Finite Group Databasebeta

← Group #134809

Character table — Group #134809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444488888888888888888888883232323232323232
order12222244442244444488888888222444444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
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
χ7111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ911111111111111-1-1-1-111111111-111-111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−ii−ii−i
χ1011111111111111-1-1-1-111111111-111-111-1-1-1-1-1-1-1-1-1-1-1-11111−ii−ii−ii−ii
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−ii−i−ii−ii
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−iii−ii−i
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1i−i−iii−i−ii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1−iii−i−iii−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111i−i−ii−iii−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111−iii−ii−i−ii
χ172222222222-2-2-2-222-2-22222-2-2-2-2-2002000000000022-2-2000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-22222-20020000000000-2-222000000000000
χ192222222222-2-2-2-2-2-2222222-2-2-2-2200-20000000000-2-222000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-22222200-2000000000022-2-2000000000000
χ21222222-2-2-2-222-2-2222200000000-222-2-2-222-2-200000000000000000000
χ22222222-2-2-2-222-2-2222200000000-2-2-2-222-2-22200000000000000000000
χ23222222-2-2-2-222-2-2-2-2-2-2000000002222-2-2-2-22200000000000000000000
χ24222222-2-2-2-222-2-2-2-2-2-2000000002-2-222222-2-200000000000000000000
χ25222222-2-2-2-2-2-22222-2-200000000200-20000002i2i−2i−2i00002i2i−2i−2i00000000
χ26222222-2-2-2-2-2-22222-2-200000000200-2000000−2i−2i2i2i0000−2i−2i2i2i00000000
χ27222222-2-2-2-2-2-222-2-22200000000-20020000002i2i−2i−2i0000−2i−2i2i2i00000000
χ28222222-2-2-2-2-2-222-2-22200000000-2002000000−2i−2i2i2i00002i2i−2i−2i00000000
χ2922-2-22-200002-2002i−2i2i−2i22−2−222−2−200002i−2i002-22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ3022-2-22-200002-2002i−2i2i−2i22−2−222−2−20000−2i2i00-22−22−22i2−i2i2−i2−i2i2−i2i200000000
χ3122-2-22-200002-2002i−2i2i−2i−2−222−2−22200002i−2i002-2−22−22−i2i2−i2i2−i2i2−i2i200000000
χ3222-2-22-200002-2002i−2i2i−2i−2−222−2−2220000−2i2i00-222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ3322-2-22-200002-200−2i2i−2i2i22−2−222−2−200002i−2i00-22−22−22−i2i2−i2i2i2−i2i2−i200000000
χ3422-2-22-200002-200−2i2i−2i2i22−2−222−2−20000−2i2i002-22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ3522-2-22-200002-200−2i2i−2i2i−2−222−2−22200002i−2i00-222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ3622-2-22-200002-200−2i2i−2i2i−2−222−2−2220000−2i2i002-2−22−22i2−i2i2−i2i2−i2i2−i200000000
χ3722-2-22-20000-22002i−2i−2i2i22−2−2−2−22202-20002i−2i00i2−i2−i2i2i2−i2−i2i2−222−200000000
χ3822-2-22-20000-22002i−2i−2i2i22−2−2−2−2220-22000−2i2i00−i2i2i2−i2i2−i2−i2i22−2−2200000000
χ3922-2-22-20000-22002i−2i−2i2i−2−22222−2−202-20002i−2i00−i2i2i2−i2−i2i2i2−i22−2−2200000000
χ4022-2-22-20000-22002i−2i−2i2i−2−22222−2−20-22000−2i2i00i2−i2−i2i2−i2i2i2−i2−222−200000000
χ4122-2-22-20000-2200−2i2i2i−2i22−2−2−2−22202-2000−2i2i00−i2i2i2−i2−i2i2i2−i2−222−200000000
χ4222-2-22-20000-2200−2i2i2i−2i22−2−2−2−2220-220002i−2i00i2−i2−i2i2−i2i2i2−i22−2−2200000000
χ4322-2-22-20000-2200−2i2i2i−2i−2−22222−2−202-2000−2i2i00i2−i2−i2i2i2−i2−i2i22−2−2200000000
χ4422-2-22-20000-2200−2i2i2i−2i−2−22222−2−20-220002i−2i00−i2i2i2−i2i2−i2−i2i2−222−200000000
χ454444-4-444-4-40000000000004i−4i4i−4i000000000000000000000000000000
χ464444-4-444-4-4000000000000−4i4i−4i4i000000000000000000000000000000
χ474444-4-4-4-444000000004-44-40000000000000000000000000000000000
χ484444-4-4-4-44400000000-44-440000000000000000000000000000000000
χ4944-4-4-440000004i−4i000022−22−22222i2−2i2−2i22i2000000000000000000000000000000
χ5044-4-4-440000004i−4i0000−222222−22−2i22i22i2−2i2000000000000000000000000000000
χ5144-4-4-44000000−4i4i000022−22−2222−2i22i22i2−2i2000000000000000000000000000000
χ5244-4-4-44000000−4i4i0000−222222−222i2−2i2−2i22i2000000000000000000000000000000
χ538-88-8008i−8i000000000000000000000000000000000000000000000000
χ548-88-800−8i8i000000000000000000000000000000000000000000000000
χ558-8-8800008-80000000000000000000000000000000000000000000000
χ568-8-880000-880000000000000000000000000000000000000000000000

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