Finite Group Databasebeta

← Group #116019

Character table — Group #116019

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222244444444444422444444444444448888888844448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ911111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iiiii−i−i−i−iii
χ1111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii−i−iii
χ1511111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i−i−iii
χ1611111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−iii−i−i
χ172222222222-2-2-2-22222-2-22-22-2-2-200000000000000000000000000002-22-20000
χ182222222222-2-2-2-22222-2-22-22-2-2-20000000000000000000000000000-22-220000
χ1922222222-2-222-2-2-2-2-2-2-2-22-2-222200000000000000000000000000002i−2i−2i2i0000
χ2022222222-2-222-2-2-2-2-2-2-2-22-2-22220000000000000000000000000000−2i2i2i−2i0000
χ21222222-2-2222222-2-222-2-2-22-22-2-222-2-222-2-20000000000000000000000000000
χ22222222-2-2222222-2-222-2-2-22-22-2-2-2-222-2-2220000000000000000000000000000
χ23222222-2-222-2-2-2-2-2-22222-2-2-2-2220000000022-2-222-2-200000000000000000000
χ24222222-2-222-2-2-2-2-2-22222-2-2-2-22200000000-2-222-2-22200000000000000000000
χ25222222-2-2-2-222-2-222-2-222-2-222-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ26222222-2-2-2-222-2-222-2-222-2-222-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ27222222-2-2-2-2-2-22222-2-2-2-2-222-22222-2-2-2-2220000000000000000000000000000
χ28222222-2-2-2-2-2-22222-2-2-2-2-222-222-2-22222-2-20000000000000000000000000000
χ292222-2-2222222-2-222-2-22-2-22-2-2-22000000000000000000002i−2i2i−2i000000000000
χ302222-2-2222222-2-222-2-22-2-22-2-2-2200000000000000000000−2i2i−2i2i000000000000
χ312222-2-22222-2-22222-2-2-22-2-2-222-2000000000000000000000000000000002i−2i2i−2i
χ322222-2-22222-2-22222-2-2-22-2-2-222-200000000000000000000000000000000−2i2i−2i2i
χ332222-2-222-2-22222-2-222-22-2-22-2-22000000000000000000000000000000002-2-22
χ342222-2-222-2-22222-2-222-22-2-22-2-2200000000000000000000000000000000-222-2
χ352222-2-222-2-2-2-2-2-2-2-2222-2-22222-2000000000000000000002i−2i−2i2i000000000000
χ362222-2-222-2-2-2-2-2-2-2-2222-2-22222-200000000000000000000−2i2i2i−2i000000000000
χ372222-2-2-2-22222-2-2-2-2-2-2-22222-22-200000000000000002-22-20000000000000000
χ382222-2-2-2-22222-2-2-2-2-2-2-22222-22-20000000000000000-22-220000000000000000
χ392222-2-2-2-222-2-222-2-2-2-22-22-222-220000000000000000000000002i−2i2i−2i00000000
χ402222-2-2-2-222-2-222-2-2-2-22-22-222-22000000000000000000000000−2i2i−2i2i00000000
χ412222-2-2-2-2-2-2222222222-22-2-2-22-20000000000000000000000002-2-2200000000
χ422222-2-2-2-2-2-2222222222-22-2-2-22-2000000000000000000000000-222-200000000
χ432222-2-2-2-2-2-2-2-2-2-22222-2222-22-2200000000000000002-2-220000000000000000
χ442222-2-2-2-2-2-2-2-2-2-22222-2222-22-220000000000000000-222-20000000000000000
χ454-44-40000004i−4i4i−4i004-400000000000000002-22i−2i2-22i−2i00000000000000000000
χ464-44-40000004i−4i4i−4i004-40000000000000000-22−2i2i-22−2i2i00000000000000000000
χ474-44-40000004i−4i−4i4i00-4400000000000000002i−2i2-2−2i2i-2200000000000000000000
χ484-44-40000004i−4i−4i4i00-440000000000000000−2i2i-222i−2i2-200000000000000000000
χ494-44-4000000−4i4i4i−4i00-4400000000000000002i−2i-22−2i2i2-200000000000000000000
χ504-44-4000000−4i4i4i−4i00-440000000000000000−2i2i2-22i−2i-2200000000000000000000
χ514-44-4000000−4i4i−4i4i004-400000000000000002-2−2i2i2-2−2i2i00000000000000000000
χ524-44-4000000−4i4i−4i4i004-40000000000000000-222i−2i-222i−2i00000000000000000000
χ534-4-44004i−4i4i−4i00004-400000000002-22i−2i2i−2i2-20000000000000000000000000000
χ544-4-44004i−4i4i−4i00004-40000000000-22−2i2i−2i2i-220000000000000000000000000000
χ554-4-44004i−4i−4i4i0000-4400000000002-22i−2i−2i2i-220000000000000000000000000000
χ564-4-44004i−4i−4i4i0000-440000000000-22−2i2i2i−2i2-20000000000000000000000000000
χ574-4-4400−4i4i4i−4i0000-4400000000002-2−2i2i2i−2i-220000000000000000000000000000
χ584-4-4400−4i4i4i−4i0000-440000000000-222i−2i−2i2i2-20000000000000000000000000000
χ594-4-4400−4i4i−4i4i00004-400000000002-2−2i2i−2i2i2-20000000000000000000000000000
χ604-4-4400−4i4i−4i4i00004-40000000000-222i−2i2i−2i-220000000000000000000000000000
χ6188-8-88-800000000000000000000000000000000000000000000000000000000
χ6288-8-8-8800000000000000000000000000000000000000000000000000000000

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