Finite Group Databasebeta

← Group #113806

Character table — Group #113806

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222222444444244444444444444444222444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111-111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111-1-1-1-111-1-1-1-11111-1-1-11-11iiii−i−i−i−i1-111-11-1-1ii−i−iii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1-11-11iiii−i−i−i−i1-1-1-111-11−i−iii−i−iiiii−i−i-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1-11-11iiii−i−i−i−i-1111-1-11-1−i−iiiii−i−i−i−iii-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1-11-11iiii−i−i−i−i-11-1-11-111ii−i−i−i−iii−i−iii11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-1-11-11−i−i−i−iiiii1-111-11-1-1−i−iii−i−iii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-1-11-11−i−i−i−iiiii1-1-1-111-11ii−i−iii−i−i−i−iii-1-111
χ151111-1-1-1-111-1-1-1-11111-1-1-11-11−i−i−i−iiiii-1111-1-11-1ii−i−i−i−iiiii−i−i-1-111
χ161111-1-1-1-111-1-1-1-11111-1-1-11-11−i−i−i−iiiii-11-1-11-111−i−iiiii−i−iii−i−i11-1-1
χ1722222222222-2-222-2-2-2-2-2-222-20000000000000000000000002-22-20000
χ1822222222222-2-222-2-2-2-2-2-222-2000000000000000000000000-22-220000
χ1922222222-2-2-222-2222-22-2-2-2-2-2000000000000000000002-22-200000000
χ2022222222-2-2-222-2222-22-2-2-2-2-200000000000000000000-22-2200000000
χ2122222222-2-2-2-2-2-22-2-22-222-2-2200000000000000000000000000002-22-2
χ2222222222-2-2-2-2-2-22-2-22-222-2-220000000000000000000000000000-22-22
χ2322222-2-2222-222-2-22-2-2-22-2-22200000000002-2200-20000000000000000
χ2422222-2-2222-222-2-22-2-2-22-2-2220000000000-22-20020000000000000000
χ2522222-2-2222-2-2-2-2-2-2222-22-22-200000000000000002i−2i2i−2i000000000000
χ2622222-2-2222-2-2-2-2-2-2222-22-22-20000000000000000−2i2i−2i2i000000000000
χ2722222-2-22-2-22222-22-22-2-222-2-222-2-222-2-2000000000000000000000000
χ2822222-2-22-2-22222-22-22-2-222-2-2-2-222-2-222000000000000000000000000
χ2922222-2-22-2-22-2-22-2-22-222-22-220000000022000-2-200000000000000000
χ3022222-2-22-2-22-2-22-2-22-222-22-2200000000-2-20002200000000000000000
χ312222-222-2222222-2-222-22-2-2-2-200000000000000002-2-22000000000000
χ322222-222-2222222-2-222-22-2-2-2-20000000000000000-222-2000000000000
χ332222-222-2222-2-22-22-2-22-22-2-2200000000002-2-20020000000000000000
χ342222-222-2222-2-22-22-2-22-22-2-220000000000-22200-20000000000000000
χ352222-222-2-2-2-222-2-2-22-2-2-22222000000002-2000-2200000000000000000
χ362222-222-2-2-2-222-2-2-22-2-2-2222200000000-220002-200000000000000000
χ372222-222-2-2-2-2-2-2-2-22-2222-222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ382222-222-2-2-2-2-2-2-2-22-2222-222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ392222-2-2-2-222-222-22-2-2-22222-2-20000000000000000000000002i−2i−2i2i0000
χ402222-2-2-2-222-222-22-2-2-22222-2-2000000000000000000000000−2i2i2i−2i0000
χ412222-2-2-2-2-2-222222-2-222-2-2-22200000000000000000000000000002-2-22
χ422222-2-2-2-2-2-222222-2-222-2-2-2220000000000000000000000000000-222-2
χ432222-2-2-2-2-2-22-2-22222-2-222-22-2000000000000000000002i−2i−2i2i00000000
χ442222-2-2-2-2-2-22-2-22222-2-222-22-200000000000000000000−2i2i2i−2i00000000
χ454-4-4404-404-4400-400000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ464-4-4404-404-4400-40000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ474-4-4404-40-44-400400000000002-2-22-222-2000000000000000000000000
χ484-4-4404-40-44-40040000000000-222-22-2-22000000000000000000000000
χ494-4-440-4404-4-400400000000002-22-2-22-22000000000000000000000000
χ504-4-440-4404-4-40040000000000-22-222-22-2000000000000000000000000
χ514-4-440-440-44400-400000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ524-4-440-440-44400-40000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ5388-8-800000008i−8i0000000000000000000000000000000000000000000
χ5488-8-80000000−8i8i0000000000000000000000000000000000000000000
χ558-88-8800-8000000000000000000000000000000000000000000000000
χ568-88-8-8008000000000000000000000000000000000000000000000000

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