Finite Group Databasebeta

← Group #116358

Character table — Group #116358

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12224444224422222244444422224444444444448888888888888888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ121111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ131111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111ii−i−iii−i−i−i−iii−i−iii
χ141111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111−i−iii−i−iiiii−i−iii−i−i
χ151111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-22-2-2-22-2000000000000000000002-22-200000000
χ1822222222222222-2-2-2-22-2-2-22-200000000000000000000-22-2200000000
χ19222222222222-2-222-2-2-22-2-2-2200000000000000002-22-2000000000000
χ20222222222222-2-222-2-2-22-2-2-220000000000000000-22-22000000000000
χ21222222222222-2-2-2-222-2-222-2-2000000002-22-200000000000000000000
χ22222222222222-2-2-2-222-2-222-2-200000000-22-2200000000000000000000
χ2322222222-2-2-2-22-22-22-2222-2-2-222-2-2-2-222000000000000000000000000
χ2422222222-2-2-2-22-22-22-2222-2-2-2-2-22222-2-2000000000000000000000000
χ2522222222-2-2-2-22-2-22-222-2-22-2200000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-22-2-22-222-2-22-220000000000000000000000000000−2i2i−2i2i
χ2722222222-2-2-2-2-222-2-22-22-222-20000000000000000000000002i−2i2i−2i0000
χ2822222222-2-2-2-2-222-2-22-22-222-2000000000000000000000000−2i2i−2i2i0000
χ2922222222-2-2-2-2-22-222-2-2-22-2220000000000002i−2i2i−2i0000000000000000
χ3022222222-2-2-2-2-22-222-2-2-22-222000000000000−2i2i−2i2i0000000000000000
χ312222-2-2-2-222-2-222-2-2-2-2-2222-22000000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-222-2-222-2-2-2-2-2222-2200000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-222-2-2-2-222-2-22-2222-200000000000000002i−2i−2i2i000000000000
χ342222-2-2-2-222-2-2-2-222-2-22-2222-20000000000000000−2i2i2i−2i000000000000
χ352222-2-2-2-222-2-2-2-2-2-22222-2-222000000002-2-2200000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-22222-2-22200000000-222-200000000000000000000
χ372222-2-2-2-2-2-2222-22-22-2-2-2-22222222-2-2-2-2000000000000000000000000
χ382222-2-2-2-2-2-2222-22-22-2-2-2-2222-2-2-2-22222000000000000000000000000
χ392222-2-2-2-2-2-2222-2-22-22-222-22-200000000000000000000000000002-2-22
χ402222-2-2-2-2-2-2222-2-22-22-222-22-20000000000000000000000000000-222-2
χ412222-2-2-2-2-2-222-222-2-222-22-2-220000000000000000000000002-2-220000
χ422222-2-2-2-2-2-222-222-2-222-22-2-22000000000000000000000000-222-20000
χ432222-2-2-2-2-2-222-22-222-222-22-2-20000000000002i−2i−2i2i0000000000000000
χ442222-2-2-2-2-2-222-22-222-222-22-2-2000000000000−2i2i2i−2i0000000000000000
χ454-4-4444-4-44-44-40000000000002-22-22-22-2000000000000000000000000
χ464-4-4444-4-44-44-4000000000000-22-22-22-22000000000000000000000000
χ474-4-4444-4-4-44-440000000000002-2-22-222-2000000000000000000000000
χ484-4-4444-4-4-44-44000000000000-222-22-2-22000000000000000000000000
χ494-4-44-4-4444-4-440000000000002-2-222-2-22000000000000000000000000
χ504-4-44-4-4444-4-44000000000000-222-2-222-2000000000000000000000000
χ514-4-44-4-444-444-40000000000002-22-2-22-22000000000000000000000000
χ524-4-44-4-444-444-4000000000000-22-222-22-2000000000000000000000000
χ5388-8-88i−8i8i−8i000000000000000000000000000000000000000000000000
χ5488-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

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