Finite Group Databasebeta

← Group #247167

Character table — Group #247167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422224444444888888888888888822224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-1111-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-11111-1-111
χ11111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-11-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11111-1-11111-1-1-1-11111-1-1-1-111-1-11-1-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1-1-111
χ172222222222-2-2222222-2-2-2-2222222-2-2-2-222-200-2-200000000000000000000000000000000
χ182222222222-2-2222222-2-2-2-222-2-2-2-2-2-222-2-2-2002200000000000000000000000000000000
χ192222222222-2-2-2-2-2-222-2-222-2-22222-2-2-2-2-2-22002200000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-22222200-2-200000000000000000000000000000000
χ2122222222-2-2222222-2-22222-2-20000-2-20000-222002200000000000000000000-2-200000000
χ2222222222-2-2222222-2-22222-2-20000-2-20000-2-2-200-2-2000000000000000000002200000000
χ2322222222-2-222-2-2-2-2-2-222-2-2220000-2-2000022200-2-200000000000000000000-2200000000
χ2422222222-2-222-2-2-2-2-2-222-2-2220000-2-200002-2-20022000000000000000000002-200000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-20000220000200000000000000000000002-200002-2000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2000022000020000000000000000000000-220000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-200000000000000000000002-20000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-20000000000000000000000-2200002-2000000
χ292-2222-2-2-22-2002i2i−2i−2i2-200002i−2i2i2i−2i−2i00002-2000000000000000i2i2−i2−i222−2−200000000002−2i2−i2
χ302-2222-2-2-22-2002i2i−2i−2i2-200002i−2i2i2i−2i−2i00002-2000000000000000−i2−i2i2i2−2−2220000000000−22−i2i2
χ312-2222-2-2-22-2002i2i−2i−2i2-200002i−2i−2i−2i2i2i0000-22000000000000000i2i2−i2−i222−2−20000000000−22−i2i2
χ322-2222-2-2-22-2002i2i−2i−2i2-200002i−2i−2i−2i2i2i0000-22000000000000000−i2−i2i2i2−2−22200000000002−2i2−i2
χ332-2222-2-2-22-200−2i−2i2i2i2-20000−2i2i2i2i−2i−2i0000-22000000000000000i2i2−i2−i2−2−22200000000002−2−i2i2
χ342-2222-2-2-22-200−2i−2i2i2i2-20000−2i2i2i2i−2i−2i0000-22000000000000000−i2−i2i2i222−2−20000000000−22i2−i2
χ352-2222-2-2-22-200−2i−2i2i2i2-20000−2i2i−2i−2i2i2i00002-2000000000000000i2i2−i2−i2−2−2220000000000−22i2−i2
χ362-2222-2-2-22-200−2i−2i2i2i2-20000−2i2i−2i−2i2i2i00002-2000000000000000−i2−i2i2i222−2−200000000002−2−i2i2
χ372-22-2-22-2200-2-22-22-200222-200000000000002-2002-222−2−222−2−22−22−22−22−200000000000000
χ382-22-2-22-2200-2-22-22-200222-200000000000002-2002-2−2−222−2−222−22−22−22−2200000000000000
χ392-22-2-22-2200-2-22-22-200222-20000000000000-2200-2222−2−222−2−2−22−22−22−2200000000000000
χ402-22-2-22-2200-2-22-22-200222-20000000000000-2200-22−2−222−2−2222−22−22−22−200000000000000
χ412-22-2-22-2200-2-2-22-220022-2200000000000002-200-2222−2−2−2−2222−22−2−22−2200000000000000
χ422-22-2-22-2200-2-2-22-220022-2200000000000002-200-22−2−22222−2−2−22−222−22−200000000000000
χ432-22-2-22-2200-2-2-22-220022-220000000000000-22002-222−2−2−2−222−22−222−22−200000000000000
χ442-22-2-22-2200-2-2-22-220022-220000000000000-22002-2−2−22222−2−22−22−2−22−2200000000000000
χ452-2-22-2-222-2-22-20000222-200002-22-22-22-200000000000002-22-200000000000000002-20000
χ462-2-22-2-222-2-22-20000222-200002-22-22-22-20000000000000-22-220000000000000000-220000
χ472-2-22-2-222-2-22-20000222-20000-22-222-2-2200000000000002-22-20000000000000000-220000
χ482-2-22-2-222-2-22-20000222-20000-22-222-2-220000000000000-22-2200000000000000002-20000
χ492-2-22-2-222-2-2-22000022-2200002-22-2-22-220000000002-22-2000000000000002-20000000000
χ502-2-22-2-222-2-2-22000022-2200002-22-2-22-22000000000-22-2200000000000000-220000000000
χ512-2-22-2-222-2-2-22000022-220000-22-22-222-20000000002-22-200000000000000-220000000000
χ522-2-22-2-222-2-2-22000022-220000-22-22-222-2000000000-22-22000000000000002-20000000000
χ53444-4-4-44-400004i−4i−4i4i0000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ54444-4-4-44-400004i−4i−4i4i000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ55444-4-4-44-40000−4i4i4i−4i0000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ56444-4-4-44-40000−4i4i4i−4i000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ5744-44-44-4-44-4000000-4400000000000000000004i−4i00000000000000000000000000000000
χ5844-44-44-4-44-4000000-440000000000000000000−4i4i00000000000000000000000000000000
χ5944-44-44-4-4-440000004-40000004i−4i−4i4i0000000000000000000000000000000000000000000
χ6044-44-44-4-4-440000004-4000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ6144-4-44-4-44004-4000000-4400000000000000000000022−22−222200000000000000000000000000
χ6244-4-44-4-44004-4000000-44000000000000000000000−222222−2200000000000000000000000000
χ6344-4-44-4-4400-440000004-4000000000000000000000000022−22−22220000000000000000000000
χ6444-4-44-4-4400-440000004-40000000000000000000000000−222222−220000000000000000000000
χ654-4444-4-4-4-44004i4i−4i−4i-440000−4i4i00000000000000000000000000000000000000000000000
χ664-4444-4-4-4-4400−4i−4i4i4i-4400004i−4i00000000000000000000000000000000000000000000000
χ674-44-4-44-4400444-44-400-4-4-440000000000000000000000000000000000000000000000000
χ684-44-4-44-440044-44-4400-4-44-40000000000000000000000000000000000000000000000000
χ694-4-44-4-444444-40000-4-44-400000000-4400000000000000000000000000000000000000000
χ704-4-44-4-44444-440000-4-4-44000000004-400000000000000000000000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).