Finite Group Databasebeta

← Group #121713

Character table — Group #121713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444222222444488888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-2-2-222-2-222-2-200000000000000002i−2i2i−2i000000000000
χ182222222222-2-2-2-2-2-222-2-222-2-20000000000000000−2i2i−2i2i000000000000
χ192222222222-2-2-2-2-2-2-2-222-2-22200000000000000002-2-22000000000000
χ202222222222-2-2-2-2-2-2-2-222-2-2220000000000000000-222-2000000000000
χ21222222-2-2-2-22222-2-222-2-2-2-22222-2-222-2-2000000000000000000000000
χ22222222-2-2-2-22222-2-222-2-2-2-222-2-222-2-222000000000000000000000000
χ23222222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-222000000000000000000000000
χ24222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ25222222-2-2-2-2-2-2-2-2222222-2-2-2-2000000000000000000002i−2i2i−2i00000000
χ26222222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000−2i2i−2i2i00000000
χ27222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000002-2-2200000000
χ28222222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000-222-200000000
χ292222-2-222-2-222-2-22-22-22-22-22-200000000000000000000000000002-22-2
χ302222-2-222-2-222-2-22-22-22-22-22-20000000000000000000000000000-22-22
χ312222-2-222-2-222-2-22-2-22-22-22-2200000000000000000000000000002i−2i−2i2i
χ322222-2-222-2-222-2-22-2-22-22-22-220000000000000000000000000000−2i2i2i−2i
χ332222-2-222-2-2-2-222-222-2-222-2-220000000000002i−2i2i−2i0000000000000000
χ342222-2-222-2-2-2-222-222-2-222-2-22000000000000−2i2i−2i2i0000000000000000
χ352222-2-222-2-2-2-222-22-222-2-222-20000000000002i−2i−2i2i0000000000000000
χ362222-2-222-2-2-2-222-22-222-2-222-2000000000000−2i2i2i−2i0000000000000000
χ372222-2-2-2-22222-2-2-222-2-22-222-20000000000000000000000002i−2i2i−2i0000
χ382222-2-2-2-22222-2-2-222-2-22-222-2000000000000000000000000−2i2i−2i2i0000
χ392222-2-2-2-22222-2-2-22-222-22-2-220000000000000000000000002-2-220000
χ402222-2-2-2-22222-2-2-22-222-22-2-22000000000000000000000000-222-20000
χ412222-2-2-2-222-2-2222-22-22-2-22-22000000002i−2i2i−2i00000000000000000000
χ422222-2-2-2-222-2-2222-22-22-2-22-2200000000−2i2i−2i2i00000000000000000000
χ432222-2-2-2-222-2-2222-2-22-222-22-2000000002i−2i−2i2i00000000000000000000
χ442222-2-2-2-222-2-2222-2-22-222-22-200000000−2i2i2i−2i00000000000000000000
χ454-4-444-400004-44-400000000000000004i−4i000000000000000000000000
χ464-4-444-400004-44-40000000000000000−4i4i000000000000000000000000
χ474-4-444-40000-44-4400000000004-4000000000000000000000000000000
χ484-4-444-40000-44-440000000000-44000000000000000000000000000000
χ494-4-44-4400004-4-440000000000004-40000000000000000000000000000
χ504-4-44-4400004-4-44000000000000-440000000000000000000000000000
χ514-4-44-440000-444-4000000000000004i−4i00000000000000000000000000
χ524-4-44-440000-444-400000000000000−4i4i00000000000000000000000000
χ5388-8-800008i−8i0000000000000000000000000000000000000000000000
χ5488-8-80000−8i8i0000000000000000000000000000000000000000000000
χ558-88-8008i−8i000000000000000000000000000000000000000000000000
χ568-88-800−8i8i000000000000000000000000000000000000000000000000

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