2i−2i2i2i2i−2i−2i0000000000000000000000000000002-200−2i2i000000
χ362-222-2-22-22-22-2-2-222-2-2220000−2i2i−2i2i2i2i−2i−2i000000000000000000000000000000-22002i−2i000000
χ372-22-2-22-2222-2-2000000002-22-200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200002i−2ii2−i2i2−i22−22−2000000000000
χ382-22-2-22-2222-2-2000000002-22-200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200002i−2i−i2i2−i2i2−22−22000000000000
χ392-22-2-22-2222-2-2000000002-22-20000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000−2i2ii2−i2i2−i2−22−22000000000000
χ402-22-2-22-2222-2-2000000002-22-20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000−2i2i−i2i2−i2i22−22−2000000000000
χ412-22-2-22-2222-2-200000000-22-2200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000−2i2i−i2i2−i2i2−22−22000000000000
χ422-22-2-22-2222-2-200000000-22-2200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000−2i2ii2−i2i2−i22−22−2000000000000
χ432-22-2-22-2222-2-200000000-22-220000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200002i−2i−i2i2−i2i22−22−2000000000000
χ442-22-2-22-2222-2-200000000-22-220000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200002i−2ii2−i2i2−i2−22−22000000000000
χ452-22-2-22-22-2-2222222-2-2-2-22-2-22000000002i2i−2i−2i−2i−2i2i2i00000000002-2002i−2i−2i2i0000000000000000
χ462-22-2-22-22-2-2222222-2-2-2-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000002-200−2i2i2i−2i0000000000000000
χ472-22-2-22-22-2-2222222-2-2-2-2-222-2000000002i2i−2i−2i−2i−2i2i2i0000000000-2200−2i2i2i−2i0000000000000000
χ482-22-2-22-22-2-2222222-2-2-2-2-222-200000000−2i−2i2i2i2i2i−2i−2i0000000000-22002i−2i−2i2i0000000000000000
χ492-22-2-22-22-2-222-2-2-2-222222-2-22000000000000000022-2-2-2-22200-220000002-2-22000000000000
χ502-22-2-22-22-2-222-2-2-2-222222-2-220000000000000000-2-22222-2-200-22000000-222-2000000000000
χ512-22-2-22-22-2-222-2-2-2-22222-222-2000000000000000022-2-2-2-222002-2000000-222-2000000000000
χ522-22-2-22-22-2-222-2-2-2-22222-222-20000000000000000-2-22222-2-2002-20000002-2-22000000000000
χ53444-44-4-4-44-4-4400000000000000004-4-44000000000000000000000000000000000000000000
χ54444-44-4-4-44-4-440000000000000000-444-4000000000000000000000000000000000000000000
χ55444-44-4-4-4-444-444-4-4-4-444000000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4-444-4-4-44444-4-4000000000000000000000000000000000000000000000000000000
χ5744-44-4-4-44000022−2222−2222−2222−220000000000002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000
χ5844-44-4-4-44000022−2222−2222−2222−22000000000000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000
χ5944-44-4-4-440000−2222−2222−2222−22220000000000002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000
χ6044-44-4-4-440000−2222−2222−2222−2222000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000
χ6144-4-4-444-4000022−22−2222−222222−22000000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ6244-4-4-444-4000022−22−2222−222222−2200000000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ6344-4-4-444-40000−222222−2222−22−2222000000000000000000002ζ+2ζ7−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ6444-4-4-444-40000−222222−2222−22−222200000000000000000000−2ζ−2ζ72ζ+2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ654-444-4-44-4-44-440000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-444-4-44-4-44-44000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-4444-4-4000022−22−222222−22−2222000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000
χ684-4-4444-4-4000022−22−222222−22−222200000000000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000
χ694-4-4444-4-40000−222222−22−222222−22000000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000
χ704-4-4444-4-40000−222222−22−222222−2200000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000
χ714-4-4-44-444000022−2222−22−2222−22220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000
χ724-4-4-44-444000022−2222−22−2222−2222000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000
χ734-4-4-44-4440000−2222−222222−2222−220000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000
χ744-4-4-44-4440000−2222−222222−2222−22000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000

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