Finite Group Databasebeta

← Group #281721

Character table — Group #281721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444488888888888888882244444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ91111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1111111-1-1-1-111-1-1111-1
χ121111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-11111-1-111-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-111111111111111-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-111-1-1-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-111-1-11111-1-11-1
χ17222222222-2-222-2-222222-2-2-2-2000000000000000022-2-2-2-2-2220000000000000000000000
χ18222222222-2-222-2-222222-2-2-2-20000000000000000-2-222-222-2-20000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2-2-222000000000000000022222-2-2-2-20000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-2220000000000000000-2-2-2-2222220000000000000000000000
χ2122222222-222-2-222-222-2-2-2-2-2-22222-2-2-2-200000000000020000-2-222000000000000000000
χ2222222222-222-2-222-222-2-2-2-2-2-2-2-2-2-222220000000000002000022-2-2000000000000000000
χ2322222222-222-2-222-2-2-222-2-22222222222000000000000-20000-2-2-2-2000000000000000000
χ2422222222-222-2-222-2-2-222-2-222-2-2-2-2-2-2-2-2000000000000-200002222000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22222000000002i2i2i2i−2i−2i−2i−2i0000-2000000002i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2222200000000−2i−2i−2i−2i2i2i2i2i0000-200000000−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i0000200000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i00002000000002i2i−2i−2i00000000000000
χ2922-2-2-222-2200-2-20022-22-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-2000002-2i2−i2i2−i2i2−i2i2−i200000000000000
χ3022-2-2-222-2200-2-20022-22-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-2200000-22i2−i2i2−i2−i2i2−i2i200000000000000
χ3122-2-2-222-2200-2-20022-22-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-2200000-22−i2i2−i2i2i2−i2i2−i200000000000000
χ3222-2-2-222-2200-2-20022-22-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-2000002-2−i2i2−i2i2−i2i2−i2i200000000000000
χ3322-2-2-222-2200-2-2002-22-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-22000002-2i2−i2−i2i2−i2i2−i2i200000000000000
χ3422-2-2-222-2200-2-2002-22-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-200000-22i2−i2−i2i2i2−i2i2−i200000000000000
χ3522-2-2-222-2200-2-2002-22-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-200000-22−i2i2i2−i2−i2i2−i2i200000000000000
χ3622-2-2-222-2200-2-2002-22-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-22000002-2−i2i2i2−i2i2−i2i2−i200000000000000
χ3722-2-2-222-2-2002200-22-2-220000i2i2−i2−i2−i2−i2i2i222−2−2−2−222002i−2i02i−2i00−i2i2i2−i22−2−2200000000000000
χ3822-2-2-222-2-2002200-22-2-220000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200−2i2i0−2i2i00−i2i2i2−i2−222−200000000000000
χ3922-2-2-222-2-2002200-22-2-220000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200−2i2i0−2i2i00i2−i2−i2i22−2−2200000000000000
χ4022-2-2-222-2-2002200-22-2-220000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2002i−2i02i−2i00i2−i2−i2i2−222−200000000000000
χ4122-2-2-222-2-2002200-2-222-20000i2i2−i2−i2i2i2−i2−i222−2−2−2−222002i−2i0−2i2i00−i2i2−i2i2−222−200000000000000
χ4222-2-2-222-2-2002200-2-222-20000i2i2−i2−i2i2i2−i2−i2−2−22222−2−200−2i2i02i−2i00−i2i2−i2i22−2−2200000000000000
χ4322-2-2-222-2-2002200-2-222-20000−i2−i2i2i2−i2−i2i2i222−2−2−2−22200−2i2i02i−2i00i2−i2i2−i2−222−200000000000000
χ4422-2-2-222-2-2002200-2-222-20000−i2−i2i2i2−i2−i2i2i2−2−22222−2−2002i−2i0−2i2i00i2−i2i2−i22−2−2200000000000000
χ452-2-2-222-222222-2-2-2-200002-200000000002i−2i2i−2i2i−2i2i−2i00000000000000000002-20000002i−2i00
χ462-2-2-222-222222-2-2-2-200002-200000000002i−2i2i−2i2i−2i2i−2i0000000000000000000-22000000−2i2i00
χ472-2-2-222-222222-2-2-2-200002-20000000000−2i2i−2i2i−2i2i−2i2i00000000000000000002-2000000−2i2i00
χ482-2-2-222-222222-2-2-2-200002-20000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000-220000002i−2i00
χ492-2-2-222-22-2-2-2-2222200002-200000000002-22-2-22-22000000000000000002-20000002-20000
χ502-2-2-222-22-2-2-2-2222200002-200000000002-22-2-22-2200000000000000000-22000000-220000
χ512-2-2-222-22-2-2-2-2222200002-20000000000-22-222-22-2000000000000000002-2000000-220000
χ522-2-2-222-22-2-2-2-2222200002-20000000000-22-222-22-200000000000000000-220000002-20000
χ53444-44-4-4-404-4004-400000000000004-44-4000000000000000000000000000000000000000
χ54444-44-4-4-404-4004-40000000000000-44-44000000000000000000000000000000000000000
χ55444-44-4-4-40-4400-440000000004-44-40000000000000000000000000000000000000000000
χ56444-44-4-4-40-4400-44000000000-44-440000000000000000000000000000000000000000000
χ5744-44-4-4-44000000000000004-42i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ5844-44-4-4-44000000000000004-4−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ5944-44-4-4-4400000000000000-442i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ6044-44-4-4-4400000000000000-44−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ614-444-44-4-4400-4400-4000000000000000022−22−222222−22−22220000000000000000000000000000000
χ624-444-44-4-4400-4400-40000000000000000−222222−22−222222−220000000000000000000000000000000
χ634-444-44-4-4-4004-400400000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ644-444-44-4-4-4004-40040000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ654-4-444-44-404-400-4400000000000000000000000000000000000000000000002i2−2i200000000
χ664-4-444-44-404-400-440000000000000000000000000000000000000000000000−2i22i200000000
χ674-4-444-44-40-44004-40000000000000000000000000000000000000000000000002i2−2i2000000
χ684-4-444-44-40-44004-4000000000000000000000000000000000000000000000000−2i22i2000000
χ694-4-4-444-444-4-44-444-40000-440000000000000000000000000000000000000000000000000
χ704-4-4-444-44-444-44-4-440000-440000000000000000000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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