Finite Group Databasebeta

← Group #267689

Character table — Group #267689

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244442222444444444422444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1111-111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-11111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-11-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ12111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111111-1-1-111111-1-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-1-111111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-11-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-11-1-1-1-111
χ172222222222222222-2-2-2-22222-2-222-2-2-2-222-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2122222222-2-2-2-2222222-2-200002-2-2-22-20000000000000000000000202-20000-20000000
χ2222222222-2-2-2-2222222-2-200002-2-2-22-20000000000000000000000-20-22000020000000
χ2322222222-2-2-2-22222-2-2220000-22-2-2-22000000000000000000000002002-2000-2000000
χ2422222222-2-2-2-22222-2-2220000-22-2-2-2200000000000000000000000-200-220002000000
χ2522222222-2-2-2-2-2-2-2-222-2-20000-2222-2200000000000000000000000200-22000-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-20000-2222-2200000000000000000000000-2002-20002000000
χ2722222222-2-2-2-2-2-2-2-2-2-22200002-2222-2000000000000000000000020-220000-20000000
χ2822222222-2-2-2-2-2-2-2-2-2-22200002-2222-20000000000000000000000-202-2000020000000
χ2922-22-2-22-22-22-22i2i−2i−2i000022-2-2002i−2i00002i−2i0022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ3022-22-2-22-22-22-22i2i−2i−2i000022-2-2002i−2i00002i−2i00−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ3122-22-2-22-22-22-22i2i−2i−2i0000-2-222002i−2i0000−2i2i0022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ3222-22-2-22-22-22-22i2i−2i−2i0000-2-222002i−2i0000−2i2i00−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ3322-22-2-22-22-22-2−2i−2i2i2i000022-2-200−2i2i0000−2i2i0022−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ3422-22-2-22-22-22-2−2i−2i2i2i000022-2-200−2i2i0000−2i2i00−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ3522-22-2-22-22-22-2−2i−2i2i2i0000-2-22200−2i2i00002i−2i0022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ3622-22-2-22-22-22-2−2i−2i2i2i0000-2-22200−2i2i00002i−2i00−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ372-22-2-2-2222-2-22000000002-22-22200-2-200002-22i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ382-22-2-2-2222-2-22000000002-22-22200-2-200002-2−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ392-22-2-2-2222-2-22000000002-22-2-2-200220000-2200002-22-200002-22-20000000000000000
χ402-22-2-2-2222-2-22000000002-22-2-2-200220000-220000-22-220000-22-220000000000000000
χ412-22-2-2-2222-2-2200000000-22-222200-2-20000-222i−2i2i−2i0000−2i2i−2i2i00000000000000000000
χ422-22-2-2-2222-2-2200000000-22-222200-2-20000-22−2i2i−2i2i00002i−2i2i−2i00000000000000000000
χ432-22-2-2-2222-2-2200000000-22-22-2-2002200002-200002-22-20000-22-220000000000000000
χ442-22-2-2-2222-2-2200000000-22-22-2-2002200002-20000-22-2200002-22-20000000000000000
χ452-2-2-2222-222-2-200002-22-22-2-220000002-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ462-2-2-2222-222-2-200002-22-22-2-220000002-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ472-2-2-2222-222-2-200002-22-2-222-2000000-220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ482-2-2-2222-222-2-200002-22-2-222-2000000-220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ492-2-2-2222-222-2-20000-22-222-2-22000000-220000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ502-2-2-2222-222-2-20000-22-222-2-22000000-220000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ512-2-2-2222-222-2-20000-22-22-222-20000002-20000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ522-2-2-2222-222-2-20000-22-22-222-20000002-20000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ5344-44-4-44-4-44-444i4i−4i−4i0000000000−4i4i0000000000000000000000000000000000000000
χ5444-44-4-44-4-44-44−4i−4i4i4i00000000004i−4i0000000000000000000000000000000000000000
χ554-4444-4-4-400004i−4i4i−4i0000000000000000000000000000000000000000000000002i−2i2-2
χ564-4444-4-4-400004i−4i4i−4i000000000000000000000000000000000000000000000000−2i2i-22
χ574-4444-4-4-40000−4i4i−4i4i0000000000000000000000000000000000000000000000002i−2i-22
χ584-4444-4-4-40000−4i4i−4i4i000000000000000000000000000000000000000000000000−2i2i2-2
χ594-44-4-4-444-444-40000000000004-400-4400000000000000000000000000000000000000
χ604-44-4-4-444-444-4000000000000-44004-400000000000000000000000000000000000000
χ614-4-44-44-4400004-4-440000000000000000000000000000000000000000002-2002-20000
χ624-4-44-44-4400004-4-44000000000000000000000000000000000000000000-2200-220000
χ634-4-44-44-440000-444-40000000000000000000000000000000000000000002-200-220000
χ644-4-44-44-440000-444-4000000000000000000000000000000000000000000-22002-20000
χ654-4-4-4444-4-4-44400004-4-44000000000000000000000000000000000000000000000000
χ664-4-4-4444-4-4-4440000-444-4000000000000000000000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-88-8-88000000000000000000000000000000000000000000000000000000000000

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