Finite Group Databasebeta

← Group #510521

Character table — Group #510521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444488888888224444448888161616161616161616161616161616164488881616161616161616444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1111
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-11111111-1-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-111-1-11111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1-1-1-111-1-1-1-111-11
χ911111111111111111111-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ1111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ1211111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-111-11-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-111-1-11-111
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111111111-1-1-1-1-11
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-11111-1-1-1-1-1-111111-1
χ17222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222200000000000000002-222-2-200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000-2-2222200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-22-2-22200000000000000000000
χ2122222222-2-2-2-2000000002222-2-22200002222−2−2−2−22222−2−2−2−2-2-2000022−2−222−2−2000000000000
χ2222222222-2-2-2-2000000002222-2-2220000−2−2−2−22222−2−2−2−22222-2-20000−2−222−2−222000000000000
χ2322222222-2-2-2-20000000022-2-222-2-200002222−2−2−2−2−2−2−2−22222-220000−2−22222−2−2000000000000
χ2422222222-2-2-2-20000000022-2-222-2-20000−2−2−2−222222222−2−2−2−2-22000022−2−2−2−222000000000000
χ2522222222-2-2-2-200000000-2-222-2-2-2-200002222−2−2−2−22222−2−2−2−2220000−2−222−2−222000000000000
χ2622222222-2-2-2-200000000-2-222-2-2-2-20000−2−2−2−22222−2−2−2−2222222000022−2−222−2−2000000000000
χ2722222222-2-2-2-200000000-2-2-2-2222200002222−2−2−2−2−2−2−2−222222-2000022−2−2−2−222000000000000
χ2822222222-2-2-2-200000000-2-2-2-222220000−2−2−2−222222222−2−2−2−22-20000−2−22222−2−2000000000000
χ292-2222-2-2-2-22-22-2-222-2-22200000000000022-2-222-2-20000000000000000000000002i−2i002i−2i0000
χ302-2222-2-2-2-22-22-2-222-2-22200000000000022-2-222-2-2000000000000000000000000−2i2i00−2i2i0000
χ312-2222-2-2-2-22-22-2-222-2-222000000000000-2-222-2-2220000000000000000000000002i−2i00−2i2i0000
χ322-2222-2-2-2-22-22-2-222-2-222000000000000-2-222-2-222000000000000000000000000−2i2i002i−2i0000
χ332-22-2-22-22-2-2222222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000002i−2i002-2000000
χ342-22-2-22-22-2-2222222-2-2-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000−2i2i00-22000000
χ352-22-2-22-22-2-2222222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000002i−2i00-22000000
χ362-22-2-22-22-2-2222222-2-2-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000−2i2i002-2000000
χ372-2-22-222-200002−22−22−22−22-22-2002-222−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ382-2-22-222-200002−22−22−22−22-22-2002-222−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ392-2-22-222-200002−22−22−22−22-2-2200-22−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ402-2-22-222-200002−22−22−22−22-2-2200-22−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ412-2-22-222-200002−22−22−22−2-222-200-2222−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ422-2-22-222-200002−22−22−22−2-222-200-2222−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ432-2-22-222-200002−22−22−22−2-22-22002-2−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ442-2-22-222-200002−22−22−22−2-22-22002-2−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ452-2-22-222-20000−22−22−22−222-22-2002-2−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ462-2-22-222-20000−22−22−22−222-22-2002-2−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ472-2-22-222-20000−22−22−22−222-2-2200-2222−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ482-2-22-222-20000−22−22−22−222-2-2200-2222−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ492-2-22-222-20000−22−22−22−22-222-200-22−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ502-2-22-222-20000−22−22−22−22-222-200-22−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ512-2-22-222-20000−22−22−22−22-22-22002-222−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ522-2-22-222-20000−22−22−22−22-22-22002-222−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ53444-4-4-44-44-4-4444-4-4-4-444000000000000000000000000000000000000000000000000000000
χ54444-4-4-44-44-4-44-4-44444-4-4000000000000000000000000000000000000000000000000000000
χ55444-4-4-44-4-444-400000000000000004-44-4000000000000000000000000000000000000000000
χ56444-4-4-44-4-444-40000000000000000-44-44000000000000000000000000000000000000000000
χ5744-44-4-4-44000022−22−222222−22−22220000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ70000000000000000000000000000000000
χ5844-44-4-4-44000022−22−222222−22−2222000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ70000000000000000000000000000000000
χ5944-44-4-4-440000−222222−22−222222−220000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000000000
χ6044-44-4-4-440000−222222−22−222222−22000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000000000
χ6144-4-444-4-4000022−2222−22−2222−2222000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ6244-4-444-4-4000022−2222−22−2222−222200000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ6344-4-444-4-40000−2222−222222−2222−22000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ6444-4-444-4-40000−2222−222222−2222−2200000000000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ654-4444-4-4-44-44-4000000000000000000002222−22−22−22−2222220000000000000000000000000000000000
χ664-4444-4-4-44-44-400000000000000000000−22−2222222222−22−220000000000000000000000000000000000
χ674-4444-4-4-4-44-4444-4-444-4-4000000000000000000000000000000000000000000000000000000
χ684-44-4-44-4444-4-400000000000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ694-44-4-44-4444-4-40000000000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ704-44-4-44-44-4-444-4-4-4-44444000000000000000000000000000000000000000000000000000000
χ714-4-4-44-444000022−22−2222−222222−2200004-40022−22−2222000000000000000000000000000000000000000000
χ724-4-4-44-444000022−22−2222−222222−220000-4400−222222−22000000000000000000000000000000000000000000
χ734-4-4-44-4440000−222222−2222−22−222200004-400−222222−22000000000000000000000000000000000000000000
χ744-4-4-44-4440000−222222−2222−22−22220000-440022−22−2222000000000000000000000000000000000000000000

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