Finite Group Databasebeta

← Group #262853

Character table — Group #262853

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822244444448888888888882222444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ17222222222-2-2-2-2222-2-222-2-22222-2-2-2-2-2002000000220000-2-200000000000000000000
χ18222222222-2-2-2-2222-2-222-2-2-2-2-2-22222-2002000000-2-200002200000000000000000000
χ19222222222-2-2-2-2222-2-2-2-2222222-2-2-2-2200-2000000-2-200002200000000000000000000
χ20222222222-2-2-2-2222-2-2-2-222-2-2-2-22222200-2000000220000-2-200000000000000000000
χ2122222222-22222-2-2-2-2-2222200000000-222-222-2-2-2-20000000000000000000000000000
χ2222222222-22222-2-2-2-2-2222200000000-2-2-2-2-2-222220000000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2000000002222-2-222-2-20000000000000000000000000000
χ2422222222-22222-2-2-2-2-2-2-2-2-2000000002-2-2222-2-2220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000200-2000000002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000200-200000000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-2002000000002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-200200000000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-222-2-2-2022-2-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000002-22i−2i2−2i2−i2i2−i22−22−22−20000000000000000
χ3022-222-2-2-2022-2-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000-22−2i2i2−2−i2i2−i2i22−2−22−220000000000000000
χ3122-222-2-2-2022-2-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000002-22i−2i−22−i2i2−i2i2−22−22−220000000000000000
χ3222-222-2-2-2022-2-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000000-22−2i2i−22i2−i2i2−i2−222−22−20000000000000000
χ3322-222-2-2-2022-2-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000002-2−2i2i−22i2−i2i2−i2−22−22−220000000000000000
χ3422-222-2-2-2022-2-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000000-222i−2i−22−i2i2−i2i2−222−22−20000000000000000
χ3522-222-2-2-2022-2-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000002-2−2i2i2−2−i2i2−i2i22−22−22−20000000000000000
χ3622-222-2-2-2022-2-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000-222i−2i2−2i2−i2i2−i22−2−22−220000000000000000
χ3722-222-2-2-20-2-222000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i202-202i−2i00002−22−2−22−22−i2i2i2−i20000000000000000
χ3822-222-2-2-20-2-222000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20-220−2i2i00002−2−222−2−22i2−i2−i2i20000000000000000
χ3922-222-2-2-20-2-222000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i202-202i−2i0000−22−222−22−2i2−i2−i2i20000000000000000
χ4022-222-2-2-20-2-222000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20-220−2i2i0000−222−2−222−2−i2i2i2−i20000000000000000
χ4122-222-2-2-20-2-22200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i202-20−2i2i0000−22−222−22−2−i2i2i2−i20000000000000000
χ4222-222-2-2-20-2-22200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20-2202i−2i0000−222−2−222−2i2−i2−i2i20000000000000000
χ4322-222-2-2-20-2-22200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i202-20−2i2i00002−22−2−22−22i2−i2−i2i20000000000000000
χ4422-222-2-2-20-2-22200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20-2202i−2i00002−2−222−2−22−i2i2i2−i20000000000000000
χ452-2-22-2-222-22-22-22-222-200002-22-22-22-20000000000000000000000002-22-20000000000
χ462-2-22-2-222-22-22-22-222-200002-22-22-22-2000000000000000000000000-22-220000000000
χ472-2-22-2-222-22-22-22-222-20000-22-22-22-220000000000000000000000002-2-220000000000
χ482-2-22-2-222-22-22-22-222-20000-22-22-22-22000000000000000000000000-222-20000000000
χ492-2-22-2-222-2-22-222-22-2200002-22-2-22-2200000000000000000000002-200002-200000000
χ502-2-22-2-222-2-22-222-22-2200002-22-2-22-220000000000000000000000-220000-2200000000
χ512-2-22-2-222-2-22-222-22-220000-22-222-22-200000000000000000000002-20000-2200000000
χ522-2-22-2-222-2-22-222-22-220000-22-222-22-20000000000000000000000-2200002-200000000
χ53444-4-4-4-44400004-4-400000000000000000000000000000000000000000000002i2−2i20000
χ54444-4-4-4-44400004-4-40000000000000000000000000000000000000000000000−2i22i20000
χ55444-4-4-4-44-40000-4440000000000000000000000000000000000000000000022−22000000
χ56444-4-4-4-44-40000-44400000000000000000000000000000000000000000000−2222000000
χ574-444-44-4-404-4-440000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-444-44-4-404-4-44000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-444-44-4-40-444-40000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-444-44-4-40-444-4000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-44-4-44444-44-4-44-4-4400000000000000000000000000000000000000000000000000
χ624-4-44-4-4444-44-44-44-44-400000000000000000000000000000000000000000000000000
χ634-4-4-444-4440000-4-4400000000000000000000000000000000000000000000000022−2200
χ644-4-4-444-4440000-4-44000000000000000000000000000000000000000000000000−222200
χ654-4-4-444-44-4000044-40000000000000000000000000000000000000000000000000022−22
χ664-4-4-444-44-4000044-400000000000000000000000000000000000000000000000000−2222
χ6788-8-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-88-88-88-8000000000000000000000000000000000000000000000000000000000000

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