Finite Group Databasebeta

← Group #291032

Character table — Group #291032

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444444444444444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11-1-1-1-1
χ511111111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1
χ811111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111
χ91111111111111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1
χ101111111111111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-11-11
χ111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11-11-1
χ121111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-11-1-11
χ131111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-11-11
χ141111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11-111-1
χ151111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-11
χ161111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11111-11-1
χ172222222222-2-2-2222222-2-2-222-2-222-22200000000000000000000000000000000-200-20000
χ182222222222-2-2-2222222-2-2-222-2-2-2-2-2-2-20000000000000000000000000000000020020000
χ192222222222-2-2-2-2-2-2-222-222-2-2-2-2222-2-200000000000000000000000000000000-20020000
χ202222222222-2-2-2-2-2-2-222-222-2-2-2-2-2-222200000000000000000000000000000000200-20000
χ2122222222-2-22222222-2-2222-2-2-2-200-200222200000000000000000000000000000000-2-200
χ2222222222-2-22222222-2-2222-2-2-2-200-200-2-2-2-2000000000000000000000000000000002200
χ2322222222-2-2222-2-2-2-2-2-22-2-222-2-20020022-2-2000000000000000000000000000000002-200
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-200200-2-22200000000000000000000000000000000-2200
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22200200000022-2-200000000000000000000000002-200000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-222002000000-2-2220000000000000000000000000-2200000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-200000022-2-20000000000000000000000000-2200000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000-2-22200000000000000000000000002-200000
χ292-222-2-2-222-20002i2i−2i−2i2-20002i−2i002i−2i02-20000000000000000i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000
χ302-222-2-2-222-20002i2i−2i−2i2-20002i−2i002i−2i02-20000000000000000−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000
χ312-222-2-2-222-20002i2i−2i−2i2-20002i−2i00−2i2i0-220000000000000000i2i2−i2−i222−2−2−2−222−i2−i2i2i200000000
χ322-222-2-2-222-20002i2i−2i−2i2-20002i−2i00−2i2i0-220000000000000000−i2−i2i2i2−2−22222−2−2i2i2−i2−i200000000
χ332-222-2-2-222-2000−2i−2i2i2i2-2000−2i2i002i−2i0-220000000000000000i2i2−i2−i2−2−22222−2−2−i2−i2i2i200000000
χ342-222-2-2-222-2000−2i−2i2i2i2-2000−2i2i002i−2i0-220000000000000000−i2−i2i2i222−2−2−2−222i2i2−i2−i200000000
χ352-222-2-2-222-2000−2i−2i2i2i2-2000−2i2i00−2i2i02-20000000000000000i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000
χ362-222-2-2-222-2000−2i−2i2i2i2-2000−2i2i00−2i2i02-20000000000000000−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000
χ372-22-2-222-2222-2-20000-2-2200002-20000000002i−2i2i−2i2i2i−2i−2i000000002-22-20000000000000000
χ382-22-2-222-2222-2-20000-2-2200002-20000000002i−2i2i−2i−2i−2i2i2i00000000-22-220000000000000000
χ392-22-2-222-2222-2-20000-2-2200002-2000000000−2i2i−2i2i2i2i−2i−2i00000000-22-220000000000000000
χ402-22-2-222-2222-2-20000-2-2200002-2000000000−2i2i−2i2i−2i−2i2i2i000000002-22-20000000000000000
χ412-22-2-222-2-2-2-222000022-200002-20000000002i−2i−2i2i000022-2-22i−2i2i−2i00000000000000000000
χ422-22-2-222-2-2-2-222000022-200002-20000000002i−2i−2i2i0000-2-222−2i2i−2i2i00000000000000000000
χ432-22-2-222-2-2-2-222000022-200002-2000000000−2i2i2i−2i000022-2-2−2i2i−2i2i00000000000000000000
χ442-22-2-222-2-2-2-222000022-200002-2000000000−2i2i2i−2i0000-2-2222i−2i2i−2i00000000000000000000
χ452-2-2-22-2220022-22-22-200-22-20000000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−200000000
χ462-2-2-22-2220022-22-22-200-22-20000000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i200000000−22−22−22−2200000000
χ472-2-2-22-2220022-22-22-200-22-2000000000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i200000000−22−22−22−2200000000
χ482-2-2-22-2220022-22-22-200-22-2000000000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−200000000
χ492-2-2-22-2220022-2-22-2200-2-220000000002i−2i−2i2i0000i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−2200000000
χ502-2-2-22-2220022-2-22-2200-2-220000000002i−2i−2i2i0000−i2i2−i2i2i2−i2i2−i200000000−22−222−22−200000000
χ512-2-2-22-2220022-2-22-2200-2-22000000000−2i2i2i−2i0000i2−i2i2−i2−i2i2−i2i200000000−22−222−22−200000000
χ522-2-2-22-2220022-2-22-2200-2-22000000000−2i2i2i−2i0000−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−2200000000
χ53444-44-4-4-44-40000000-440000000000000000000000000000000022−22−22220000000000000000
χ54444-44-4-4-44-40000000-4400000000000000000000000000000000−222222−220000000000000000
χ55444-44-4-4-4-4400000004-4000000000000000000000000000022−22−222200000000000000000000
χ56444-44-4-4-4-4400000004-40000000000000000000000000000−222222−2200000000000000000000
χ5744-44-4-44-4004-44000000-4000000000000000000022−22−22220000000000000000000000000000
χ5844-44-4-44-4004-44000000-40000000000000000000−222222−220000000000000000000000000000
χ5944-44-4-44-400-44-40000004000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ6044-44-4-44-400-44-4000000400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ6144-4-4-44-44000004i−4i−4i4i000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ6244-4-4-44-44000004i−4i−4i4i00000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ6344-4-4-44-4400000−4i4i4i−4i000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ6444-4-4-44-4400000−4i4i4i−4i00000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ654-444-4-4-44-440004i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ664-444-4-4-44-44000−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ674-44-4-444-444-4440000-4-4-40000-44000000000000000000000000000000000000000000000
χ684-44-4-444-4-4-44-4-400004440000-44000000000000000000000000000000000000000000000
χ694-4-4-44-44400-4-444-44-4004-440000000000000000000000000000000000000000000000000
χ704-4-4-44-44400-4-44-44-440044-40000000000000000000000000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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