Finite Group Databasebeta

← Group #112960

Character table — Group #112960

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order12222244444444224444444444444444444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111-1-111-1-1-1-1-1-11-1111-11-11-111-1-111-1-11-11-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ101111-1-111-1-1-1-1-1-11-1111-11-11-111-1-111-1-11-11-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ111111-1-111-1-1-1-1-1-11-1111-11-11-111-1-111-1-1-11-11ii−i−i−i−iii-1-111ii−i−i−i−iii
χ121111-1-111-1-1-1-1-1-11-1111-11-11-111-1-111-1-1-11-11−i−iiiii−i−i-1-111−i−iiiii−i−i
χ131111-1-111-1-1-1-1-1-11-1111-11-11-1-1-111-1-1111-11-1ii−i−i−i−iii-1-111−i−iiiii−i−i
χ141111-1-111-1-1-1-1-1-11-1111-11-11-1-1-111-1-1111-11-1−i−iiiii−i−i-1-111ii−i−i−i−iii
χ151111-1-111-1-1-1-1-1-11-1111-11-11-1-1-111-1-111-11-11ii−i−iii−i−i11-1-1−i−iii−i−iii
χ161111-1-111-1-1-1-1-1-11-1111-11-11-1-1-111-1-111-11-11−i−iii−i−iii11-1-1ii−i−iii−i−i
χ172222222222-2-2-2-2-2-22-2-222-2-2200000000000000000000000000002i−2i2i−2i
χ182222222222-2-2-2-2-2-22-2-222-2-220000000000000000000000000000−2i2i−2i2i
χ1922222222-2-22222-2-2-22-22-2-22-2000000000000000000002-22-200000000
χ2022222222-2-22222-2-2-22-22-2-22-200000000000000000000-22-2200000000
χ2122222222-2-2-2-2-2-222-2-222-22-2-20000000000000000000000002i−2i2i−2i0000
χ2222222222-2-2-2-2-2-222-2-222-22-2-2000000000000000000000000−2i2i−2i2i0000
χ23222222-2-22222-2-22222-2-2-2-2-2-20000000000002i−2i2i−2i0000000000000000
χ24222222-2-22222-2-22222-2-2-2-2-2-2000000000000−2i2i−2i2i0000000000000000
χ25222222-2-222-2-222-2-22-22-2-222-20000000022-2-200000000000000000000
χ26222222-2-222-2-222-2-22-22-2-222-200000000-2-22200000000000000000000
χ27222222-2-2-2-222-2-2-2-2-222-222-2200000000000000002-22-2000000000000
χ28222222-2-2-2-222-2-2-2-2-222-222-220000000000000000-22-22000000000000
χ29222222-2-2-2-2-2-22222-2-2-2-22-2222222-2-2-2-2000000000000000000000000
χ30222222-2-2-2-2-2-22222-2-2-2-22-222-2-2-2-22222000000000000000000000000
χ312222-2-2222222222-2-2-22-2-2-2-220000000000000000000000002-2-220000
χ322222-2-2222222222-2-2-22-2-2-2-22000000000000000000000000-222-20000
χ332222-2-22222-2-2-2-2-22-22-2-2-2222000000000000000000002-2-2200000000
χ342222-2-22222-2-2-2-2-22-22-2-2-222200000000000000000000-222-200000000
χ352222-2-222-2-22222-222-2-2-222-2-200000000000000000000000000002-2-22
χ362222-2-222-2-22222-222-2-2-222-2-20000000000000000000000000000-222-2
χ372222-2-2-2-22222-2-22-2-2-2-22222-222-2-2-2-222000000000000000000000000
χ382222-2-2-2-22222-2-22-2-2-2-22222-2-2-22222-2-2000000000000000000000000
χ392222-2-2-2-222-2-222-22-22222-2-2-200000000000000002i−2i−2i2i000000000000
χ402222-2-2-2-222-2-222-22-22222-2-2-20000000000000000−2i2i2i−2i000000000000
χ412222-2-2-2-2-2-222-2-2-222-222-2-222000000002-2-2200000000000000000000
χ422222-2-2-2-2-2-222-2-2-222-222-2-22200000000-222-200000000000000000000
χ432222-2-2-2-2-2-2-2-2222-222-22-22-220000000000002-2-220000000000000000
χ442222-2-2-2-2-2-2-2-2222-222-22-22-22000000000000-222-20000000000000000
χ454-4-44004i−4i004i−4i4-400000000002i−2i2i−2i2-22-2000000000000000000000000
χ464-4-44004i−4i004i−4i4-40000000000−2i2i−2i2i-22-22000000000000000000000000
χ474-4-44004i−4i00−4i4i-4400000000002i−2i−2i2i2-2-22000000000000000000000000
χ484-4-44004i−4i00−4i4i-440000000000−2i2i2i−2i-222-2000000000000000000000000
χ494-4-4400−4i4i004i−4i-4400000000002i−2i−2i2i-222-2000000000000000000000000
χ504-4-4400−4i4i004i−4i-440000000000−2i2i2i−2i2-2-22000000000000000000000000
χ514-4-4400−4i4i00−4i4i4-400000000002i−2i2i−2i-22-22000000000000000000000000
χ524-4-4400−4i4i00−4i4i4-40000000000−2i2i−2i2i2-22-2000000000000000000000000
χ5388-8-800008-80000000000000000000000000000000000000000000000
χ5488-8-80000-880000000000000000000000000000000000000000000000
χ558-88-88-800000000000000000000000000000000000000000000000000
χ568-88-8-8800000000000000000000000000000000000000000000000000

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