Finite Group Databasebeta

← Group #262861

Character table — Group #262861

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888822244444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-111-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-11111-1-11111-1-111-1-1111111-1-1-1-1
χ9111111111111111111-1-1-1-111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111
χ12111111111111111111-1-1-1-111111111-1-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-111
χ1722222222222-2-2-2-22-2-222-2-22222-2-2-2-2-2000000002220000-2-200000000000000000000
χ1822222222222-2-2-2-22-2-222-2-2-2-2-2-22222-2000000002-2-200002200000000000000000000
χ1922222222222-2-2-2-22-2-2-2-2222222-2-2-2-2200000000-2-2-200002200000000000000000000
χ2022222222222-2-2-2-22-2-2-2-222-2-2-2-22222200000000-2220000-2-200000000000000000000
χ2122222222-2-2-22222-2-2-2222200000000-22222-2-2-2-2-20000000000000000000000000000
χ2222222222-2-2-22222-2-2-2222200000000-2-2-2-2-22222-20000000000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-200000000222-2-222-2-220000000000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2000000002-2-222-2-22220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000200000000-2002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000200000000-200−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-22200000000-2000000002002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-22200000000-200000000200−2i−2i2i2i002i2i−2i−2i0000000000000000
χ2922-22-2-2-2200022-2-20002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000002-22i−2i02−2i2−i2i2−i22−22−22−20000000000000000
χ3022-22-2-2-2200022-2-20002i−2i2i−2ii2i2−i2−i2i2i2−i2−i200000-22−2i2i02−2−i2i2−i2i22−2−22−220000000000000000
χ3122-22-2-2-2200022-2-20002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000002-22i−2i0−22−i2i2−i2i2−22−22−220000000000000000
χ3222-22-2-2-2200022-2-20002i−2i2i−2i−i2−i2i2i2−i2−i2i2i200000-22−2i2i0−22i2−i2i2−i2−222−22−20000000000000000
χ3322-22-2-2-2200022-2-2000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000002-2−2i2i0−22i2−i2i2−i2−22−22−220000000000000000
χ3422-22-2-2-2200022-2-2000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200000-222i−2i0−22−i2i2−i2i2−222−22−20000000000000000
χ3522-22-2-2-2200022-2-2000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000002-2−2i2i02−2−i2i2−i2i22−22−22−20000000000000000
χ3622-22-2-2-2200022-2-2000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200000-222i−2i02−2i2−i2i2−i22−2−22−220000000000000000
χ3722-22-2-2-22000-2-2220002i−2i−2i2ii2i2−i2−i2−i2−i2i2i202-22i−2i000002−22−2−22−22−i2i2i2−i20000000000000000
χ3822-22-2-2-22000-2-2220002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20-22−2i2i000002−2−222−2−22i2−i2−i2i20000000000000000
χ3922-22-2-2-22000-2-2220002i−2i−2i2i−i2−i2i2i2i2i2−i2−i202-22i−2i00000−22−222−22−2i2−i2−i2i20000000000000000
χ4022-22-2-2-22000-2-2220002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20-22−2i2i00000−222−2−222−2−i2i2i2−i20000000000000000
χ4122-22-2-2-22000-2-222000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i202-2−2i2i00000−22−222−22−2−i2i2i2−i20000000000000000
χ4222-22-2-2-22000-2-222000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20-222i−2i00000−222−2−222−2i2−i2−i2i20000000000000000
χ4322-22-2-2-22000-2-222000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i202-2−2i2i000002−22−2−22−22i2−i2−i2i20000000000000000
χ4422-22-2-2-22000-2-222000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20-222i−2i000002−2−222−2−22−i2i2i2−i20000000000000000
χ452-2-2-2-2222-22-22-22-222-200002-22-22-22-20000000000000000000000002-22-20000000000
χ462-2-2-2-2222-22-22-22-222-200002-22-22-22-2000000000000000000000000-22-220000000000
χ472-2-2-2-2222-22-22-22-222-20000-22-22-22-220000000000000000000000002-2-220000000000
χ482-2-2-2-2222-22-22-22-222-20000-22-22-22-22000000000000000000000000-222-20000000000
χ492-2-2-2-2222-22-2-22-222-2200002-22-2-22-2200000000000000000000002-200002-200000000
χ502-2-2-2-2222-22-2-22-222-2200002-22-2-22-220000000000000000000000-220000-2200000000
χ512-2-2-2-2222-22-2-22-222-220000-22-222-22-200000000000000000000002-20000-2200000000
χ522-2-2-2-2222-22-2-22-222-220000-22-222-22-20000000000000000000000-2200002-200000000
χ53444-4-4-44-444-40000-40000000000000000000000000000000000000000000000000022−22
χ54444-4-4-44-444-40000-400000000000000000000000000000000000000000000000000−2222
χ55444-4-4-44-4-4-44000040000000000000000000000000000000000000000000000002i2−2i200
χ56444-4-4-44-4-4-4400004000000000000000000000000000000000000000000000000−2i22i200
χ574-44-44-4-440004-4-4400000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ584-44-44-4-440004-4-440000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ594-44-44-4-44000-444-400000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ604-44-44-4-44000-444-40000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-4-444-44-44-4-400004000000000000000000000000000000000000000000002i2−2i2000000
χ624-4-444-44-44-4-40000400000000000000000000000000000000000000000000−2i22i2000000
χ634-4-444-44-4-4440000-400000000000000000000000000000000000000000000002i2−2i20000
χ644-4-444-44-4-4440000-40000000000000000000000000000000000000000000000−2i22i20000
χ654-4-4-4-44444-444-44-4-4-4400000000000000000000000000000000000000000000000000
χ664-4-4-4-44444-44-44-44-44-400000000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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