Finite Group Databasebeta

← Group #500313

Character table — Group #500313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222222244448888888844444488881616161616161616161616161616161624444488881616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ911111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1
χ1011111111-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-11
χ1111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1-1-1-11111-1-1-1-111-1-111-11
χ1211111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-11-1
χ1311111111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-111-1-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1111-1
χ1511111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11111111-1-11111-1-1-1-111-1-1-1-1-1-1111-1
χ1611111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-11111-1-1-1-1-1-1111111-1-1-11
χ172222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000200002-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-20000-2222200000000000000000000
χ19222222222222-2-2-2-200000000-2-2222200002222−2−2−2−22222−2−2−2−2-20000-2000022−2−222−2−2000000000000
χ20222222222222-2-2-2-200000000-2-222220000−2−2−2−22222−2−2−2−22222-20000-20000−2−222−2−222000000000000
χ21222222222222-2-2-2-200000000-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−22000020000−2−222−2−222000000000000
χ22222222222222-2-2-2-200000000-2-2-2-2-2-20000−2−2−2−22222−2−2−2−22222200002000022−2−222−2−2000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000020000-222-2-200000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-200002-2-22200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-200002222−2−2−2−2−2−2−2−22222-200002000022−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-20000−2−2−2−222222222−2−2−2−2-2000020000−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22200002222−2−2−2−2−2−2−2−2222220000-20000−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-2220000−2−2−2−222222222−2−2−2−220000-2000022−2−2−2−222000000000000
χ29222-2-2-2-2222-2-200002−222−2−22−2002i−2i2i−2i22−2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000i2−i2i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ30222-2-2-2-2222-2-200002−222−2−22−2002i−2i2i−2i22−2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000i2−i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ31222-2-2-2-2222-2-200002−222−2−22−200−2i2i−2i2i22−2−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−i2i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ32222-2-2-2-2222-2-200002−222−2−22−200−2i2i−2i2i22−2−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−i2i2−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ33222-2-2-2-2222-2-20000−22−2−222−22002i−2i2i−2i−2−222ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−i2i2−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ34222-2-2-2-2222-2-20000−22−2−222−22002i−2i2i−2i−2−222−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−i2i2−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ35222-2-2-2-2222-2-20000−22−2−222−2200−2i2i−2i2i−2−222ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000i2−i2i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ36222-2-2-2-2222-2-20000−22−2−222−2200−2i2i−2i2i−2−222−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000i2−i2i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ37222-2-2-2-22-2-22200002−222−2−22−2002i−2i−2i2i−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−i2i2i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ38222-2-2-2-22-2-22200002−222−2−22−2002i−2i−2i2i−2−222−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−i2i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ39222-2-2-2-22-2-22200002−222−2−22−200−2i2i2i−2i−2−222ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000i2−i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ40222-2-2-2-22-2-22200002−222−2−22−200−2i2i2i−2i−2−222−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000i2−i2−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ41222-2-2-2-22-2-2220000−22−2−222−22002i−2i−2i2i22−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000i2−i2−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ42222-2-2-2-22-2-2220000−22−2−222−22002i−2i−2i2i22−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000i2−i2−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ43222-2-2-2-22-2-2220000−22−2−222−2200−2i2i2i−2i22−2−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−i2i2i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ44222-2-2-2-22-2-2220000−22−2−222−2200−2i2i2i−2i22−2−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−i2i2i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4522-222-2-2-200002-2-22-2-22-22-2220000000000000000002-22-22-22-202i2i−2i−2i0000000000000000000002i−2i00
χ4622-222-2-2-200002-2-22-2-22-22-2220000000000000000002-22-22-22-20−2i−2i2i2i000000000000000000000−2i2i00
χ4722-222-2-2-200002-2-22-2-22-22-222000000000000000000-22-22-22-2202i2i−2i−2i000000000000000000000−2i2i00
χ4822-222-2-2-200002-2-22-2-22-22-222000000000000000000-22-22-22-220−2i−2i2i2i0000000000000000000002i−2i00
χ492-222-22-2-20000-22-22-2-2-22-222200000000002-22-22-22-20000000002i−2i2i−2i00000000000000000002i−2i0000
χ502-222-22-2-20000-22-22-2-2-22-222200000000002-22-22-22-2000000000−2i2i−2i2i0000000000000000000−2i2i0000
χ512-222-22-2-20000-22-22-2-2-22-22220000000000-22-22-22-220000000002i−2i2i−2i0000000000000000000−2i2i0000
χ522-222-22-2-20000-22-22-2-2-22-22220000000000-22-22-22-22000000000−2i2i−2i2i00000000000000000002i−2i0000
χ532-2-22-2-2222-22-2-2-22222-2-2-2-2222-200002-22-2000000000000000002-2-220000000000000002-200000000
χ542-2-22-2-2222-22-2-2-22222-2-2-2-2222-200002-22-200000000000000000-222-2000000000000000-2200000000
χ552-2-22-2-2222-22-2-2-222-2-22222-2-22-20000-22-2200000000000000000000000000000000002-2002-2000000
χ562-2-22-2-2222-22-2-2-222-2-22222-2-22-20000-22-220000000000000000000000000000000000-2200-22000000
χ572-2-22-2-222-22-22-2-22222-2-2-2-222-220000-22-22000000000000000002-2-22000000000000000-2200000000
χ582-2-22-2-222-22-22-2-22222-2-2-2-222-220000-22-2200000000000000000-222-20000000000000002-200000000
χ592-2-22-2-222-22-22-2-222-2-22222-2-2-2200002-22-200000000000000000000000000000000002-200-22000000
χ602-2-22-2-222-22-22-2-222-2-22222-2-2-2200002-22-20000000000000000000000000000000000-22002-2000000
χ6144-444-4-4-400004-4-4444-44-44-4-400000000000000000000000000000000000000000000000000000000
χ6244-444-4-4-40000-444-40000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ6344-444-4-4-40000-444-400000000000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ6444-4-4-444-40000000022−22−222222−22−22220000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000
χ6544-4-4-444-40000000022−22−222222−22−2222000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000
χ6644-4-4-444-400000000−222222−22−222222−220000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000
χ6744-4-4-444-400000000−222222−22−222222−22000000000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000
χ684-444-44-4-400004-44-400000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ694-444-44-4-400004-44-4000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ704-444-44-4-40000-44-44444-44-4-4-400000000000000000000000000000000000000000000000000000000
χ714-44-44-44-40000000022−2222−22−2222−222200000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000
χ724-44-44-44-40000000022−2222−22−2222−22220000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000
χ734-44-44-44-400000000−2222−222222−2222−2200000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000
χ744-44-44-44-400000000−2222−222222−2222−220000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000
χ754-4-44-4-4444-44-444-4-400000000-44000000000000000000000000000000000000000000000000000000
χ764-4-44-4-444-44-4444-4-4000000004-4000000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-44000022−22−22−22222222−2200000022−22−22220000000000000000000000000000000000000000000000
χ784-4-4-444-444-4-440000−22222222−22−22−2222000000−222222−220000000000000000000000000000000000000000000000
χ794-4-4-444-44-444-4000022−22−22−22222222−22000000−222222−220000000000000000000000000000000000000000000000
χ804-4-4-444-44-444-40000−22222222−22−22−222200000022−22−22220000000000000000000000000000000000000000000000

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