Finite Group Databasebeta

← Group #134818

Character table — Group #134818

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444488888888888888888888883232323232323232
order12222244444444444488888888444444444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
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
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ911111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−ii−ii−i
χ1011111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−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
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iii−i−ii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−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
χ172222222222-2-2-2-222-2-22222-2-2-2-22-200000000000022-2-2000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-222222-2000000000000-2-222000000000000
χ192222222222-2-2-2-2-2-2222222-2-2-2-2-22000000000000-2-222000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-22222-2200000000000022-2-2000000000000
χ21222222-2-2-2-222-2-2222200000000-2-222-2-222-2-200000000000000000000
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
χ24222222-2-2-2-222-2-2-2-2-2-20000000022-2-22222-2-200000000000000000000
χ25222222-2-2-2-2-2-22222-2-200000000-22000000002i2i−2i−2i00002i2i−2i−2i00000000
χ26222222-2-2-2-2-2-22222-2-200000000-2200000000−2i−2i2i2i0000−2i−2i2i2i00000000
χ27222222-2-2-2-2-2-222-2-222000000002-2000000002i2i−2i−2i0000−2i−2i2i2i00000000
χ28222222-2-2-2-2-2-222-2-222000000002-200000000−2i−2i2i2i00002i2i−2i−2i00000000
χ292-22-22-200002-2002i−2i2i−2i22−2−222−2−200002i−2i002-22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ302-22-22-200002-2002i−2i2i−2i22−2−222−2−20000−2i2i00-22−22−22i2−i2i2−i2−i2i2−i2i200000000
χ312-22-22-200002-2002i−2i2i−2i−2−222−2−22200002i−2i002-2−22−22−i2i2−i2i2−i2i2−i2i200000000
χ322-22-22-200002-2002i−2i2i−2i−2−222−2−2220000−2i2i00-222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ332-22-22-200002-200−2i2i−2i2i22−2−222−2−200002i−2i00-22−22−22−i2i2−i2i2i2−i2i2−i200000000
χ342-22-22-200002-200−2i2i−2i2i22−2−222−2−20000−2i2i002-22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ352-22-22-200002-200−2i2i−2i2i−2−222−2−22200002i−2i00-222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ362-22-22-200002-200−2i2i−2i2i−2−222−2−2220000−2i2i002-2−22−22i2−i2i2−i2i2−i2i2−i200000000
χ372-22-22-20000-22002i−2i−2i2i22−2−2−2−222002-2002i−2i00i2−i2−i2i2i2−i2−i2i2−222−200000000
χ382-22-22-20000-22002i−2i−2i2i22−2−2−2−22200-2200−2i2i00−i2i2i2−i2i2−i2−i2i22−2−2200000000
χ392-22-22-20000-22002i−2i−2i2i−2−22222−2−2002-2002i−2i00−i2i2i2−i2−i2i2i2−i22−2−2200000000
χ402-22-22-20000-22002i−2i−2i2i−2−22222−2−200-2200−2i2i00i2−i2−i2i2−i2i2i2−i2−222−200000000
χ412-22-22-20000-2200−2i2i2i−2i22−2−2−2−222002-200−2i2i00−i2i2i2−i2−i2i2i2−i2−222−200000000
χ422-22-22-20000-2200−2i2i2i−2i22−2−2−2−22200-22002i−2i00i2−i2−i2i2−i2i2i2−i22−2−2200000000
χ432-22-22-20000-2200−2i2i2i−2i−2−22222−2−2002-200−2i2i00i2−i2−i2i2i2−i2−i2i22−2−2200000000
χ442-22-22-20000-2200−2i2i2i−2i−2−22222−2−200-22002i−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
χ494-44-4-440000004i−4i000022−22−22222i2−2i2−2i22i2000000000000000000000000000000
χ504-44-4-440000004i−4i0000−222222−22−2i22i22i2−2i2000000000000000000000000000000
χ514-44-4-44000000−4i4i000022−22−2222−2i22i22i2−2i2000000000000000000000000000000
χ524-44-4-44000000−4i4i0000−222222−222i2−2i2−2i22i2000000000000000000000000000000
χ5388-8-800008-80000000000000000000000000000000000000000000000
χ5488-8-80000-880000000000000000000000000000000000000000000000
χ558-8-88008i−8i000000000000000000000000000000000000000000000000
χ568-8-8800−8i8i000000000000000000000000000000000000000000000000

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