Finite Group Databasebeta

← Group #134754

Character table — Group #134754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444488888888888888888888883232323232323232
order12222244442222444488888888444444444488888888888844448888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ9111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−ii−ii−i
χ10111111111111-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−ii−ii−ii−ii
χ11111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1i−ii−i−ii−ii
χ12111111111111-1-111-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−ii−iii−ii−i
χ13111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iii−i−ii
χ14111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−iii−i
χ15111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111i−i−ii−iii−i
χ16111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111−iii−ii−i−ii
χ172222222222-2-222-2-2-2-22222-2-2-2-22-200000000220000-2-2000000000000
χ182222222222-2-222-2-2-2-2-2-2-2-222222-200000000-2-2000022000000000000
χ192222222222-2-2-2-2-2-2222222-2-2-2-2-2200000000-2-2000022000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-22222-2200000000220000-2-2000000000000
χ21222222-2-2-2-22222-2-22200000000-2-222-2-222-2-200000000000000000000
χ22222222-2-2-2-22222-2-22200000000-2-2-2-222-2-22200000000000000000000
χ23222222-2-2-2-222-2-2-2-2-2-2000000002222-2-2-2-22200000000000000000000
χ24222222-2-2-2-222-2-2-2-2-2-20000000022-2-22222-2-200000000000000000000
χ25222222-2-2-2-2-2-22222-2-200000000-2200000000002i2i−2i−2i002i2i−2i−2i00000000
χ26222222-2-2-2-2-2-22222-2-200000000-220000000000−2i−2i2i2i00−2i−2i2i2i00000000
χ27222222-2-2-2-2-2-2-2-22222000000002-200000000002i2i−2i−2i00−2i−2i2i2i00000000
χ28222222-2-2-2-2-2-2-2-22222000000002-20000000000−2i−2i2i2i002i2i−2i−2i00000000
χ2922-2-22-200002-22-2002-222−2−222−2−200002-2002-22−22−22−22−22−22−200000000
χ3022-2-22-200002-22-2002-222−2−222−2−20000-2200-222−2−22−222−2−22−2200000000
χ3122-2-22-200002-22-2002-2−2−222−2−22200002-2002-2−22−22−22−22−22−2200000000
χ3222-2-22-200002-22-2002-2−2−222−2−2220000-2200-22−222−22−2−222−22−200000000
χ3322-2-22-200002-2-2200-2222−2−222−2−200002-200-22−22−22−22−222−22−200000000
χ3422-2-22-200002-2-2200-2222−2−222−2−20000-22002-2−222−22−2−22−22−2200000000
χ3522-2-22-200002-2-2200-22−2−222−2−22200002-200-222−22−22−22−2−22−2200000000
χ3622-2-22-200002-2-2200-22−2−222−2−2220000-22002-22−2−22−222−22−22−200000000
χ3722-2-22-20000-222-200-2222−2−2−2−222002i−2i002i−2i002−2i2−i2−i2i2−22i2−i2−i2i200000000
χ3822-2-22-20000-222-200-2222−2−2−2−22200−2i2i00−2i2i002−2−i2i2i2−i2−22−i2i2i2−i200000000
χ3922-2-22-20000-222-200-22−2−22222−2−2002i−2i002i−2i00−22−i2i2i2−i22−2−i2i2i2−i200000000
χ4022-2-22-20000-222-200-22−2−22222−2−200−2i2i00−2i2i00−22i2−i2−i2i22−2i2−i2−i2i200000000
χ4122-2-22-20000-22-22002-222−2−2−2−222002i−2i00−2i2i00−22−i2i2i2−i22−2i2−i2−i2i200000000
χ4222-2-22-20000-22-22002-222−2−2−2−22200−2i2i002i−2i00−22i2−i2−i2i22−2−i2i2i2−i200000000
χ4322-2-22-20000-22-22002-2−2−22222−2−2002i−2i00−2i2i002−2i2−i2−i2i2−22−i2i2i2−i200000000
χ4422-2-22-20000-22-22002-2−2−22222−2−200−2i2i002i−2i002−2−i2i2i2−i2−22i2−i2−i2i200000000
χ454444-4-444-4-4000000004i−4i4i−4i0000000000000000000000000000000000
χ464444-4-444-4-400000000−4i4i−4i4i0000000000000000000000000000000000
χ474444-4-4-4-4440000000000004-44-4000000000000000000000000000000
χ484444-4-4-4-444000000000000-44-44000000000000000000000000000000
χ4944-4-4-44000000004i−4i002i2−2i2−2i22i222−22−2222000000000000000000000000000000
χ5044-4-4-44000000004i−4i00−2i22i22i2−2i2−222222−22000000000000000000000000000000
χ5144-4-4-4400000000−4i4i002i2−2i2−2i22i2−222222−22000000000000000000000000000000
χ5244-4-4-4400000000−4i4i00−2i22i22i2−2i222−22−2222000000000000000000000000000000
χ538-88-800008-80000000000000000000000000000000000000000000000
χ548-88-80000-880000000000000000000000000000000000000000000000
χ558-8-88008i−8i000000000000000000000000000000000000000000000000
χ568-8-8800−8i8i000000000000000000000000000000000000000000000000

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