Finite Group Databasebeta

← Group #116392

Character table — Group #116392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111122222244444444444416161616161616161616161616161616161616161616161616161616
order12222222222222444444442444444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-1-1-11-11-1-111111-1-1-1-111-1-1i−i11-1-1i−iii−i−i11-1-1ii−i−iii−i−i
χ1011111-1-1-11-11-1-111111-1-1-1-111-1-1i−i-1-111i−i−i−iii-1-111ii−i−i−i−iii
χ1111111-1-1-11-11-1-111111-1-1-1-111-1-1−ii11-1-1−ii−i−iii11-1-1−i−iii−i−iii
χ1211111-1-1-11-11-1-111111-1-1-1-111-1-1−ii-1-111−iiii−i−i-1-111−i−iiiii−i−i
χ1311111-1-1-11-11-1-111111-1-1-1-1-1-111i−i11-1-1i−iii−i−i-1-111−i−iii−i−iii
χ1411111-1-1-11-11-1-111111-1-1-1-1-1-111i−i-1-111i−i−i−iii11-1-1−i−iiiii−i−i
χ1511111-1-1-11-11-1-111111-1-1-1-1-1-111−ii11-1-1−ii−i−iii-1-111ii−i−iii−i−i
χ1611111-1-1-11-11-1-111111-1-1-1-1-1-111−ii-1-111−iiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-2-2-20000002-22-2000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2000000-22-22000000000000000000
χ192222222222-2-2-2-222-2-22-22-20000000000002-22-2000000000000
χ202222222222-2-2-2-222-2-22-22-2000000000000-22-22000000000000
χ212222222222-2-2-2-2-2-222-22-220000220000-2-20000000000000000
χ222222222222-2-2-2-2-2-222-22-220000-2-20000220000000000000000
χ2322222-2-2-22-22-2-22-2-2-2-222220000002-2-22000000000000000000
χ2422222-2-2-22-22-2-22-2-2-2-22222000000-222-2000000000000000000
χ2522222-2-2-22-2-222-222-2-2-22-220000000000002i−2i−2i2i000000000000
χ2622222-2-2-22-2-222-222-2-2-22-22000000000000−2i2i2i−2i000000000000
χ2722222-2-2-22-2-222-2-2-2222-22-200002i−2i0000−2i2i0000000000000000
χ2822222-2-2-22-2-222-2-2-2222-22-20000−2i2i00002i−2i0000000000000000
χ292222-222-2-2-222-2-22-22-222-2-22-2-22000000000000000000000000
χ302222-222-2-2-222-2-22-22-222-2-2-222-2000000000000000000000000
χ312222-222-2-2-222-2-2-22-22-2-22200000000000000002i−2i2i−2i00000000
χ322222-222-2-2-222-2-2-22-22-2-2220000000000000000−2i2i−2i2i00000000
χ332222-222-2-2-2-2-2222-2-222-2-220000000000000000000000002i−2i2i−2i
χ342222-222-2-2-2-2-2222-2-222-2-22000000000000000000000000−2i2i−2i2i
χ352222-222-2-2-2-2-222-222-2-222-2000000000000000000002i−2i2i−2i0000
χ362222-222-2-2-2-2-222-222-2-222-200000000000000000000−2i2i−2i2i0000
χ372222-2-2-22-222-22-22-22-2-2-2222-22-2000000000000000000000000
χ382222-2-2-22-222-22-22-22-2-2-222-22-22000000000000000000000000
χ392222-2-2-22-222-22-2-22-2222-2-200000000000000002i−2i−2i2i00000000
χ402222-2-2-22-222-22-2-22-2222-2-20000000000000000−2i2i2i−2i00000000
χ412222-2-2-22-22-22-222-2-22-222-20000000000000000000000002-2-22
χ422222-2-2-22-22-22-222-2-22-222-2000000000000000000000000-222-2
χ432222-2-2-22-22-22-22-222-22-2-22000000000000000000002-2-220000
χ442222-2-2-22-22-22-22-222-22-2-2200000000000000000000-222-20000
χ4588-8-800080-80000000000000000000000000000000000000000
χ4688-8-8000-8080000000000000000000000000000000000000000
χ478-88-88000-800000000000000000000000000000000000000000
χ488-88-8-8000800000000000000000000000000000000000000000
χ498-8-8808-80000000000000000000000000000000000000000000
χ508-8-880-880000000000000000000000000000000000000000000

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