Finite Group Databasebeta

← Group #262857

Character table — Group #262857

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444442244448888888822444444448888888888882222224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ101111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ111111111111111111-1-111-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ121111111111111111-1-111-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-11111-1-111-1-1-1-111
χ17222222222-2-2222-2-222-2-2-2-22222-2-2-2-200-20000200-2-200002200000000000000000000
χ18222222222-2-2222-2-222-2-2-2-2-2-2-2-2222200-20000200220000-2-200000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2222222-2-2-2-20020000-200220000-2-200000000000000000000
χ20222222222-2-2222-2-2-2-2-2-222-2-2-2-222220020000-200-2-200002200000000000000000000
χ2122222222-222-2-2-22222-2-2220000000022-222-2-2-2-2-20000000000000000000000000000
χ2222222222-222-2-2-22222-2-22200000000-2-2-2-2-222-2220000000000000000000000000000
χ2322222222-222-2-2-222-2-2-2-2-2-200000000222-2-2222-2-20000000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-2-2-200000000-2-2222-2-22220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000000020000-200002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000000020000-20000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000000-20000200002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000000-2000020000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-22-2-2-22022000-2-22-2002-222−2−222−2−2000002i−2i02i−2i2−2i2−i2i2−i22−2i2−i2i2−i20000000000000000
χ3022-22-2-2-22022000-2-22-2002-222−2−222−2−200000−2i2i0−2i2i2−2−i2i2−i2i22−2−i2i2−i2i20000000000000000
χ3122-22-2-2-22022000-2-22-2002-2−2−222−2−222000002i−2i02i−2i−22−i2i2−i2i2−22−i2i2−i2i20000000000000000
χ3222-22-2-2-22022000-2-22-2002-2−2−222−2−22200000−2i2i0−2i2i−22i2−i2i2−i2−22i2−i2i2−i20000000000000000
χ3322-22-2-2-22022000-2-2-2200-2222−2−222−2−2000002i−2i0−2i2i−22i2−i2i2−i2−22−i2i2−i2i20000000000000000
χ3422-22-2-2-22022000-2-2-2200-2222−2−222−2−200000−2i2i02i−2i−22−i2i2−i2i2−22i2−i2i2−i20000000000000000
χ3522-22-2-2-22022000-2-2-2200-22−2−222−2−222000002i−2i0−2i2i2−2−i2i2−i2i22−2i2−i2i2−i20000000000000000
χ3622-22-2-2-22022000-2-2-2200-22−2−222−2−22200000−2i2i02i−2i2−2i2−i2i2−i22−2−i2i2−i2i20000000000000000
χ3722-22-2-2-220-2-2000222-200-2222−2−2−2−2222-202-200000−222−2−222−22−2−220000000000000000
χ3822-22-2-2-220-2-2000222-200-2222−2−2−2−222-220-2200000−22−222−22−2−222−20000000000000000
χ3922-22-2-2-220-2-2000222-200-22−2−22222−2−22-202-2000002−2−222−2−22−222−20000000000000000
χ4022-22-2-2-220-2-2000222-200-22−2−22222−2−2-220-22000002−22−2−22−222−2−220000000000000000
χ4122-22-2-2-220-2-200022-22002-222−2−2−2−2222-20-22000002−2−222−2−222−2−220000000000000000
χ4222-22-2-2-220-2-200022-22002-222−2−2−2−222-2202-2000002−22−2−22−22−222−20000000000000000
χ4322-22-2-2-220-2-200022-22002-2−2−22222−2−22-20-2200000−222−2−222−2−222−20000000000000000
χ4422-22-2-2-220-2-200022-22002-2−2−22222−2−2-2202-200000−22−222−22−22−2−220000000000000000
χ452-2-2-22-222-22-22-222-2002-2002-22-22-22-20000000000000000000000002-2002-200000000
χ462-2-2-22-222-22-22-222-2002-2002-22-22-22-2000000000000000000000000-2200-2200000000
χ472-2-2-22-222-22-22-222-2002-200-22-22-22-220000000000000000000000002-200-2200000000
χ482-2-2-22-222-22-22-222-2002-200-22-22-22-22000000000000000000000000-22002-200000000
χ492-2-2-22-222-2-222-22-2200-22002-22-2-22-2200000000000000000000002-2002-20000000000
χ502-2-2-22-222-2-222-22-2200-22002-22-2-22-220000000000000000000000-2200-220000000000
χ512-2-2-22-222-2-222-22-2200-2200-22-222-22-200000000000000000000002-200-220000000000
χ522-2-2-22-222-2-222-22-2200-2200-22-222-22-20000000000000000000000-22002-20000000000
χ53444-4-4-44-44004-4-400000000000000000000000000000000000000000000000000002i2−2i2
χ54444-4-4-44-44004-4-40000000000000000000000000000000000000000000000000000−2i22i2
χ55444-4-4-44-4-400-4440000000000000000000000000000000000000000000000000022−2200
χ56444-4-4-44-4-400-44400000000000000000000000000000000000000000000000000−222200
χ574-44-4-44-4404-4000-4400000022−22−222222−22−222200000000000000000000000000000000000000
χ584-44-4-44-4404-4000-44000000−222222−22−222222−2200000000000000000000000000000000000000
χ594-44-4-44-440-440004-400000022−22−2222−222222−2200000000000000000000000000000000000000
χ604-44-4-44-440-440004-4000000−222222−2222−22−222200000000000000000000000000000000000000
χ614-4-44-444-4400-4-44000000000000000000000000000000000000000000000022−22000000
χ624-4-44-444-4400-4-440000000000000000000000000000000000000000000000−2222000000
χ634-4-44-444-4-40044-400000000000000000000000000000000000000000000000022−220000
χ644-4-44-444-4-40044-4000000000000000000000000000000000000000000000000−22220000
χ654-4-4-44-44444-4-44-44-400-44000000000000000000000000000000000000000000000000
χ664-4-4-44-4444-44-44-4-44004-4000000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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