Finite Group Databasebeta

← Group #112124

Character table — Group #112124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444488888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1311111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ1411111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ1511111111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-2222-22-2-2-2-2-20000000000000000000000002i−2i2i−2i0000
χ182222222222-2-2-2-2222-22-2-2-2-2-2000000000000000000000000−2i2i−2i2i0000
χ1922222222-2-2-2-222-2-22-2-22-2-2220000000000000000000000002-2-220000
χ2022222222-2-2-2-222-2-22-2-22-2-222000000000000000000000000-222-20000
χ21222222-2-2222222-2-2-2-2222-2-2-200000000000000000000000000002i−2i2i−2i
χ22222222-2-2222222-2-2-2-2222-2-2-20000000000000000000000000000−2i2i−2i2i
χ23222222-2-222-2-2-2-2-2-2-222-2-2222000000002-2002-2000000000000000000
χ24222222-2-222-2-2-2-2-2-2-222-2-222200000000-2200-22000000000000000000
χ25222222-2-2-2-222-2-222-2-2-2-22-22200000000000000000000000000002-2-22
χ26222222-2-2-2-222-2-222-2-2-2-22-2220000000000000000000000000000-222-2
χ27222222-2-2-2-2-2-22222-22-22-22-2-2000000002-200-22000000000000000000
χ28222222-2-2-2-2-2-22222-22-22-22-2-200000000-22002-2000000000000000000
χ292222-2-222222222-22-22-2-2-2-22-2000000000000000000002-22-200000000
χ302222-2-222222222-22-22-2-2-2-22-200000000000000000000-22-2200000000
χ312222-2-22222-2-2-2-2-22-2-2-2222-2200000000002-2002-20000000000000000
χ322222-2-22222-2-2-2-2-22-2-2-2222-220000000000-2200-220000000000000000
χ332222-2-222-2-222-2-22-2-2222-2-2-22000000000000000000002i−2i−2i2i00000000
χ342222-2-222-2-222-2-22-2-2222-2-2-2200000000000000000000−2i2i2i−2i00000000
χ352222-2-222-2-2-2-2222-2-2-22-2222-200000000002-200-220000000000000000
χ362222-2-222-2-2-2-2222-2-2-22-2222-20000000000-22002-20000000000000000
χ372222-2-2-2-22222222-22-2-2-2-22-2222-2-222-2-2000000000000000000000000
χ382222-2-2-2-22222222-22-2-2-2-22-22-2-222-2-222000000000000000000000000
χ392222-2-2-2-222-2-2-2-22-222-222-22-200000000000000002i−2i2i−2i000000000000
χ402222-2-2-2-222-2-2-2-22-222-222-22-20000000000000000−2i2i−2i2i000000000000
χ412222-2-2-2-2-2-222-2-2-222-222-222-222-2-2-2-222000000000000000000000000
χ422222-2-2-2-2-2-222-2-2-222-222-222-2-2-22222-2-2000000000000000000000000
χ432222-2-2-2-2-2-2-2-222-22222-22-2-2200000000000000002-2-22000000000000
χ442222-2-2-2-2-2-2-2-222-22222-22-2-220000000000000000-222-2000000000000
χ454-4-4400004i−4i4-44i−4i00000000000022−22002i2−2i2000000000000000000000000
χ464-4-4400004i−4i4-44i−4i000000000000−222200−2i22i2000000000000000000000000
χ474-4-4400004i−4i-44−4i4i000000000022−22002i2−2i200000000000000000000000000
χ484-4-4400004i−4i-44−4i4i0000000000−222200−2i22i200000000000000000000000000
χ494-4-440000−4i4i4-4−4i4i00000000000022−2200−2i22i2000000000000000000000000
χ504-4-440000−4i4i4-4−4i4i000000000000−2222002i2−2i2000000000000000000000000
χ514-4-440000−4i4i-444i−4i000000000022−2200−2i22i200000000000000000000000000
χ524-4-440000−4i4i-444i−4i0000000000−2222002i2−2i200000000000000000000000000
χ5388-8-8008-8000000000000000000000000000000000000000000000000
χ5488-8-800-88000000000000000000000000000000000000000000000000
χ558-88-88-800000000000000000000000000000000000000000000000000
χ568-88-8-8800000000000000000000000000000000000000000000000000

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