Finite Group Databasebeta

← Group #267178

Character table — Group #267178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442222224444444444888888884444488888888888844448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ611111111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ711111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-11
χ811111111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ91111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1
χ121111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-111-1-111-1-1-1-111-11
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ17222222222-2-222-2-22222222-2-222-2-2-2-2-2-20000000022-2-2-200000000000000000000000000
χ18222222222-2-222-2-222222-2-2-2-2-2-222-2-2-2-200000000-2-222200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-222-2-222-2-2222200000000-2-222-200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-2-2-2-2-22222220000000022-2-2200000000000000000000000000
χ2122222222-222-2-222-2000022-2-2-2-2-2-200002222-2-2-2-200002-2-2220000000000000000000000
χ2222222222-222-2-222-2000022-2-2-2-2-2-20000-2-2-2-222220000222-2-20000000000000000000000
χ2322222222-222-2-222-20000-2-2-2-222220000222222220000-2-2-2-2-20000000000000000000000
χ2422222222-222-2-222-20000-2-2-2-222220000-2-2-2-2-2-2-2-20000-222220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-2220000000000000000-200002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-2220000000000000000-20000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-22222-2-20000000000000000200002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-22222-2-2000000000000000020000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-2-222-2-2200-2-200200002-2002-2002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2002i−2i0i2−i2i2−i22−22−22−22−200000000000000
χ3022-2-222-2-2200-2-200200002-2002-2002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2002i−2i0−i2i2−i2i2−22−22−22−2200000000000000
χ3122-2-222-2-2200-2-200200002-2002-200−2i−2i2i2ii2i2−i2−i2i2i2−i2−i200−2i2i0i2−i2i2−i2−22−22−22−2200000000000000
χ3222-2-222-2-2200-2-200200002-2002-200−2i−2i2i2i−i2−i2i2i2−i2−i2i2i200−2i2i0−i2i2−i2i22−22−22−22−200000000000000
χ3322-2-222-2-2200-2-20020000-2200-22002i2i−2i−2ii2i2−i2−i2−i2−i2i2i200−2i2i0i2−i2−i2i22−22−2−22−2200000000000000
χ3422-2-222-2-2200-2-20020000-2200-22002i2i−2i−2i−i2−i2i2i2i2i2−i2−i200−2i2i0−i2i2i2−i2−22−222−22−200000000000000
χ3522-2-222-2-2200-2-20020000-2200-2200−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2002i−2i0i2−i2−i2i2−22−222−22−200000000000000
χ3622-2-222-2-2200-2-20020000-2200-2200−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2002i−2i0−i2i2i2−i22−22−2−22−2200000000000000
χ3722-2-222-2-2-2002200-222-2-22-200-22000000i2i2−i2−i2−i2−i2i2i22-2000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000
χ3822-2-222-2-2-2002200-222-2-22-200-22000000−i2−i2i2i2i2i2−i2−i22-2000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000
χ3922-2-222-2-2-2002200-222-2-2-22002-2000000i2i2−i2−i2i2i2−i2−i2-22000−i2i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000
χ4022-2-222-2-2-2002200-222-2-2-22002-2000000−i2−i2i2i2−i2−i2i2i2-22000i2−i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000
χ4122-2-222-2-2-2002200-2-2-2222-200-22000000i2i2−i2−i2−i2−i2i2i2-22000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ4222-2-222-2-2-2002200-2-2-2222-200-22000000−i2−i2i2i2i2i2−i2−i2-22000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ4322-2-222-2-2-2002200-2-2-222-22002-2000000i2i2−i2−i2i2i2−i2−i22-2000−i2i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000
χ4422-2-222-2-2-2002200-2-2-222-22002-2000000−i2−i2i2i2−i2−i2i2i22-2000i2−i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000
χ452-2-2-22-222-22-22-22-222-22-2002-200002-22-200000000000000000000000002-20000002-20000
χ462-2-2-22-222-22-22-22-222-22-2002-200002-22-20000000000000000000000000-22000000-220000
χ472-2-2-22-222-22-22-22-22-22-22002-20000-22-2200000000000000000000000002-2000000-220000
χ482-2-2-22-222-22-22-22-22-22-22002-20000-22-220000000000000000000000000-220000002-20000
χ492-2-2-22-222-2-222-2-2222-22-200-220000-22-220000000000000000000000000002-20000002-200
χ502-2-2-22-222-2-222-2-2222-22-200-220000-22-22000000000000000000000000000-22000000-2200
χ512-2-2-22-222-2-222-2-222-22-2200-2200002-22-20000000000000000000000000002-2000000-2200
χ522-2-2-22-222-2-222-2-222-22-2200-2200002-22-2000000000000000000000000000-220000002-200
χ53444-4-4-4-4404400-4-40000000000000000000000000000000000000000000000002i2−2i2000000
χ54444-4-4-4-4404400-4-4000000000000000000000000000000000000000000000000−2i22i2000000
χ55444-4-4-4-440-4-40044000000000000000000000000000000000000000000000022−2200000000
χ56444-4-4-4-440-4-400440000000000000000000000000000000000000000000000−222200000000
χ574-4444-4-4-44004-400-44-4-44000000000000000000000000000000000000000000000000000
χ584-4444-4-4-44004-400-4-444-4000000000000000000000000000000000000000000000000000
χ594-4444-4-4-4-400-440040000000000004i−4i−4i4i000000000000000000000000000000000000000
χ604-4444-4-4-4-400-44004000000000000−4i4i4i−4i000000000000000000000000000000000000000
χ614-44-4-444-40000000000000000004-400002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000
χ624-44-4-444-40000000000000000004-40000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000
χ634-44-4-444-4000000000000000000-4400002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000
χ644-44-4-444-4000000000000000000-440000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000
χ654-4-44-44-4404-400-440000000000000000000004-4-440000000000000000000000000000000
χ664-4-44-44-4404-400-44000000000000000000000-444-40000000000000000000000000000000
χ674-4-44-44-440-44004-4000000000000000004-4-4400000000000000000000000000000000000
χ684-4-44-44-440-44004-400000000000000000-444-400000000000000000000000000000000000
χ694-4-4-44-44444-4-444-4-4000000-4400000000000000000000000000000000000000000000000
χ704-4-4-44-4444-44-44-44-40000004-400000000000000000000000000000000000000000000000
χ7188-88-8-88-8000000000000000000000000000000000000000000000000000000000000000

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