Finite Group Databasebeta

← Group #291066

Character table — Group #291066

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444224444444444488888888888888888888888844444444
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
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-11-1-1-1
χ511111111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-11-11-1-1
χ611111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-1111
χ711111111111111111111111111-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ811111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111111111111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1
χ101111111111111-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-11
χ111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-11-1
χ121111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-11
χ131111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-11-11
χ141111111111111-1-1-1-1111-1-1-1-111-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-111-1
χ151111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-11
χ161111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-11-1
χ172222222222-2-2-2222222-2-2-222-2-222-2220000000000000000000000000000000000-20-2000
χ182222222222-2-2-2222222-2-2-222-2-2-2-2-2-2-20000000000000000000000000000000000202000
χ192222222222-2-2-2-2-2-2-222-222-2-2-2-2222-2-2000000000000000000000000000000000020-2000
χ202222222222-2-2-2-2-2-2-222-222-2-2-2-2-2-22220000000000000000000000000000000000-202000
χ2122222222-2-22222222-2-2222-2-2-2-200-20022220000000000000000000000000000000-20-200
χ2222222222-2-22222222-2-2222-2-2-2-200-200-2-2-2-2000000000000000000000000000000020200
χ2322222222-2-2222-2-2-2-2-2-22-2-222-2-20020022-2-2000000000000000000000000000000020-200
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-200200-2-2220000000000000000000000000000000-20200
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22200200000022-2-20000000000000000000000002-2000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-222002000000-2-222000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-200000022-2-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000-2-2220000000000000000000000002-2000000
χ2922-22-2-2-22222-2-20000-2-2200002-20000000002i−2i2i−2i2i2i−2i−2i0000000022-2-20000000000000000
χ3022-22-2-2-22222-2-20000-2-2200002-20000000002i−2i2i−2i−2i−2i2i2i00000000-2-2220000000000000000
χ3122-22-2-2-22222-2-20000-2-2200002-2000000000−2i2i−2i2i2i2i−2i−2i00000000-2-2220000000000000000
χ3222-22-2-2-22222-2-20000-2-2200002-2000000000−2i2i−2i2i−2i−2i2i2i0000000022-2-20000000000000000
χ3322-22-2-2-22-2-2-222000022-200002-20000000002i−2i−2i2i000022-2-22i2i−2i−2i00000000000000000000
χ3422-22-2-2-22-2-2-222000022-200002-20000000002i−2i−2i2i0000-2-222−2i−2i2i2i00000000000000000000
χ3522-22-2-2-22-2-2-222000022-200002-2000000000−2i2i2i−2i000022-2-2−2i−2i2i2i00000000000000000000
χ3622-22-2-2-22-2-2-222000022-200002-2000000000−2i2i2i−2i0000-2-2222i2i−2i−2i00000000000000000000
χ3722-2-2-222-22-20002i2i−2i−2i2-20002i−2i002-202i−2i0000000000000000i2−i2i2−i22−22−2i2i2−i2−i222−2−200000000
χ3822-2-2-222-22-20002i2i−2i−2i2-20002i−2i002-202i−2i0000000000000000−i2i2−i2i2−22−22−i2−i2i2i2−2−22200000000
χ3922-2-2-222-22-20002i2i−2i−2i2-20002i−2i00-220−2i2i0000000000000000i2−i2i2−i22−22−2−i2−i2i2i2−2−22200000000
χ4022-2-2-222-22-20002i2i−2i−2i2-20002i−2i00-220−2i2i0000000000000000−i2i2−i2i2−22−22i2i2−i2−i222−2−200000000
χ4122-2-2-222-22-2000−2i−2i2i2i2-2000−2i2i002-20−2i2i0000000000000000i2−i2i2−i2−22−22i2i2−i2−i2−2−22200000000
χ4222-2-2-222-22-2000−2i−2i2i2i2-2000−2i2i002-20−2i2i0000000000000000−i2i2−i2i22−22−2−i2−i2i2i222−2−200000000
χ4322-2-2-222-22-2000−2i−2i2i2i2-2000−2i2i00-2202i−2i0000000000000000i2−i2i2−i2−22−22−i2−i2i2i222−2−200000000
χ4422-2-2-222-22-2000−2i−2i2i2i2-2000−2i2i00-2202i−2i0000000000000000−i2i2−i2i22−22−2i2i2−i2−i2−2−22200000000
χ452-22-2-2-2220022-22-22-200-22-20000000002i−2i2i−2i00002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i200000000
χ462-22-2-2-2220022-22-22-200-22-20000000002i−2i2i−2i0000−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i200000000
χ472-22-2-2-2220022-22-22-200-22-2000000000−2i2i−2i2i00002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i200000000
χ482-22-2-2-2220022-22-22-200-22-2000000000−2i2i−2i2i0000−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i200000000
χ492-22-2-2-2220022-2-22-2200-2-220000000002i−2i−2i2i00002−22−2−22−2200000000i2−i2i2−i2−i2i2−i2i200000000
χ502-22-2-2-2220022-2-22-2200-2-220000000002i−2i−2i2i0000−22−222−22−200000000−i2i2−i2i2i2−i2i2−i200000000
χ512-22-2-2-2220022-2-22-2200-2-22000000000−2i2i2i−2i00002−22−2−22−2200000000−i2i2−i2i2i2−i2i2−i200000000
χ522-22-2-2-2220022-2-22-2200-2-22000000000−2i2i2i−2i0000−22−222−22−200000000i2−i2i2−i2−i2i2−i2i200000000
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
χ5744-44-4-4-4444-4440000-4-4-40000-44000000000000000000000000000000000000000000000
χ5844-44-4-4-44-4-44-4-400004440000-44000000000000000000000000000000000000000000000
χ5944-4-4-444-4-440004i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ6044-4-4-444-4-44000−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ614-44-4-4-44400-4-444-44-4004-440000000000000000000000000000000000000000000000000
χ624-44-4-4-44400-4-44-44-440044-40000000000000000000000000000000000000000000000000
χ634-4-444-44-4000004i−4i−4i4i000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ644-4-444-44-4000004i−4i−4i4i00000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ654-4-444-44-400000−4i4i4i−4i000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ664-4-444-44-400000−4i4i4i−4i00000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ674-4-4-444-44004-44000000-400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ684-4-4-444-44004-44000000-40000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ694-4-4-444-4400-44-400000040000000000000000000000022−22−2222000000000000000000000000
χ704-4-4-444-4400-44-4000000400000000000000000000000−222222−22000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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